📄 Cheat Sheets — Physics

Key facts, formulas and common mistakes for 1 of 1 chapters

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7 key facts·16 formulas·6 common mistakes·27 definitions·6 exam tips

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Definitions

physical quantity: A feature of something which can be measured, consisting of a numerical value and a unit.
scientific method: A process of observing, measuring, collecting data, analysing patterns, developing theories, testing them, and modifying theories based on results.
theory: A pattern discovered from analysed data that can be used to explain other events.
Système Internationale (SI): A single, internationally agreed-upon system of units based on the metric system of measurement.
base quantities: The fundamental physical quantities upon which the SI system is founded.
base units: The unique units defined at world conventions for each of the seven fundamental or base quantities.
derived units: Units for quantities that are expressed as products or quotients of the SI base units.
homogeneous: An equation is homogeneous if each term involved in the equation has the same base units.
physical quantity: A feature of something which can be measured, consisting of a numerical value and a unit.
order of magnitude: The power of ten to which a number is raised, used to estimate the size of a quantity.
uncertainty: The total range of values within which a measurement is likely to lie.
absolute uncertainty: The range of values (e.g., ±0.5 cm) that directly indicates the uncertainty in a measurement.
percentage uncertainty: The absolute uncertainty expressed as a percentage of the measured value.
accuracy: The closeness of a measured value to the 'true' or 'known' value.
precision: How close a set of measured values are to each other.
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.
zero error: A type of systematic error where the scale reading is not zero before measurements are taken.
reaction time: The delay between an experimenter observing an event and starting a timing device.
random error: An error that results in readings being scattered around the accepted value.
parallax error: An error in reading a scale from different angles, causing the apparent position of the indicator to shift.
scalar quantity: A quantity which can be described fully by giving its magnitude and unit.
vector quantity: A quantity which has magnitude, unit, and direction.
resultant: The combined effect of two or more vectors.
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.
resolution of vectors: The process of splitting a single vector into two or more component vectors.
components: The two or more vectors into which a single vector may be split.
micrometer screw gauge: A precision measuring instrument used to measure small lengths, typically to the nearest one-hundredth of a millimetre.

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Formulas

Ch 01

Uncertainty in sum/difference

Δ x = Δ y + Δ z

Calculates the absolute uncertainty in a final result when quantities are added or subtracted by summing their individual absolute uncertainties.

Ch 01

Fractional uncertainty in product/quotient

\frac{Δ x}{x} = \frac{Δ y}{y} + \frac{Δ z}{z}

Calculates the fractional uncertainty in a final result when quantities are multiplied or divided by summing their individual fractional uncertainties.

Ch 01

Percentage uncertainty in product/quotient

(\frac{Δ x}{x}) \times 100 = (\frac{Δ y}{y}) \times 100 + (\frac{Δ z}{z}) \times 100

Calculates the percentage uncertainty in a final result when quantities are multiplied or divided by summing their individual percentage uncertainties.

Ch 01

Fractional uncertainty with powers

\frac{Δ x}{x} = a (\frac{Δ y}{y}) + b (\frac{Δ z}{z})

Calculates the fractional uncertainty in a final result when quantities are raised to powers by multiplying their fractional uncertainties by their respective powers and summing them.

Ch 01

Percentage uncertainty with powers

(\frac{Δ x}{x}) \times 100 = a (\frac{Δ y}{y}) \times 100 + b (\frac{Δ z}{z}) \times 100

Calculates the percentage uncertainty in a final result when quantities are raised to powers by multiplying their percentage uncertainties by their respective powers and summing them.

Ch 01

Horizontal component of vector

F_{H} = F cos θ

Calculates the horizontal component of a vector given its magnitude and angle relative to the horizontal.

Ch 01

Vertical component of vector

F_{V} = F sin θ

Calculates the vertical component of a vector given its magnitude and angle relative to the horizontal.

Ch 01

Pythagoras' theorem

h^{2} = o^{2} + a^{2}

Relates the lengths of the sides of a right-angled triangle, allowing calculation of an unknown side if two are known.

Ch 01

Sine rule

\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}

Relates the sides of a triangle to the sines of their opposite angles, useful for solving non-right-angled triangles.

Ch 01

Cosine rule

a^{2} = b^{2} + c^{2} - 2 b c cos A

Relates the sides of a triangle to one of its angles, useful for solving non-right-angled triangles when two sides and the included angle, or all three sides, are known.

Ch 01

Speed

speed = \frac{distance}{time}

Defines speed as the rate of change of distance with respect to time.

Ch 01

Kinetic Energy

K E = \frac{1}{2} m v^{2}

Calculates the kinetic energy of an object based on its mass and speed.

Ch 01

Gravitational Potential Energy

GP E = m g h

Calculates the gravitational potential energy of an object based on its mass, acceleration of free fall, and height.

Ch 01

Work Done

W = F d

Calculates the work done by a force when an object moves a certain distance in the direction of the force.

Ch 01

Volume of a cylinder

V = \frac{π d ^{2} l}{4}

Calculates the volume of a cylinder given its diameter and length.

Ch 01

Acceleration of free fall (pendulum)

g = \frac{4 π ^{2} l}{T ^{2}}

Calculates the acceleration of free fall using the length and period of a simple pendulum.

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Key Facts

All physical quantities consist of a numerical magnitude and a unit.Ch 01
The SI base quantities and their units are: mass (kg), length (m), time (s), current (A), temperature (K).Ch 01
Derived units are expressed as products or quotients of SI base units.Ch 01
An equation is homogeneous if each term has the same base units, which can be used to check its dimensional consistency.Ch 01
Accuracy is the closeness of a measured value to the true value, while precision is the consistency of repeated measurements.Ch 01
Systematic errors cause all readings to be consistently above or below the true value; random errors cause readings to scatter around the true value.Ch 01
Scalars have magnitude only; vectors have both magnitude and direction and must be added/resolved using vector rules.Ch 01

⚠️

Common Mistakes

✗Don't confuse a number alone with a physical quantity; units are essential for meaning.Ch 01
✗Don't confuse accuracy (closeness to true value) with precision (consistency of readings).Ch 01
✗Don't assume homogeneity guarantees an equation's correctness; it only confirms dimensional consistency.Ch 01
✗Don't add vectors algebraically like scalars; always consider their directions.Ch 01
✗Don't think systematic errors can be reduced by averaging; averaging only reduces random errors.Ch 01
✗Remember to use appropriate prefixes (e.g., milli, kilo) for decimal submultiples or multiples of units.Ch 01

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Exam Tips

→Always include units with all numerical answers; marks are often awarded for correct units.Ch 01
→When checking homogeneity, clearly show the base units for each term in the equation.Ch 01
→For uncertainty calculations, remember to add absolute uncertainties for sums/differences and fractional/percentage uncertainties for products/quotients/powers.Ch 01
→When asked to estimate, provide a reasonable order of magnitude for the quantity.Ch 01
→Clearly distinguish between systematic and random errors in explanations, providing examples for each.Ch 01
→Practice resolving vectors into perpendicular components (FH = F cos θ, FV = F sin θ) and recombining them using Pythagoras' theorem and trigonometry.Ch 01

📄 Cheat Sheets — Physics

Physics — Cheat Sheets

Definitions

Formulas

Key Facts

Common Mistakes

Exam Tips

📄 Cheat Sheets — Physics

Physics — Cheat Sheets

Definitions

Formulas

Key Facts

Common Mistakes

Exam Tips