Physics

physical quantity — A feature of something which can be measured, consisting of a numerical value and a unit.

Physical quantities are fundamental to physics, allowing for objective description and comparison of phenomena. Like a recipe ingredient that needs both a number (e.g., 2) and a unit (e.g., cups) to be meaningful, a physical quantity needs both a magnitude and a unit for complete specification.

Système Internationale (SI) — A single, internationally agreed-upon system of units based on the metric system of measurement.

The SI system provides a coherent set of units for all physical quantities, facilitating global scientific communication and consistency in measurements. Like a universal language for measurements, SI ensures that scientists worldwide can understand and replicate each other's work without confusion over different unit systems.

base quantities — The fundamental physical quantities upon which the SI system is founded.

These are quantities that are considered to be dimensionally independent and cannot be expressed in terms of other base quantities. There are seven SI base quantities, each with a defined base unit, acting like the primary colours from which all other colours can be mixed.

base units — The unique units defined at world conventions for each of the seven fundamental or base quantities.

These units form the foundation of the SI system, with all other units (derived units) being expressed as combinations of these base units. Their precise definitions ensure consistency in measurement, much like standard weights and measures kept in a national vault.

derived units — Units for quantities that are expressed as products or quotients of the SI base units.

All physical quantities apart from the base quantities have derived units. These units are formed by combining base units according to the physical relationships between quantities, similar to how complex words are formed by combining simpler letters.

homogeneous — An equation is homogeneous if each term involved in the equation has the same base units.

Checking for homogeneity is a crucial way to verify the dimensional consistency of an equation. If an equation is not homogeneous, it is dimensionally incorrect and therefore invalid, much like ensuring all ingredients in a recipe are measured in the same type of unit before adding them.

order of magnitude — The power of ten to which a number is raised, used to estimate the size of a quantity.

Estimating the order of magnitude provides a quick way to check if a calculated answer is sensible, especially in physics where quantities can vary enormously. It helps in identifying gross errors in calculations, like quickly estimating if a number is in the hundreds, thousands, or millions.

uncertainty — The total range of values within which a measurement is likely to lie.

Uncertainty quantifies the doubt associated with a measurement, indicating the interval where the true value is expected to be found. It is inherent in all measurements and can be expressed as absolute or percentage uncertainty, much like a weather forecast giving a temperature range rather than a single exact value.

absolute uncertainty — The range of values (e.g., ±0.5 cm) that directly indicates the uncertainty in a measurement.

This is the direct numerical value of the uncertainty, expressed in the same units as the measured quantity. It represents the maximum possible deviation from the stated value. For example, if a length is 10 cm ± 0.1 cm, the ±0.1 cm is the absolute uncertainty.

percentage uncertainty — The absolute uncertainty expressed as a percentage of the measured value.

This provides a relative measure of uncertainty, useful for comparing the precision of different measurements or for combining uncertainties in multiplication and division. It is calculated as (absolute uncertainty / measured value) × 100%. If a measurement is 100 g ± 1 g, the percentage uncertainty is 1%.

accuracy — The closeness of a measured value to the 'true' or 'known' value.

Accuracy reflects how well a measurement represents the actual value of the quantity being measured. It is affected by systematic errors and can be improved by reducing them, much like hitting the bullseye on a dartboard.

precision — How close a set of measured values are to each other.

Precision refers to the reproducibility and consistency of measurements. A precise set of readings will have a small spread of values, indicating low random error, even if they are not close to the true value. This is like hitting the same spot on a dartboard repeatedly, even if it's not the bullseye.

systematic error — An error that results in all readings being either above or below the true value by a fixed amount and in the same direction.

Systematic errors consistently shift measurements away from the true value. They cannot be reduced by repeating readings and averaging, but rather by improving experimental techniques or calibrating instruments. These errors affect accuracy, similar to a weighing scale that always reads 1 kg too high.

zero error — A type of systematic error where the scale reading is not zero before measurements are taken.

This occurs when an instrument does not read zero when it should, leading to all subsequent measurements being consistently offset. It must be checked and corrected for before or during an experiment, like a ruler that starts at 1 cm instead of 0 cm.

reaction time — The delay between an experimenter observing an event and starting a timing device.

This is a systematic error in manual timing experiments. To minimize its effect, the duration of the event being timed should be significantly longer than the typical human reaction time, much like the slight delay between seeing a traffic light turn green and pressing the accelerator.

random error — An error that results in readings being scattered around the accepted value.

Random errors cause unpredictable variations in measurements, leading to a spread of readings. They can be reduced by repeating measurements and averaging the results, or by plotting graphs and drawing best-fit lines. These errors affect precision, like darts landing randomly around the bullseye.

parallax error — An error in reading a scale from different angles, causing the apparent position of the indicator to shift.

This error occurs when the observer's eye is not perpendicular to the scale, leading to an incorrect reading. It can be a random error if viewing angle varies, or systematic if always viewed from the same non-normal angle, similar to looking at a speedometer from the passenger seat.

micrometer screw gauge — A precision measuring instrument used to measure small lengths, typically to the nearest one-hundredth of a millimetre.

It consists of a U-shaped frame, an anvil, a spindle, a thimble, and a ratchet. The object to be measured is placed between the anvil and spindle, and the thimble is rotated until the ratchet slips, ensuring consistent pressure, much like a very fine-tuned caliper.

scalar quantity — A quantity which can be described fully by giving its magnitude and unit.

Scalar quantities have only size (magnitude) and a unit, and can be added algebraically using normal arithmetic rules. Examples include mass, speed, energy, and time, much like telling someone you have '5 dollars'.

vector quantity — A quantity which has magnitude, unit, and direction.

Vector quantities require both a size (magnitude) and a specific direction for their complete description. They cannot be added algebraically but require vector addition methods. Examples include velocity, acceleration, and force, similar to giving directions to 'walk 5 blocks north'.

resultant — The combined effect of two or more vectors.

The resultant vector represents the single vector that would produce the same effect as all the individual vectors acting together. It is found by vector addition. If two people push a box, the resultant force is the single push that would move the box in the same way as both people pushing together.

vector triangle — A graphical method for adding two vectors by representing them as two sides of a triangle, with the third side representing the resultant.

In a vector triangle, the vectors are drawn head-to-tail, and the resultant is drawn from the tail of the first vector to the head of the second. This method accounts for both magnitude and direction, like a treasure map where each step is an arrow, and the final arrow from start to finish is the resultant.

resolution of vectors — The process of splitting a single vector into two or more component vectors.

A vector can be resolved into components, typically two perpendicular components, whose combined effect is equivalent to the original vector. This simplifies problem-solving, especially when dealing with forces or velocities at angles, much like breaking down a complex task into smaller, simpler sub-tasks.

components — The two or more vectors into which a single vector may be split.

These component vectors, when added together, produce the original vector. Resolving a vector into perpendicular components (e.g., horizontal and vertical) is a common and powerful technique in physics, similar to the x and y coordinates that define a point on a graph.

Distance — The length along the actual path travelled from the starting point to the finishing point.

Distance is a scalar quantity, meaning it only has magnitude. It measures the total path covered by an object, regardless of its direction.

Displacement — The change of position of a particle.

Displacement is a vector quantity, representing the length travelled in a straight line in a specified direction from the starting point to the finishing point. It indicates both the magnitude and direction of the change in position.

Average speed — The distance moved along the actual path divided by the time taken.

Average speed is a scalar quantity that describes how fast an object is moving over a period, calculated by dividing the total distance by the total time.

Velocity — A vector quantity representing the magnitude of how fast a particle is moving, and the direction in which it is moving.

Velocity is a vector quantity, meaning it has both magnitude (speed) and direction. It describes the rate at which an object's displacement changes.

Average velocity — The displacement divided by the time taken.

Average velocity is a vector quantity, calculated by dividing the total displacement by the total time taken. Its sign indicates the direction of motion.

Instantaneous velocity — The velocity of a particle at a particular moment in time, defined by making the intervals of time over which average velocity is measured shorter and shorter, equivalent to the gradient of the tangent to the displacement–time curve.

Instantaneous velocity provides the velocity at a specific point in time. On a displacement-time graph, it is found by calculating the gradient of the tangent at that particular moment.

Acceleration — A measure of the rate at which the velocity of the particle is changing.

Acceleration is a vector quantity that describes how quickly an object's velocity changes. This change can be in magnitude (speeding up or slowing down) or direction.

Average acceleration — The change in velocity divided by the time taken.

Average acceleration is a vector quantity, calculated by dividing the total change in velocity by the total time taken. Its sign indicates the direction of the acceleration.

Instantaneous acceleration — The average acceleration measured over extremely small time intervals, equivalent to the gradient of the tangent to the velocity–time curve.

Instantaneous acceleration gives the acceleration at a precise moment. On a velocity-time graph, it is determined by the gradient of the tangent at that specific time.

Deceleration — A negative acceleration, indicating that the final velocity is less than the initial velocity.

Deceleration specifically refers to a negative acceleration, which means the object is slowing down. It's important to note that a negative acceleration can also mean speeding up in the negative direction.

Acceleration of free fall — The uniform acceleration experienced by all objects falling freely near the Earth’s surface in the absence of air resistance, represented by the symbol g, with a value of 9.81 m s–2 and directed downwards.

Free fall is a specific case of uniformly accelerated motion where the only force acting on an object is gravity. The acceleration due to gravity, 'g', is approximately 9.81 m s⁻² and is always directed downwards.

Projectile motion — The motion of a particle moving in a plane under the action of a constant force, such as a ball thrown at an angle to the vertical.

Projectile motion is characterised by a constant horizontal velocity and a constant vertical acceleration (g). Air resistance is typically neglected in introductory problems.

Range — For a particle projected from a point on level ground, the horizontal distance from the point of projection to the point at which the particle reaches the ground again.

The range is a specific measure of horizontal displacement for projectiles launched and landing at the same vertical level. It depends on the initial velocity, launch angle, and acceleration of free fall.

mass — Mass is a measure of the inertia of an object to change in velocity.

It is an intrinsic property of an object that quantifies its resistance to acceleration when a force is applied. The bigger the mass, the more difficult it is to change its state of rest or velocity. Imagine pushing an empty shopping cart versus a full one; the full cart has more mass and thus more inertia, making it harder to start or stop.

inertia — Inertia is the property of an object to stay in a state of rest or uniform velocity.

This property is directly related to an object's mass; objects with greater mass have greater inertia and thus resist changes to their motion more strongly. It is a key concept in Newton's first law. When a bus suddenly brakes, passengers lurch forward due to their inertia, as their bodies tend to continue moving at the bus's original velocity.

force — A force is an influence that can change the shape or dimensions of objects, or disturb the state of rest or uniform velocity of an object.

Forces are vector quantities, possessing both magnitude and direction, and their combined effect is known as the resultant force. They are fundamental to understanding motion and interactions between objects. Pushing a swing to make it move faster or in a different direction is an example of exerting a force.

newton — One newton is defined as the force which will give a 1 kg mass an acceleration of 1 m s−2 in the direction of the force.

It is the SI unit of force, derived from Newton's second law (F=ma). This definition provides a precise way to quantify force based on measurable quantities of mass and acceleration. Holding a small apple (about 100g) in your hand exerts a force of approximately 1 Newton due to gravity.

weight — The force of gravity which acts on an object is called the weight of the object.

Weight is a vector quantity, always directed towards the center of the Earth, and is calculated as the product of an object's mass and the acceleration of free fall (W = mg). It is measured in Newtons. If you stand on a bathroom scale, it measures your weight, which is the force with which Earth's gravity pulls you down.

normal contact force — A normal contact force is a force exerted by a surface on an object that acts perpendicularly to the plane of contact.

This force arises due to the contact between two objects and prevents them from passing through each other. For an object resting on a horizontal surface, it balances the object's weight. When you stand on the floor, the floor pushes up on your feet with a normal contact force, preventing you from falling through it.

momentum — The momentum of a particle is defined as the product of its mass and its velocity.

It is a vector quantity, meaning it has both magnitude and direction, and its SI unit is kg m s−1 or N s. Momentum is a crucial concept for understanding collisions and interactions between objects, as it is conserved in isolated systems. A small bullet moving very fast can have the same momentum as a large, slow-moving bowling ball, illustrating that both mass and velocity contribute to momentum.

linear momentum — Linear momentum is the product of an object's mass and its velocity.

This term is used to distinguish it from angular momentum, which is not covered in this context. It is a vector quantity, and its conservation is a fundamental principle in physics, particularly in analyzing collisions. A train moving on a straight track has linear momentum, while a spinning top has angular momentum.

impulse — If a constant force F acts on an object for a time Δt, the impulse of the force is given by FΔt.

Impulse is a vector quantity, measured in Newton seconds (N s), and is equal to the change in momentum of the object. It is particularly useful for analyzing forces that act over short durations, such as in collisions. When a baseball bat hits a ball, the impulse delivered by the bat causes a large change in the ball's momentum over a very short contact time.

isolated system — An isolated system is one on which no external resultant force acts.

In such a system, the total momentum remains constant, a principle known as the conservation of momentum. This concept is crucial for analyzing collisions and interactions where external influences are negligible. Imagine two billiard balls colliding on a perfectly frictionless table; the table and air are not exerting significant external forces, so the balls form an isolated system.

elastic collision — An elastic collision is one in which the total kinetic energy remains constant.

In such collisions, no energy is lost to permanent deformation, heat, or sound. The relative speed of approach is equal to the relative speed of separation, and both momentum and kinetic energy are conserved. The collision of ideal gas molecules with the walls of a container is often modeled as a perfectly elastic collision.

inelastic collision — An inelastic collision is one in which the total kinetic energy is not the same before and after the event.

While total energy and momentum are still conserved, some kinetic energy is transformed into other forms, such as heat, sound, or energy for permanent deformation. Objects may stick together after an inelastic collision. When a car crashes and crumples, it's an inelastic collision because kinetic energy is converted into deformation, heat, and sound.

frictional force — A frictional force acts along the common surface of contact between two objects and always acts in the opposite direction to the relative motion of the objects.

This force opposes motion or attempted motion between surfaces in contact. It is larger for rough surfaces and can be reduced by making surfaces smoother or applying lubricants. When you push a box across a floor, the force that makes it hard to move is friction, acting against your push.

viscous force — Viscous force (or drag force) describes the frictional force in a fluid (a liquid or a gas).

This force depends on the viscosity of the fluid and increases with the speed of the object moving through it. Air resistance is a common example of a viscous force. Swimming through water is harder than walking through air because water has a higher viscosity, resulting in a greater viscous force.

drag force — Drag force is another term used to describe the frictional force in a fluid (a liquid or a gas).

It opposes the motion of an object through the fluid and increases with the object's speed. Air resistance is a specific type of drag force. The force you feel pushing against you when you stick your hand out of a moving car window is drag force.

air resistance — Air resistance is an example of a viscous force that opposes the motion of an object through the air.

It is zero when an object's velocity is zero and increases with speed. For falling objects, it eventually balances the gravitational force, leading to terminal velocity. A feather falls slower than a stone because it experiences much greater air resistance relative to its weight.

upthrust — Upthrust (or buoyancy force) is an upward force experienced by an object immersed in a fluid due to the pressure of the fluid on it.

This force depends on the density of the fluid and the volume of the object submerged. While negligible in air for most objects, it is significant in denser fluids like water or oil. When you push a beach ball underwater, you feel an upward force pushing it back up; that's upthrust.

buoyancy force — Buoyancy force (or upthrust) is an upward force experienced by an object immersed in a fluid due to the pressure of the fluid on it.

This force is a consequence of the pressure difference between the top and bottom surfaces of the submerged object. It is proportional to the weight of the fluid displaced by the object. A boat floats because the buoyancy force from the water is equal to the boat's weight.

terminal velocity — Terminal velocity is the maximum (constant) velocity reached by an object moving through a resistive fluid when the resultant force on it becomes zero.

This occurs when the resistive force (viscous force/drag) becomes equal in magnitude and opposite in direction to the object's weight (and upthrust, if present). At this point, the object no longer accelerates. A parachutist reaches terminal velocity when the upward air resistance force equals their downward weight, allowing them to fall at a constant speed.

Centre of gravity (C.G.) — The centre of gravity of an object is the point at which the whole weight of the object may be considered to act.

This point represents the average position of all the weight particles that make up an object. For uniform objects, it's often at the geometrical center. When an object is balanced at its C.G., it does not turn. Imagine trying to balance a complex toy on your finger; the specific point where it balances perfectly without tipping is its centre of gravity.

Moment of a force — The moment of a force is defined as the product of the force and the perpendicular distance of the line of action of the force from the pivot.

This quantity measures the turning effect of a force about a pivot. It depends on both the magnitude of the force and how far it acts from the pivot, specifically the perpendicular distance to the line of action. Opening a door: pushing closer to the hinges (pivot) requires more force to open it than pushing further away, because the perpendicular distance is smaller.

Couple — A couple consists of two forces, equal in magnitude but opposite in direction whose lines of action do not coincide.

A couple produces a pure rotational effect without causing any linear acceleration. The forces are parallel but separated, creating a turning effect. Turning a steering wheel: you apply equal and opposite forces on opposite sides of the wheel to make it turn without moving the car sideways.

Torque of a couple — The torque of a couple is the product of one of the forces and the perpendicular distance between the forces.

This is the turning effect produced by a couple. Unlike the moment of a single force, torque specifically refers to the rotational effect of two forces forming a couple. Tightening a nut with a spanner (torque wrench): the torque applied determines how tight the nut becomes, which is a measure of the turning effect.

Principle of moments — The principle of moments states that, for an object to be in rotational equilibrium, the sum of the clockwise moments about any point must equal the sum of the anticlockwise moments about that same point.

This principle is fundamental for analyzing objects that are not rotating or are rotating at a constant angular velocity. It ensures that there is no net turning effect on the object. A seesaw perfectly balanced: the turning effect of the child on one side (clockwise moment) is exactly equal to the turning effect of the child on the other side (anticlockwise moment).

Density — The density of a substance is defined as its mass per unit volume.

Density is a measure of how much mass is contained in a given volume of a substance. It is an intrinsic property of a material and helps distinguish different substances. Imagine a box filled with feathers versus the same box filled with rocks; the box of rocks has a higher density because it contains more mass in the same volume.

Pressure — Pressure is defined as force per unit area, where the force F acts perpendicularly to the area A.

Pressure describes how concentrated a force is over a given area. A smaller area for the same force results in higher pressure, and vice-versa. A sharp knife cuts better than a blunt one because the sharp edge has a much smaller area, concentrating the force into higher pressure.

Upthrust — The upthrust acting on an object immersed in a fluid is equal to the weight of the fluid displaced.

Upthrust, also known as buoyancy force, is an upward force exerted by a fluid that opposes the weight of an immersed object. It arises from the pressure difference between the top and bottom surfaces of the object. When you push a beach ball underwater, you feel an upward force pushing it back up; that's the upthrust from the water.

Archimedes’ principle — The rule that the upthrust acting on an object immersed in a fluid is equal to the weight of the fluid displaced is known as Archimedes’ principle.

This principle explains why objects float or sink. If the upthrust is greater than the object's weight, it floats; if less, it sinks. It is a fundamental concept in fluid mechanics. A boat floats because it displaces a weight of water equal to its own weight, generating an upthrust that balances its weight.

Work — Work is done when a force moves the point at which it acts (the point of application) in the direction of the force.

Work is a scalar quantity, measured in joules (J). It quantifies the energy transferred by a force acting over a distance. If the force and displacement are not aligned, only the component of the force in the direction of displacement does work. Imagine pushing a heavy box across a room; the effort you put in to move the box is the work done. If you push down on the box, but it only moves horizontally, only the horizontal component of your push does work.

Displacement — The term displacement represents the distance moved in a particular direction.

Displacement is a vector quantity, meaning it has both magnitude and direction. It is crucial for calculating work done, as work depends on the movement in the direction of the applied force. For example, if you walk 5 metres north, your displacement is 5 metres north. If you walk 5 metres north and then 5 metres south, your total displacement is zero, even though you walked a total distance of 10 metres.

Energy — Anything that is able to do work is said to have energy.

Energy is a scalar quantity, measured in joules (J), representing the capacity to do work. It exists in various forms and can be converted from one form to another, but the total energy in the Universe remains constant. Think of energy as money in a bank account; you can convert it from cash to digital, or spend it on different things (doing work), but the total amount of money you have (or the total energy in the system) is conserved unless you add or remove it from the system.

Law of conservation of energy — Energy cannot be created or destroyed. It can only be converted from one form to another.

This fundamental law states that the total energy within a closed system remains constant. While energy can change forms (e.g., chemical to kinetic), the overall quantity of energy does not change. Imagine a set amount of water in a closed bottle; you can pour it into different shaped containers, or freeze it into ice, or boil it into steam, but the total amount of water in the bottle remains the same.

Efficiency — Efficiency gives a measure of how much of the total energy may be considered useful and is not 'lost'.

Efficiency is the ratio of useful energy output to total energy input, expressed as a ratio or percentage. It can never be greater than 100% because energy cannot be created. If you put 100 units of effort into a task and only 80 units of that effort contribute to the desired outcome, your efficiency is 80%. The other 20 units were 'wasted' on things like friction or heat.

Power — Power is the rate of doing work.

Power is a scalar quantity, measured in watts (W), which is equivalent to joules per second (J s⁻¹). It describes how quickly energy is converted or work is done. Two people might lift the same heavy box (doing the same amount of work), but the person who lifts it faster is more powerful.

Potential energy — Potential energy is the ability of an object to do work as a result of its position or shape.

This stored energy can be converted into other forms, such as kinetic energy, when the object's position or shape changes. Examples include gravitational potential energy and elastic potential energy. Imagine a stretched rubber band or a ball held high above the ground; both have stored energy due to their position or shape, which can be released to do work.

Elastic potential energy — Elastic potential energy is energy stored due to stretching or compressing an object.

This form of potential energy is stored in objects that have been deformed elastically, such as springs or stretched wires. It is released when the object returns to its original shape. A wound-up toy car spring stores elastic potential energy, which is then released to make the car move.

Gravitational potential energy — Gravitational potential energy is energy possessed by a mass due to its position in a gravitational field.

This energy is stored when work is done against gravity to raise a mass. It can be recovered when the mass falls, converting into kinetic energy. A book on a high shelf has gravitational potential energy; if it falls, that energy is converted into kinetic energy.

Kinetic energy — Kinetic energy is energy due to motion.

This energy is possessed by any moving object and is directly proportional to its mass and the square of its speed. It is a scalar quantity, measured in joules. A moving car has kinetic energy; the faster it moves, the more kinetic energy it has, and the more work it can do if it hits something and slows down.

Translational kinetic energy — The full name for the term Ek = 1/2mv² is translational kinetic energy because it is energy due to an object moving in a straight line.

This specific term distinguishes the kinetic energy associated with linear motion from rotational kinetic energy, which is energy due to an object spinning. A car driving straight down a road has translational kinetic energy. Its wheels also have rotational kinetic energy, but the car's overall forward motion is translational.

Rotational kinetic energy — Rotating objects also have kinetic energy and this form of energy is known as rotational kinetic energy.

This is the energy an object possesses due to its rotation around an axis. It depends on the object's moment of inertia and angular velocity. A spinning top has rotational kinetic energy; even if it's not moving across the floor, it still has energy due to its spin.

Deformation — The change of shape or size of a solid object when forces are applied to it.

Deformation occurs when external forces cause a solid material to alter its dimensions. This can involve stretching, known as tensile deformation, or squeezing, referred to as compressive deformation.

Tensile deformation — A deformation if an object is stretched.

When an object undergoes tensile deformation, its length increases due to a pulling force. This stretching is caused by a tensile force, which is the load applied to extend the object.

Compressive deformation — A deformation if the object squeezed/compressed.

Compressive deformation occurs when an object is subjected to forces that push it together, causing it to shorten or decrease in volume. This is the opposite of tensile deformation.

Tensile force — The load or force that stretches a wire.

A tensile force is the external force applied to an object that causes it to stretch. This force is often referred to as the 'load' when discussing experiments involving hanging weights.

Load — The weight attached to the spring, or the tensile force that causes the extension.

The load is the force applied to a material, typically by attaching a weight, which results in its deformation. For a spring, it's the weight causing the extension.

Extension — The increase in length or deformation of the spring, equal to extended length – natural/original length.

Extension is the measurable increase in an object's length from its original, undeformed state. It is calculated by subtracting the original length from the extended length.

Limit of proportionality — The point on a load-extension or stress-strain graph up to which the extension of the spring is proportional to the load.

The limit of proportionality marks the boundary on a force-extension graph where the linear relationship between force and extension ceases. Beyond this point, Hooke's law is no longer valid.

Spring constant (or force constant) — A constant k in Hooke's law (F = ke), representing the force per unit extension.

The spring constant, 'k', quantifies the stiffness of a spring or elastic object. A higher 'k' value indicates a stiffer object, requiring more force to achieve a given extension.

Tensile stress (σ) — The ratio of tensile force to the area normal to the force (F/A).

Tensile stress is a measure of the internal forces acting within a deformable body, specifically the force distributed over its cross-sectional area. It quantifies how concentrated the applied force is within the material.

Tensile strain (ε) — The ratio of extension to original length (e/Lo).

Tensile strain is a dimensionless quantity that describes the fractional change in length of a material when subjected to a tensile force. It indicates the relative deformation of the material.

Young modulus (E) — The constant E defined as the ratio of stress to strain, provided the limit of proportionality is not exceeded.

The Young modulus, E, is a fundamental material property that quantifies its stiffness or resistance to elastic deformation under tensile or compressive stress. It is a constant for a given material, provided the deformation remains within the limit of proportionality.

Elastic deformation — A deformation in which an object returns to its original shape and size when the force on it is removed.

Elastic deformation is a temporary change in shape or size. When the deforming force is removed, the material fully recovers its original dimensions, much like a stretched rubber band snapping back.

Elastic limit — The maximum force that can be applied to a wire/spring such that the wire/spring returns to its original length when the force is removed.

The elastic limit is the critical point beyond which a material will no longer fully return to its original shape after the deforming force is removed. If the force exceeds this limit, some permanent deformation will occur.

Plastic deformation — A deformation in which an object does not return to its original shape and size when the force on it is removed.

Plastic deformation is a permanent change in the shape or size of an object. Once a material undergoes plastic deformation, it retains some of its altered shape even after the applied force is removed.

Elastic potential energy (strain energy) — Energy stored in an object due to change of shape or size, which is completely recovered when the force causing deformation is removed.

Elastic potential energy, also known as strain energy, is the energy stored within a material when it is deformed elastically. This stored energy is fully released and recovered when the deforming force is removed, allowing the object to return to its original state.

Progressive waves — Waves which transfer energy from place to place without the transfer of matter.

Progressive waves are a mechanism for energy propagation through a medium or space. Crucially, while energy moves, the material itself does not travel with the wave; particles simply oscillate around their equilibrium positions.

Transverse wave — One in which the vibrations of the particles in the wave are at right angles to the direction in which the energy of the wave is travelling.

In a transverse wave, the particles of the medium oscillate perpendicular to the direction the wave's energy is moving. Examples include waves on a rope or electromagnetic waves.

Longitudinal wave — One in which the direction of the vibrations of the particles in the wave is along or parallel to the direction in which the energy of the wave is travelling.

For a longitudinal wave, the particles vibrate back and forth in the same direction as the wave's energy propagation. Sound waves are a common example, involving compressions and rarefactions.

Displacement — Its distance in a specified direction from its rest/equilibrium position.

Displacement describes how far a particle in a wave has moved from its undisturbed, or equilibrium, position. It is a vector quantity, meaning it has both magnitude and direction.

Amplitude — The maximum displacement of a particle in the wave from its rest/equilibrium position.

The amplitude represents the greatest distance a particle moves from its equilibrium position during an oscillation. It is a measure of the wave's intensity or energy.

Wavelength — The smallest distance that shows the section of the wave that is repeated.

Wavelength can also be defined as the minimum distance between particles which are vibrating in phase with each other. It is a key characteristic for describing the spatial extent of a wave cycle.

Cycle or oscillation — The motion of any particle in the wave from the maximum positive displacement (a crest) to a maximum negative displacement (a trough) back to a maximum positive displacement.

A cycle, or oscillation, represents one complete repetition of the wave's pattern. For a particle, this means moving through all its possible displacements and returning to its starting point and direction of motion.

Period T — The time for a particle in the wave to complete one oscillation or one cycle.

The period is the duration required for a single particle in the wave to undergo one full cycle of vibration. It is inversely related to frequency.

Frequency f — The number of oscillations (cycles) per unit time.

Frequency quantifies how many complete cycles or oscillations occur within a given unit of time. It is measured in Hertz (Hz), where 1 Hz equals one cycle per second.

Phase difference — A term used to compare the displacements and relative motions of particles in a wave.

Phase difference describes the relative positions and motions of two points on a wave, or two different waves. It indicates how 'out of step' they are, often expressed in degrees or radians.

Wavefront — Used to join points that are in phase.

A wavefront is an imaginary line or surface that connects all points on a wave that are vibrating in phase. For instance, the crests of a water wave form wavefronts.

Intensity — The power per unit area.

Intensity quantifies the rate at which energy is transferred by a wave per unit area. For a progressive wave, intensity is proportional to the square of its amplitude, meaning a small increase in amplitude leads to a significant increase in energy transfer.

Refraction — The change in direction of a wave due to a change in speed.

Refraction occurs when a wave passes from one medium to another, causing its speed to change. This change in speed typically results in a change in the wave's direction, unless it enters the new medium perpendicularly.

Doppler effect — The frequency change due to the relative motion between a source of sound or light and an observer.

The Doppler effect describes the apparent shift in frequency of a wave when there is relative motion between its source and an observer. For sound, this is heard as a change in pitch, such as a siren's pitch changing as it passes by.

Polarised wave — A transverse wave in which vibrations occur in only one of the directions at right angles to the direction in which the wave energy is travelling.

Polarisation is a phenomenon exclusively associated with transverse waves. It describes waves where the oscillations are restricted to a single plane perpendicular to the direction of energy transfer. Unpolarised light, for example, has vibrations in all possible perpendicular planes.

Principle of superposition — when two or more waves meet at a point, the resultant displacement at that point is equal to the sum of the displacements of the individual waves at that point.

This fundamental principle describes how waves combine. When waves overlap, their individual displacements add up at each point in space and time to create a new, resultant wave. This addition can lead to either an increase or decrease in amplitude.

Interference — where two or more waves meet or overlap to form a resultant wave. The resultant displacement at any point is the sum of displacements of the individual waves.

Interference is a direct consequence of the principle of superposition. When waves from different sources, or different parts of the same source, overlap, they combine to form a new wave pattern. This pattern can show regions of enhanced or diminished amplitude.

Fringes — The maxima and minima disturbances produced by interference.

When interference occurs, the resulting pattern often consists of alternating regions of maximum and minimum disturbance. These distinct bright and dark bands (for light) or loud and quiet regions (for sound) are known as fringes.

Interference pattern — The collection of fringes produced by the superposition of overlapping waves.

An interference pattern is the overall arrangement of these maxima and minima. It is a stable and observable pattern that arises when waves from coherent sources superpose, demonstrating the wave nature of phenomena like light and sound.

Coherent sources — Wave sources which maintain a constant phase difference.

For a stable and observable interference pattern to form, the waves must originate from coherent sources. This means the phase relationship between the waves must remain constant over time, ensuring that constructive and destructive interference occur at fixed locations.

Coherent waves — Two or more waves are coherent if they have a constant phase difference.

Coherent waves are essential for observing interference. If the phase difference between waves fluctuates randomly, the interference pattern will shift rapidly and average out, making it impossible to observe distinct fringes.

Monochromatic light source — a source of one colour, and hence one wavelength λ.

A monochromatic light source emits light of a single wavelength. This is crucial for producing clear and distinct interference patterns, as different wavelengths would produce overlapping patterns, making analysis difficult.

Fringe width — The distance x on the screen between successive bright fringes (or between successive dark fringes).

The fringe width, also known as fringe separation, is a measurable quantity in interference patterns. It represents the distance between the centres of adjacent bright fringes or adjacent dark fringes on the observation screen.

Fringe separation — The distance x on the screen between successive bright fringes (or between successive dark fringes).

This term is synonymous with fringe width. It is a key parameter used to calculate the wavelength of light in Young's double-slit experiment.

Stationary waves — The wave patterns on vibrating strings, or the result of the overlapping and hence interference of two waves of equal frequency and amplitude, travelling along the same line with the same speed but in opposite directions.

Stationary waves, also known as standing waves, are formed when two identical progressive waves travelling in opposite directions superpose. Unlike progressive waves, they do not transfer energy and appear to oscillate in place, with fixed points of zero and maximum displacement.

Standing waves — Another term for stationary waves.

This is an alternative name for stationary waves, emphasizing their appearance of not propagating through space.

Progressive waves — Waves that transfer energy.

In contrast to stationary waves, progressive waves carry energy from one point to another. Examples include sound waves travelling through air or light waves propagating through space.

Nodes — Points of zero amplitude on a stationary wave.

Nodes are specific points along a stationary wave where the displacement is always zero. These points remain motionless, resulting from continuous destructive interference between the two superposing waves.

Antinode — A point of maximum amplitude on a stationary wave.

Antinodes are points along a stationary wave where the amplitude of oscillation is maximum. At these points, constructive interference consistently occurs, leading to the largest possible displacement.

Fundamental mode of vibration — The simplest way a stretched string can vibrate, with a single loop.

This is the lowest frequency at which a string can vibrate to form a stationary wave. It corresponds to the first harmonic, where the string forms a single loop with nodes at both ends and an antinode in the middle.

First harmonic — Another term for the fundamental mode of vibration.

The first harmonic is the fundamental frequency of vibration for a system, such as a stretched string or an air column. It represents the simplest stationary wave pattern that can be formed.

First overtone — The next resonant frequency after the fundamental, corresponding to the second harmonic.

The first overtone is the next higher resonant frequency after the fundamental. For a stretched string, it corresponds to the second harmonic, where two loops are formed.

Second harmonic — The next resonant frequency after the fundamental, corresponding to the first overtone.

The second harmonic is twice the frequency of the fundamental. On a stretched string, it features two loops with three nodes and two antinodes.

Second overtone — The resonant frequency after the first overtone, corresponding to the third harmonic.

The second overtone is the resonant frequency after the first overtone. For a stretched string, it corresponds to the third harmonic, forming three loops.

Third harmonic — The resonant frequency after the first overtone, corresponding to the second overtone.

The third harmonic is three times the frequency of the fundamental. On a stretched string, it exhibits three loops with four nodes and three antinodes.

End-correction — The distance of the antinode from the end of the tube, slightly outside the open end.

In resonance tubes, the antinode at an open end does not form exactly at the end of the tube but slightly beyond it. This small additional distance is known as the end-correction and must be accounted for in precise measurements.

Resonant frequencies — The particular frequencies at which stationary waves are obtained in a pipe.

These are the specific frequencies at which a system, like an air column, will naturally vibrate with large amplitudes, forming stable stationary wave patterns. At these frequencies, the conditions for constructive interference are met.

Diffraction — The spreading of a wave into regions where it would not be seen if it moved only in straight lines after passing through a narrow slit or past an edge.

Diffraction is a wave phenomenon where waves bend around obstacles or spread out after passing through an aperture. This effect is most noticeable when the wavelength of the wave is comparable to the size of the obstacle or aperture.

Diffraction grating — A plate on which there is a very large number of parallel, identical, very closely spaced slits.

A diffraction grating is an optical component used to separate light into its constituent wavelengths. It consists of many parallel slits, which produce a much sharper and more widely dispersed diffraction pattern than a single or double slit.

Zero-order maximum — The straight-on direction (n=0) in a diffraction grating pattern.

The zero-order maximum is the central bright fringe in a diffraction grating pattern. It corresponds to light that passes straight through the grating without any deviation, meaning the path difference is zero.

First-order diffraction maximum — The maximum observed when n=1 in the diffraction grating equation.

The first-order maximum is the bright fringe observed at the smallest non-zero angle from the central maximum. It corresponds to a path difference of one wavelength between light from adjacent slits.

Spectrometer — A piece of apparatus used to investigate spectra, often using a diffraction grating.

A spectrometer is an instrument designed to measure the properties of light over a specific portion of the electromagnetic spectrum. It commonly uses a diffraction grating to disperse light into its component wavelengths, allowing for analysis of spectral lines.

coulomb — The unit of charge (symbol C).

Charge is a fundamental property of matter, and the coulomb is its standard unit. It represents a specific quantity of electric charge.

quantised — Exists only in discrete amounts, integral multiples of the charge on an electron.

Electric charge is not continuous but comes in fixed, indivisible packets. This means any observable charge is always a whole number multiple of the elementary charge, which is the charge on a single electron.

ampere — The SI base unit of current (symbol A).

The ampere is the standard unit for measuring electric current, representing the rate at which electric charge flows past a point in a circuit.

conventional current — The flow in the circuit from the positive terminal of the battery or power supply to the negative, in the direction of flow of positive charge.

Historically, current was thought to be the flow of positive charge. Even though we now know that electrons (negative charges) are often the charge carriers in metals, conventional current is still defined as flowing from positive to negative.

potential difference — The energy transferred per unit charge.

Potential difference, also known as voltage, quantifies the amount of energy converted from electrical to other forms (or vice versa) when a unit of charge moves between two points in a circuit. It is a measure of the 'push' or 'pull' on charges.

volt — The unit of potential difference, a joule coulomb−1 (symbol V).

The volt is the standard unit for potential difference, indicating that one joule of energy is transferred for every coulomb of charge that moves across that potential difference.

resistance — The ratio of the potential difference V across the conductor to the current I in it.

Resistance is a measure of how much a component opposes the flow of electric current. A higher resistance means that for a given potential difference, less current will flow.

ohm — The unit of resistance, a volt ampere−1 (symbol Ω).

The ohm is the standard unit for resistance. One ohm means that a potential difference of one volt will drive a current of one ampere through the component.

resistor — The general term for a device that has resistance.

A resistor is an electrical component designed to introduce a specific amount of resistance into a circuit, used to control current or voltage.

Ohm’s law — For a metallic conductor at constant temperature, the current in the conductor is proportional to the potential difference across it.

Ohm's law describes a specific relationship between current and potential difference for certain materials. It implies that the resistance of an ohmic conductor remains constant as long as its temperature does not change.

forward bias — The condition where a diode conducts, with the current in the direction of the arrowhead on the symbol, meaning the potential on the left-hand side is more positive than the potential on the right-hand side.

A semiconductor diode is a non-ohmic component that allows current to flow easily in one direction (forward bias) once a certain threshold potential difference is reached. In this state, the diode acts like a conductor.

reverse bias — The condition where the potential difference across a diode is reversed, and the diode does not conduct.

When a diode is in reverse bias, the potential difference across it is oriented in the opposite direction to forward bias. In this condition, the diode exhibits very high resistance and effectively blocks the flow of current.

resistivity — A constant for a particular material at a particular temperature, defined by ρ = RA/L.

Resistivity is a fundamental property of a material that indicates its ability to conduct electricity. It is constant for a given material at a specific temperature and is used to calculate the resistance of a component made from that material, given its dimensions.

light-dependent resistor (LDR) — A component whose resistance decreases as the light intensity increases.

An LDR is a type of resistor whose resistance is sensitive to light. It is commonly used in light-sensing circuits, such as automatic streetlights or light meters.

thermistors — Negative temperature coefficient devices made from semiconductor material, whose resistance decreases significantly with rise in temperature.

Thermistors are temperature-sensitive resistors. Their resistance changes predictably with temperature, making them useful in temperature sensing and control applications, such as thermostats or fire alarms.

electromotive force — The energy transferred from other forms to electrical per unit charge in driving charge around a complete circuit.

Electromotive force (e.m.f.) measures the energy supplied by a power source, such as a battery, to each unit of charge as it moves through the source. This energy is converted from chemical or other forms into electrical energy, enabling the charge to circulate around the entire circuit.

e.m.f. — Short for electromotive force, which measures, in volts, the energy transferred per unit of charge that passes through the power supply.

e.m.f. is simply the abbreviation for electromotive force. It quantifies the energy provided by a power supply per unit charge, expressed in volts. This energy transfer is crucial for driving current through a complete circuit.

potential difference — The energy transferred from electrical to other forms per unit charge as it passes through a component.

Potential difference (p.d.) represents the energy converted from electrical energy into other forms, such as heat or light, per unit charge as it moves through a specific component in a circuit. It is a measure of the 'push' or 'pull' on charges between two points in a circuit, causing them to do work.

internal resistance — Resistance between the terminals of a power supply.

All real power supplies possess some internal resistance, which is the resistance inherent within the source itself. This internal resistance causes some of the electrical energy generated by the source to be dissipated as heat within the source, rather than being delivered to the external circuit. Consequently, the terminal potential difference of a power supply will be less than its e.m.f. when a current is flowing.

terminal potential difference — The p.d. between the terminals of a cell or power supply when a current is being delivered.

The terminal potential difference is the actual voltage available across the external terminals of a power supply when it is actively supplying current to a circuit. Due to internal resistance, this value is typically lower than the e.m.f. of the supply. When no current is drawn, the terminal potential difference equals the e.m.f.

Kirchhoff’s first law — The sum of the currents entering a junction in a circuit is always equal to the sum of the currents leaving the junction.

Kirchhoff's first law, also known as the junction rule, is a direct consequence of the conservation of charge. It states that no charge can accumulate at a junction; therefore, the total amount of charge flowing into a junction must equal the total amount of charge flowing out of it per unit time. This means the sum of currents entering a junction equals the sum of currents leaving it.

Kirchhoff’s second law — The sum of the electromotive forces in a closed circuit is equal to the sum of the potential differences.

Kirchhoff's second law, or the loop rule, is based on the conservation of energy. It states that for any closed loop in a circuit, the algebraic sum of the e.m.f.s must equal the algebraic sum of the potential differences across the components. This means that any energy supplied by sources in a loop must be dissipated by components within that same loop.

series circuit — A circuit in which the components are connected one after another, forming one complete loop.

In a series circuit, components are arranged sequentially, forming a single path for the current to flow. The current is the same through every component in a series circuit. The total resistance is the sum of individual resistances, and the total potential difference is divided among the components.

parallel circuit — A circuit where the current can take alternative routes in different loops.

In a parallel circuit, components are connected across the same two points, providing multiple paths for the current. The potential difference across each parallel component is the same. The total current from the source splits among the parallel branches, and the equivalent resistance is less than the smallest individual resistance.

potentiometer — A continuously variable potential divider.

A potentiometer is essentially a potential divider with a sliding contact, allowing for continuous variation of the output voltage. It consists of a uniform resistance wire or track, and by moving a slider along it, the resistance of the output section can be smoothly adjusted. This makes it useful for controlling voltage or comparing e.m.f.s.

galvanometer — A sensitive current-measuring analogue meter, often with a centre-zero scale.

A galvanometer is a highly sensitive instrument used to detect and measure small electric currents. Its centre-zero scale allows it to indicate current flow in either direction. In potentiometer circuits, it is used to detect a 'null' or 'balance point' where no current flows.

balance point — The position of the sliding contact on a potentiometer wire where the galvanometer reads zero, indicating no current through the test cell.

The balance point in a potentiometer circuit is achieved when the potential difference across a section of the potentiometer wire exactly matches the e.m.f. of the test cell. At this point, no current flows through the galvanometer connected in series with the test cell, indicating a 'null' reading. This null method is advantageous as it measures the e.m.f. without any current being drawn from the cell, thus avoiding voltage drop due to internal resistance.

proton number — The number of protons in the nucleus of an atom is called the proton number (or atomic number) Z.

The proton number, denoted by Z, uniquely identifies an element. It represents the positive charge within the nucleus and determines the element's chemical properties.

nucleon number — The number of protons together with the number of neutrons in the nucleus is called the nucleon number (or mass number) A.

The nucleon number, A, represents the total count of particles within the nucleus, which are collectively known as nucleons. It is essentially the mass number of the atom.

nucleon — A nucleon is the name given to either a proton or a neutron in the nucleus.

Protons and neutrons are the constituent particles of an atomic nucleus. They are both affected by the strong nuclear force, which binds them together.

nuclide — A nuclide is the name given to a class of atoms whose nuclei contain a specified number of protons and a specified number of neutrons.

A nuclide specifies a particular type of atom based on its exact nuclear composition. This includes both the number of protons (Z) and neutrons, which together determine its nucleon number (A).

isotopes — Isotopes are different forms of the same element which have the same number of protons but different numbers of neutrons in their nuclei.

Isotopes of an element share the same proton number (Z), meaning they are the same element, but they differ in their nucleon number (A) due to varying numbers of neutrons. This difference affects their mass but not their chemical identity.

radioactive — Nuclei are said to be radioactive when they emit particles and/or electromagnetic radiation to become more stable.

Radioactive nuclei are inherently unstable and undergo a process called radioactivity to achieve a more stable configuration. This process involves the spontaneous emission of various forms of radiation.

radioactivity — The emission of particles and/or electromagnetic radiation from unstable nuclei.

Radioactivity is the phenomenon where unstable atomic nuclei spontaneously transform, releasing energy and matter in the form of particles or electromagnetic waves. This process is driven by the nucleus seeking a more stable state.

parent nuclide — The original nuclide in a radioactive decay process.

In any radioactive decay, the initial unstable nucleus is referred to as the parent nuclide. It undergoes transformation to produce a new nucleus.

daughter nuclide — The new nuclide formed after a radioactive decay process.

Following radioactive decay, the resulting nucleus is called the daughter nuclide. This daughter nuclide may itself be stable or undergo further decay.

α-particle — An α-particle consists of two protons and two neutrons and hence has a charge of +2e. An α-particle is identical to the nucleus of a helium atom.

Alpha particles are relatively heavy and carry a positive charge. Due to their composition, they are highly ionising, meaning they can dislodge electrons from atoms they interact with, forming ion pairs.

ion pair — An ionised atom and the dislodged electron, produced when an α-particle interacts with nearby atoms.

When an alpha particle passes through matter, its strong positive charge attracts electrons from atoms, pulling them away. This creates a positively charged ion and a free electron, forming an ion pair.

β-particles — Fast moving electrons, β−, or positrons, β+.

Beta particles are much lighter than alpha particles and carry either a negative or positive charge. They are emitted during beta decay processes, which involve changes within the nucleus.

positron — A positive electron (β+) also known as an antielectron, which is the antiparticle of an electron.

A positron is the antimatter counterpart of an electron. It has the same mass as an electron but carries an opposite, positive charge. Positrons are emitted during beta-plus decay.

antiparticle — An antiparticle has the same mass but opposite charge to the corresponding particle.

For every particle, there exists an antiparticle with identical mass but opposite charge and other quantum numbers. When a particle and its antiparticle meet, they can annihilate each other.

antineutrino — The antimatter equivalent of the neutrino, emitted with a β− particle.

An antineutrino is a fundamental particle with no electrical charge and very little or no mass. It is emitted alongside a beta-minus particle during beta-minus decay to conserve energy and lepton number.

neutrino — A particle with no electrical charge and little or no mass, emitted with a β+ particle.

A neutrino is a fundamental particle, similar to an antineutrino but its matter counterpart. It is emitted with a beta-plus particle during beta-plus decay, also ensuring conservation laws are upheld.

γ-radiation — Part of the electromagnetic spectrum with wavelengths between 10−11 m and 10−13 m, emitted by excited nuclei.

Gamma radiation consists of high-energy photons, meaning it is electromagnetic radiation rather than particles. It is emitted when an excited nucleus transitions to a lower energy state, similar to how electrons emit photons when changing energy levels.

radioactive decay series — A sequence of radioactive decay from parent nuclide through succeeding daughter nuclides, ending when a stable nuclide is reached.

Many heavy, unstable nuclei undergo a series of alpha and beta decays until a stable, non-radioactive nuclide is formed. This chain of transformations is known as a radioactive decay series.

fundamental particle — A particle that is not formed from other particles.

Fundamental particles are considered the most basic building blocks of matter and energy. They are not composed of any smaller, more elementary constituents.

strong nuclear force — The force that holds the nucleons in the nucleus together, acting on protons and neutrons but not on electrons, and is very short range.

The strong nuclear force is one of the four fundamental forces of nature. It is responsible for binding protons and neutrons within the atomic nucleus, overcoming the electrostatic repulsion between positively charged protons. Its extremely short range means it only acts over nuclear distances.

hadrons — Subatomic particles affected by the strong force, for example protons and neutrons.

Hadrons are composite particles that interact via the strong nuclear force. Protons and neutrons are examples of hadrons, meaning they are not fundamental particles themselves but are made up of smaller constituents.

leptons — Subatomic particles not affected by the strong force, for example electrons and positrons.

Leptons are a class of fundamental particles that do not experience the strong nuclear force. Electrons, positrons, neutrinos, and antineutrinos are all examples of leptons.

quarks — Fundamental particles that make up hadrons.

Quarks are fundamental particles that combine to form hadrons. There are six 'flavours' or types of quarks: up, down, strange, charm, top, and bottom. They carry fractional electric charges.

baryon — A type of hadron made up of three quarks or three antiquarks.

Baryons are a specific category of hadrons composed of three quarks (or three antiquarks). Protons and neutrons are the most common examples of baryons.

meson — A type of hadron made up of a quark and an antiquark.

Mesons are another type of hadron, but unlike baryons, they are composed of a quark and an antiquark pair. They are generally unstable and have shorter lifetimes.

radian (rad) — The angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.

The radian is a unit of angular measure. When the length of an arc along the circumference of a circle is exactly equal to the radius of that circle, the angle formed at the centre by this arc is defined as one radian. This provides a natural and convenient way to express angular displacement.

angular speed — The angle swept out by the radius of the circle per unit time.

Angular speed quantifies how quickly an object rotates or revolves around a central point. It measures the rate at which the radius of the circular path sweeps through an angle. For example, a faster spinning object will have a higher angular speed.

angular velocity — The angular speed in a given direction (for example, clockwise).

Angular velocity is a vector quantity that includes both the angular speed and the direction of rotation. While angular speed tells us how fast an object is rotating, angular velocity specifies this rate along with whether it's rotating clockwise or anti-clockwise.

centripetal acceleration — The acceleration towards the centre of the circle for an object travelling in a circle.

Even if an object moves at a constant speed in a circle, its velocity is continuously changing because its direction is always changing. This change in velocity means there must be an acceleration, which is always directed towards the centre of the circle. This inward acceleration is known as centripetal acceleration.

centripetal force — The resultant force acting towards the centre of the circle, required to make an object accelerate in circular motion.

According to Newton's second law, an acceleration requires a resultant force. For an object to undergo centripetal acceleration and thus move in a circle, there must be a resultant force acting towards the centre of the circle. This force is not a new type of force but is provided by existing physical forces like tension, gravity, friction, or the normal force.

gravitational field — A region of space where a mass experiences a force.

A gravitational field is an example of a field of force, meaning it is a region where objects with mass will experience a force due to the presence of other masses. This field extends infinitely, though its strength diminishes with distance.

gravitational field strength — The force per unit mass acting on a small mass placed at that point.

Gravitational field strength, denoted by 'g', quantifies the intensity of a gravitational field. It is defined as the gravitational force experienced by a small test mass divided by that mass. It also represents the acceleration of free fall at that point.

gravitational field line — The direction of the gravitational force acting on a point mass.

Gravitational field lines are used to visually represent a gravitational field. They indicate the direction a small test mass would experience a force, always pointing towards the mass creating the field. The density of these lines indicates the strength of the field.

Newton’s law of gravitation — States that two point masses attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of their separation.

Newton's law of gravitation describes the attractive force between any two point masses. This force is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. This law is fundamental to understanding gravitational interactions.

gravitational constant — The constant of proportionality G in Newton's law of gravitation.

The gravitational constant, G, is a universal constant that determines the strength of the gravitational force. Its value is approximately 6.67 × 10^-11 N m^2 kg^-2, and it is essential for calculating gravitational forces.

weight — The force acting on a mass in a gravitational field, equal to the product of mass and gravitational field strength.

Weight is the force experienced by an object due to gravity. It is calculated as the product of the object's mass and the gravitational field strength at its location. Unlike mass, which is an invariant property, weight changes depending on the local gravitational field.

Kepler’s third law of planetary motion — For planets or satellites describing circular orbits about the same central body, the square of the period is proportional to the cube of the radius of the orbit.

Kepler's third law describes a fundamental relationship for objects orbiting a common central body. It states that the square of the orbital period (T) is directly proportional to the cube of the orbital radius (r). This law can be derived from Newton's law of gravitation and the centripetal force equation.

geostationary orbit — Equatorial orbits with exactly the same period of rotation as the Earth (24 hours), and move in the same direction as the Earth (west to east) so that they are always above the same point on the Equator.

A geostationary orbit is a specific type of circular orbit around the Earth. Satellites in this orbit have a period of 24 hours, orbit from west to east, and are positioned directly above the Equator. This allows them to remain stationary relative to a point on the Earth's surface.

geostationary satellites — Satellites in geostationary orbits.

Geostationary satellites are crucial for communication and weather monitoring as their fixed position relative to the Earth's surface allows for continuous coverage of a specific region. Their unique orbital characteristics are a direct consequence of gravitational principles.

apparent weightlessness — The situation experienced in free fall, where objects appear weightless, as opposed to true weightlessness in the absence of a gravitational field.

Apparent weightlessness occurs when an object is in continuous free fall, such as astronauts in orbit. They appear weightless because they are constantly accelerating towards the Earth at the same rate as their spacecraft, not because there is no gravitational field acting on them.

Gravitational potential — At a point in a gravitational field is defined as the work done per unit mass in bringing a small test mass from infinity to the point.

Gravitational potential, denoted by Φ, is a scalar quantity that describes the potential energy per unit mass at a given point in a gravitational field. It is defined with respect to infinity, where the potential is considered zero. Due to the attractive nature of gravity, gravitational potential values are always negative.

Thermal equilibrium — When different regions in thermal contact are at the same temperature, they are said to be in thermal equilibrium.

Thermal energy is always transferred from a region of higher temperature to a region of lower temperature. When two regions in thermal contact reach the same temperature, there is no net flow of thermal energy between them, and they are said to be in thermal equilibrium.

Thermometer — An instrument for measuring temperature.

A thermometer is a device designed to quantify the degree of 'hotness' of a body. Its operation relies on a physical property that changes predictably with temperature.

Thermometric property — The physical property on which a particular thermometer is based.

For a thermometer to function, it must utilise a physical property of a substance that varies consistently with temperature. Examples include the expansion of a liquid, the resistance of a wire, or the pressure of a gas at constant volume.

Thermometric substance — The working material of the thermometer, the property of which varies with temperature.

This is the specific material within a thermometer whose thermometric property is observed. For instance, in a liquid-in-glass thermometer, the liquid (e.g., mercury or alcohol) is the thermometric substance, and its volume is the thermometric property.

Fixed points — Reference temperatures defined by the fact that substances change state at fixed temperatures.

Fixed points are crucial for establishing temperature scales. These are reproducible temperatures at which substances undergo phase changes, such as the melting point of ice (ice point) or the boiling point of water (steam point) at standard atmospheric pressure.

Ice point — The melting point of ice.

The ice point is a standard fixed point used in temperature scale calibration. It refers to the temperature at which pure ice melts under normal atmospheric pressure.

Steam point — The temperature of steam above water boiling at normal atmospheric pressure.

The steam point is another critical fixed point, representing the temperature at which pure water boils and turns into steam under normal atmospheric pressure. These two points historically defined the 0°C and 100°C marks on the Celsius scale.

Empirical scale of temperature — A temperature scale set up by taking the value of a thermometric property at two fixed points and dividing the range of values into a number of equal steps.

Empirical scales are constructed by assigning specific values to two fixed points, such as the ice point and steam point, and then linearly interpolating between them. The Celsius scale is an example of an empirical scale, initially defined by these two points.

Absolute zero — The lowest theoretically possible temperature, which is –273.15 degrees Celsius or zero kelvin.

Absolute zero represents the theoretical point at which a substance has minimum possible thermal energy. It is the fundamental lower limit of temperature, unattainable in practice but crucial for defining the thermodynamic temperature scale.

Kelvin — The unit of thermodynamic temperature, defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

The Kelvin is the SI unit for thermodynamic temperature. This scale is absolute, meaning zero Kelvin corresponds to absolute zero, and it does not depend on the properties of any particular substance, making it a fundamental scientific scale.

Specific heat capacity — The thermal energy per unit mass required to raise the temperature of the substance by one degree.

Specific heat capacity (c) quantifies how much thermal energy a substance can store for a given temperature change. A substance with a high specific heat capacity requires more energy to change its temperature than one with a low specific heat capacity, for the same mass and temperature change.

Specific latent heat — The quantity of heat per unit mass required to change the state of a substance at constant temperature.

Specific latent heat (L) is the energy absorbed or released during a phase change (e.g., melting, boiling) without any change in temperature. This energy is used to break or form intermolecular bonds, rather than increasing kinetic energy of molecules.

Latent heat of fusion — The thermal energy required to melt (fuse) a solid without any change of temperature.

Latent heat of fusion refers to the total thermal energy needed to convert a given mass of solid into liquid at its melting point. During this process, the temperature remains constant as the energy is used to overcome the forces holding the particles in a fixed lattice structure.

Specific latent heat of fusion — The quantity of thermal energy required to convert unit mass of solid to liquid without any change in temperature.

Specific latent heat of fusion (L_f) is a material property that quantifies the energy needed per kilogram to melt a substance. This energy is absorbed by the substance to change its state from solid to liquid at its melting point, without any temperature increase.

Latent heat of vaporisation — The latent heat required to vaporise a liquid without any change of temperature.

Latent heat of vaporisation is the total thermal energy needed to convert a given mass of liquid into gas at its boiling point. The temperature remains constant as the energy is used to completely separate the molecules and do work against the atmosphere.

Specific latent heat of vaporisation — The quantity of thermal energy required to convert unit mass of liquid to vapour without any change in temperature.

Specific latent heat of vaporisation (L_v) is the energy needed per kilogram to vaporise a substance. This energy is significantly greater than the specific latent heat of fusion because more energy is required to completely separate molecules and do work against the atmosphere during vaporisation.

mole — The amount of substance which contains 6.02214076 × 10^23 elementary entities, usually atoms or molecules but could also be ions or electrons.

The mole is the SI base unit for the amount of substance. It provides a convenient way to count a very large number of particles, such as atoms or molecules, by relating them to a macroscopic quantity of substance.

Avogadro constant — The number of elementary entities in 1 mole of any substance.

The Avogadro constant, denoted N_A, is approximately 6.02 × 10^23 mol^-1. It represents the fixed number of particles (atoms, molecules, ions, or electrons) present in one mole of any substance.

molar mass — The mass of 1 mole of substance.

Molar mass is the mass, typically expressed in grams per mole (g/mol), of one mole of a particular chemical substance. It is a crucial quantity for converting between the mass of a substance and its amount in moles.

Boyle’s law — The volume V of a gas is inversely proportional to its pressure p, provided that the temperature is held constant.

Boyle's law describes the inverse relationship between the pressure and volume of a fixed mass of gas when its temperature is kept constant. As pressure increases, volume decreases proportionally.

Charles’ law — The relation between initial and final volume and thermodynamic temperature of a fixed mass of gas at constant pressure, V1/T1 = V2/T2.

Charles' law states that for a fixed mass of gas at constant pressure, its volume is directly proportional to its thermodynamic temperature. This means that as temperature increases, the volume expands proportionally.

Gay-Lussac’s law — The relation between initial and final pressure and thermodynamic temperature of a fixed mass of gas at constant volume, p1/T1 = p2/T2.

Gay-Lussac's law describes the direct proportionality between the pressure and thermodynamic temperature of a fixed mass of gas when its volume is held constant. An increase in temperature leads to a proportional increase in pressure.

ideal gas — One which obeys the equation of state pV ∝ T at all pressures p, volumes V and thermodynamic temperatures T.

An ideal gas is a theoretical gas that perfectly adheres to the ideal gas equation under all conditions. Real gases approximate ideal gas behavior at low pressures and high temperatures, but deviate at extreme conditions.

molar gas constant — A constant R, with value 8.3 J K–1 mol–1, used in the ideal gas equation pV = nRT, which has the same value for all gases.

The molar gas constant, R, is a universal constant that appears in the ideal gas equation when the amount of substance is expressed in moles. It has a value of approximately 8.3 J K–1 mol–1 and is the same for all ideal gases.

universal gas equation — The equation pV = nRT, also known as the equation of state for an ideal gas.

The universal gas equation, pV = nRT, is a fundamental equation describing the state of an ideal gas. It relates pressure (p), volume (V), amount of substance (n), the molar gas constant (R), and thermodynamic temperature (T).

Boltzmann constant — A constant k, with value 1.38 × 10–23 J K–1, used in the ideal gas equation pV = NkT.

The Boltzmann constant, k, is a fundamental physical constant that relates the average kinetic energy of particles in a gas to the thermodynamic temperature of the gas. It is used in the ideal gas equation when the number of individual molecules (N) is considered, rather than moles.

mean-square speed — The average value of the square of the speeds of molecules, represented by .

The mean-square speed, denoted as , is a statistical measure used in the kinetic theory of gases. It is calculated by squaring the speed of each molecule, summing these squared speeds, and then dividing by the total number of molecules. This value is crucial for relating molecular motion to macroscopic properties like pressure.

root-mean-square speed — The quantity √, also known as r.m.s. speed of the molecules.

The root-mean-square (r.m.s.) speed is the square root of the mean-square speed. It provides a measure of the typical speed of molecules in a gas, taking into account the distribution of speeds. It is often used to characterize the average kinetic energy of gas molecules.

Thermodynamics — Thermodynamics is the study of processes involving the transfer of thermal energy and the doing of work.

Thermodynamics is a branch of physics concerned with heat and its relation to other forms of energy and work. It explores how energy is transferred and transformed within systems, particularly focusing on thermal energy and mechanical work.

internal energy — The sum of the potential energies and kinetic energies of all the molecules, owing to their random motion, is called the internal energy of the gas.

Internal energy (U) represents the total energy stored within a system at a molecular level. It comprises the random kinetic energies of the molecules due to their motion and the potential energies arising from intermolecular forces. This energy is determined by the state of the system.

adiabatic change — A thermodynamic change where no thermal energy is allowed to enter or leave the system.

An adiabatic change is a process where a system is perfectly insulated, preventing any transfer of thermal energy (q = 0) with its surroundings. This means any change in internal energy is solely due to work done on or by the system.

isothermal change — A change which takes place at constant temperature.

An isothermal change is a thermodynamic process that occurs at a constant temperature. For an ideal gas, this implies that the internal energy remains constant (ΔU = 0) because internal energy is directly related to temperature.

Oscillation — One complete movement from the starting or rest position, move up, then down and finally back up to the rest position.

An oscillation describes a repetitive motion around an equilibrium point. It encompasses the full cycle of movement, returning to the initial state.

Period T — The time taken for one complete oscillation or vibration.

The period, denoted by T, is a fundamental characteristic of an oscillation, representing the duration for a single full cycle of motion to occur.

Frequency f — The number of oscillations or vibrations per unit time.

Frequency, f, quantifies how often an oscillation repeats within a given timeframe. It is inversely related to the period.

Displacement — The distance from the equilibrium position.

Displacement refers to the instantaneous position of an oscillating object relative to its central, stable equilibrium point. It can be positive or negative depending on the direction from equilibrium.

Amplitude — The maximum displacement.

The amplitude represents the greatest distance an oscillating object moves from its equilibrium position. It is a measure of the 'size' of the oscillation.

Angular frequency — The square root of the constant \omega^2 (that is, \omega) in the defining equation for simple harmonic motion.

Angular frequency, \omega, is a measure of the rate of oscillation in radians per second. It is closely related to the frequency and period of the motion.

Simple harmonic motion (s.h.m.) — The motion of a particle about a fixed point such that its acceleration a is proportional to its displacement x from the fixed point, and is in the opposite direction.

Simple harmonic motion (SHM) is a specific type of oscillatory motion characterized by a restoring force directly proportional to the displacement and always directed towards the equilibrium position. This results in a sinusoidal variation of displacement with time.

Harmonic oscillators — Oscillators which move in s.h.m.

Harmonic oscillators are systems that exhibit simple harmonic motion, meaning their restoring force follows Hooke's Law, leading to a predictable, sinusoidal oscillation.

Restoring force — A force that is always acting towards the fixed point from which displacement is measured.

The restoring force is crucial for oscillations, as it always acts to bring the oscillating object back to its equilibrium position. In SHM, this force is directly proportional to the displacement.

Isochronous — Oscillators that have a constant time period.

Isochronous oscillators maintain a consistent time period regardless of their amplitude, within certain limits. This property is often approximated in simple harmonic motion, though not perfectly true for all oscillating systems at large amplitudes.

Free oscillations — Oscillations when the only external force acting on it is the restoring force.

Free oscillations occur when a system oscillates without any external driving forces or resistive forces. The object vibrates solely under the influence of its internal restoring force, at its natural frequency.

Natural frequency — The frequency at which a vibrating object undergoes free (undamped) oscillations.

Every oscillating system has a natural frequency, which is the specific frequency at which it will oscillate if left undisturbed and without any damping forces acting upon it.

Damped — Oscillations where frictional and other resistive forces cause the oscillator’s energy to be dissipated.

Damped oscillations occur when resistive forces, such as friction or air resistance, act on an oscillating system. These forces cause the system's mechanical energy to be gradually converted into other forms, leading to a decrease in the amplitude of oscillation over time.

Light damping — Damping where the amplitude of the oscillations decreases gradually with time.

In light damping, the resistive forces are relatively small, allowing the system to complete many oscillations before its amplitude significantly diminishes. The period of oscillation remains approximately constant.

Critical damping — The point where the displacement decreases to zero in the shortest time, without any oscillation.

Critical damping represents the optimal level of damping where the system returns to its equilibrium position as quickly as possible without oscillating. This is often desired in systems like car shock absorbers.

Overdamping or heavy damping — Any further increase in damping beyond critical damping, where the displacement decreases to zero in a longer time than for critical damping.

Heavy damping occurs when the resistive forces are very large, causing the system to return to equilibrium slowly without oscillating. The time taken to reach equilibrium is longer than with critical damping.

Forced vibrations — When a vibrating object is made to vibrate at the frequency of an applied periodic force, rather than at its natural frequency.

Forced vibrations occur when an external periodic force is applied to an oscillating system, compelling it to oscillate at the frequency of the applied force, known as the driving frequency.

Resonance — Occurs when the natural frequency of vibration of an object is equal to the driving frequency, giving a maximum amplitude of vibration.

Resonance is a phenomenon where a system's amplitude of oscillation becomes maximal when the frequency of an applied driving force matches the system's natural frequency. This can lead to very large and potentially destructive vibrations.

Resonant frequency — The frequency at which the driving frequency equals the natural frequency of oscillation, and the amplitude of the oscillations reaches a maximum.

The resonant frequency is the specific driving frequency at which resonance occurs, leading to the largest possible amplitude of oscillation for a given system.

Resonance curve — A graph illustrating the variation with driving frequency of the amplitude of vibration of a mass.

A resonance curve visually represents how the amplitude of a forced oscillation changes as the driving frequency is varied. It typically shows a peak at the resonant frequency.

Electric field — A region of space where a stationary electric charge experiences a force.

Electric fields are fundamental to understanding how charges interact. Any charged particle placed within such a region will experience an electric force.

Electric field strength — The force per unit charge acting on a small stationary positive charge placed at that point.

Electric field strength quantifies the intensity of an electric field. It is a vector quantity, with its direction defined by the force a positive test charge would experience.

Coulomb’s law — The force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.

Coulomb's law describes the fundamental electrostatic interaction between two point charges. It quantifies the attractive or repulsive force based on their magnitudes and separation.

Permittivity of free space — The quantity \epsilon_0, which is a constant in Coulomb's law for charges in a vacuum.

The permittivity of free space, ε₀, is a physical constant that represents the absolute dielectric permittivity of a vacuum. It is crucial for calculating electric forces and fields in free space.

Electric potential — The work done per unit positive charge in bringing a small test charge from infinity to the point.

Electric potential is a scalar quantity that describes the potential energy per unit charge at a given point in an electric field. It is defined relative to infinity, where the potential is considered zero.

Potential gradient — The rate of change of electric potential with distance.

The potential gradient describes how rapidly the electric potential changes over a given distance. It is directly related to the electric field strength.

Capacitance — The ratio of charge Q to potential V for a conductor.

Capacitance quantifies a conductor's ability to store electric charge at a given potential. A higher capacitance means more charge can be stored for the same potential difference.

Farad — The unit of capacitance (symbol F). One farad is one coulomb per volt.

The Farad is the SI unit for capacitance. A capacitor with a capacitance of one Farad will store one Coulomb of charge when a potential difference of one Volt is applied across it.

Capacitors — Circuit components which store charge and, therefore, have capacitance.

Capacitors are fundamental electronic components designed to store electrical energy in an electric field. They achieve this by accumulating electric charge on their plates.

Parallel-plate capacitor — The simplest capacitor in an electric circuit consisting of two metal plates, with an air gap between them which acts as an insulator.

A parallel-plate capacitor is a common type of capacitor, comprising two conductive plates separated by an insulating material. The air gap between the plates prevents charge from flowing directly between them, allowing for charge accumulation.

Dielectric — The insulating material placed between the plates of a capacitor.

A dielectric is an electrical insulator that can be polarised by an applied electric field. Placing a dielectric between the plates of a capacitor increases its capacitance compared to a vacuum or air gap.

Relative permittivity — The capacitance of a parallel-plate capacitor with the dielectric between the plates divided by the capacitance of the same capacitor with a vacuum between the plates.

Relative permittivity, \epsilon_r, is a dimensionless quantity that indicates how much an insulating material increases the capacitance of a capacitor compared to a vacuum. It reflects the dielectric's ability to store electrical energy.

Time constant — The time for the charge to have decreased to 1/e (or 1/2.718) of its initial value.

The time constant (\tau) is a crucial characteristic of an RC circuit, representing the time it takes for the charge, potential difference, or current to fall to approximately 37% (1/e) of its initial value during discharge. It indicates the rate of decay.

north-seeking pole — The pole of a freely suspended magnet that points to the north.

When a magnet is freely suspended, one end consistently points towards the Earth's geographic north. This end is designated as the north-seeking pole, indicating its alignment with the Earth's magnetic field.

south-seeking pole — The pole of a freely suspended magnet that points to the south.

Conversely, the pole of a freely suspended magnet that points towards the Earth's geographic south is known as the south-seeking pole. It aligns itself opposite to the north-seeking pole in response to the Earth's magnetic field.

magnetic field — A region of space where a magnetic pole experiences a force.

A magnetic field is an invisible area surrounding a magnet or a moving electric charge where magnetic forces are exerted. Within this region, another magnetic pole will experience a push or pull, indicating the presence and direction of the field.

neutral point — A point where there is no resultant magnetic field because two fields are equal in magnitude but opposite in direction.

A neutral point occurs when two or more magnetic fields cancel each other out precisely. At such a point, the magnetic forces from different sources are equal in strength but act in opposing directions, resulting in a net magnetic field of zero.

magnetic flux density — Numerically equal to the force per unit current per unit length on a straight wire placed at right angles to a uniform magnetic field.

Magnetic flux density, denoted by B, quantifies the strength of a magnetic field. It is defined by the force experienced by a current-carrying wire perpendicular to the field. A higher magnetic flux density means a stronger magnetic field and thus a greater force on the wire.

tesla — The uniform magnetic flux density which, acting normally to a long straight wire carrying a current of 1 ampere, causes a force per unit length of 1 N m−1 on the conductor.

The tesla (T) is the SI unit for magnetic flux density. One tesla represents a very strong magnetic field, where a one-meter length of wire carrying one ampere of current experiences a force of one newton when placed perpendicular to the field.

specific charge — The ratio of the charge q on a particle and its mass m.

Specific charge is a fundamental property of charged particles, representing the amount of charge per unit of mass. It is a crucial quantity in determining how particles behave in electric and magnetic fields, influencing their acceleration and deflection.

velocity selector — An arrangement of perpendicular electric and magnetic fields that allows only charged particles with a specific velocity to pass undeviated.

A velocity selector is a device that uses balanced electric and magnetic forces to isolate charged particles moving at a particular speed. Only particles for which the electric force precisely cancels the magnetic force will travel in a straight line, while others are deflected.

solenoid — A long coil.

A solenoid is essentially a long, cylindrical coil of wire. When an electric current passes through the wire, it generates a magnetic field, which is particularly uniform and strong inside the coil, making solenoids useful for creating controlled magnetic fields.

electromagnets — Magnets whose magnetic field can be switched off by switching off the current in the coil, typically made by winding a coil on a ferrous core.

Electromagnets are temporary magnets created by passing current through a coil, often wound around a soft iron core. Unlike permanent magnets, their magnetic field can be controlled by varying or switching off the current, making them versatile for applications requiring adjustable magnetic forces.

Hall voltage — A potential difference that develops across a conductor when charge carriers are forced to one side by a magnetic field.

When charge carriers (like electrons) move through a conductor in a magnetic field, the magnetic force pushes them to one side. This accumulation of charge creates an electric field and a measurable potential difference across the conductor, known as the Hall voltage.

Hall probe — An apparatus consisting of a thin slice of semiconductor material used to measure magnetic flux density, based on the Hall effect.

A Hall probe is a practical device that utilizes the Hall effect to measure magnetic flux density. It typically uses a semiconductor material because semiconductors have a lower charge carrier density, leading to a larger and more easily measurable Hall voltage for a given magnetic field.

magnetic flux — The product of the magnetic flux density and the area normal to the lines of flux.

Magnetic flux (\Phi) is a measure of the total number of magnetic field lines passing through a given area. It quantifies the 'amount' of magnetic field penetrating a surface, and its value depends on both the strength of the magnetic field and the orientation of the area relative to the field.

weber — The unit of magnetic flux, equal to one tesla metre-squared (T m2).

The weber (Wb) is the SI unit for magnetic flux. One weber represents the magnetic flux through an area of one square meter when the magnetic flux density is one tesla and the field lines are perpendicular to the area.

magnetic flux linkage — The product of the magnetic flux through a coil and the number of turns on the coil (N\Phi).

Magnetic flux linkage considers the total magnetic flux passing through all turns of a coil. If a coil has N turns, and each turn experiences a magnetic flux \Phi, then the total flux linkage is N\Phi. This quantity is crucial for understanding electromagnetic induction in coils.

electromagnetic induction — The effect where an e.m.f. is induced by a changing magnetic field.

Electromagnetic induction is the phenomenon where a changing magnetic field through a conductor or coil generates an electromotive force (e.m.f.). This induced e.m.f. can drive an induced current if the circuit is complete, forming the basis of generators and transformers.

eddy currents — Currents induced in a metal disc when it spins in a magnetic field, varying in magnitude and direction.

Eddy currents are circulating currents induced within a bulk conductor, such as a metal disc, when it moves through a magnetic field or when the magnetic field through it changes. These currents form closed loops within the conductor and are a consequence of electromagnetic induction.

eddy current damping — The dissipation of the energy of rotation of a disc due to heating caused by induced eddy currents.

Eddy current damping is the process where the kinetic energy of a rotating metal disc in a magnetic field is converted into heat due to the induced eddy currents. According to Lenz's law, these eddy currents create magnetic fields that oppose the motion, thus slowing down the disc.

direct current — A steady current in one direction.

Unlike alternating current, a direct current maintains a constant direction of flow. This is the type of current typically supplied by batteries.

alternating current — A current or voltage that reverses its direction regularly and is usually sinusoidal.

Alternating current (AC) is characterized by its periodic change in direction and magnitude, typically following a sine wave pattern. This is the standard form of electricity supplied to homes and businesses.

period — The time T taken for one complete cycle of the alternating current.

The period is a fundamental characteristic of an alternating current or voltage, representing the duration for one full oscillation before the pattern repeats. It is measured in seconds.

frequency — The number of complete cycles per unit time.

Frequency quantifies how often an alternating current or voltage completes a full cycle within a given time, usually one second. It is the reciprocal of the period and is measured in Hertz (Hz).

peak value — I0 or V0, the amplitude of the oscillating current or voltage.

The peak value represents the maximum instantaneous value reached by the current or voltage during a cycle. It is the amplitude of the sinusoidal waveform.

peak-to-peak value — 2I0 or 2V0, or twice the amplitude.

The peak-to-peak value is the total range of the alternating current or voltage, from its maximum positive value to its maximum negative value. It is simply twice the peak value.

root-mean-square — That value of the direct current or direct voltage that would produce thermal energy at the same rate in a resistor.

The root-mean-square (r.m.s.) value provides an effective measure of an alternating current or voltage. It is equivalent to the steady direct current or voltage that would dissipate the same average power in a resistive load.

rectification — The process of converting an alternating current into a direct current.

Rectification is a crucial process that transforms the bidirectional flow of alternating current into a unidirectional flow, which is characteristic of direct current. This is typically achieved using diodes.

half-wave rectification — A process where the output voltage across a resistor consists only of the positive half-cycles of the input voltage, rejecting the negative part.

Half-wave rectification uses a single diode to allow only one half-cycle (e.g., the positive half) of the AC input to pass through to the load, effectively blocking the other half-cycle. This results in a pulsating DC output.

full-wave rectification — A process that makes use of the negative half-cycles of the input and reverses their polarity.

Full-wave rectification converts both the positive and negative half-cycles of the AC input into a pulsating DC output of a single polarity. This is typically achieved using a bridge rectifier circuit, which inverts the negative half-cycles.

smoothing — The process of reducing fluctuations in the unidirectional output voltage by inserting a capacitor across the output terminals of a rectifier circuit.

Smoothing aims to reduce the 'ripple' in the rectified DC output, making it more constant. This is achieved by connecting a capacitor in parallel with the load resistor, which charges during voltage peaks and discharges slowly when the voltage drops, filling in the gaps.

ripple — The magnitude of the variation of the voltage or current that is superimposed on the direct voltage or current.

Ripple refers to the small, unwanted AC component that remains in the DC output after rectification and partial smoothing. A smaller ripple indicates a more stable and 'smoother' DC output.

Planck constant — A constant, h, with a value of 6.63 × 10–34 J s, used in quantum theory to relate the energy of a photon to its frequency.

The Planck constant is a fundamental constant in quantum mechanics. It quantifies the relationship between the energy of a photon and its frequency, forming the basis for understanding the discrete nature of energy at the atomic and subatomic levels.

photons — Energy packets that light radiation consists of, as proposed by Albert Einstein.