Cheat Sheet

Physics · Physical quantities and units

Key Facts

Understand that all physical quantities consist of a numerical magnitude and a unit.

Make reasonable estimates of physical quantities included within the syllabus.

Recall the SI base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K).

Express derived units as products or quotients of SI base units and use them appropriately.

Use SI base units to check the homogeneity of physical equations.

Recall and use prefixes and their symbols for decimal submultiples or multiples of units.

Understand and explain the effects of systematic and random errors in measurements.

Understand the distinction between precision and accuracy.

Formulas

Uncertainty in sum/difference

Δ x = Δ y + Δ z

Δ x

— absolute uncertainty in x

Δ y

— absolute uncertainty in y

Δ z

— absolute uncertainty in z

For quantities added or subtracted (x = y + z or x = y - z).

Fractional uncertainty in product/quotient

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

Δ x / x

— fractional uncertainty in x

Δ y / y

— fractional uncertainty in y

Δ z / z

— fractional uncertainty in z

For quantities multiplied or divided (x = Ayz or x = Ay/z, where A is a constant).

Percentage uncertainty in product/quotient

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

(Δ x / x) \times 100

— percentage uncertainty in x

(Δ y / y) \times 100

— percentage uncertainty in y

(Δ z / z) \times 100

— percentage uncertainty in z

For quantities multiplied or divided (x = Ayz or x = Ay/z, where A is a constant).

Fractional uncertainty with powers

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

a

— power of y

b

— power of z

Δ x / x

— fractional uncertainty in x

Δ y / y

— fractional uncertainty in y

Δ z / z

— fractional uncertainty in z

For quantities raised to a power (x = Ay^a z^b, where A is a constant).

Percentage uncertainty with powers

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

a

— power of y

b

— power of z

(Δ x / x) \times 100

— percentage uncertainty in x

(Δ y / y) \times 100

— percentage uncertainty in y

(Δ z / z) \times 100

— percentage uncertainty in z

For quantities raised to a power (x = Ay^a z^b, where A is a constant).

Horizontal component of vector

F_{H} = F cos θ

F

— magnitude of force (N)

F H

— horizontal component of force (N)

θ

— angle to the horizontal (degrees or radians)

Applies to any vector quantity, not just force.

Vertical component of vector

F_{V} = F sin θ

F

— magnitude of force (N)

F V

— vertical component of force (N)

θ

— angle to the horizontal (degrees or radians)

Applies to any vector quantity, not just force.

Pythagoras' theorem

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

a

— adjacent side

h

— hypotenuse

o

— opposite side

For right-angled triangles.

Sine rule

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

A, B, C

— opposite angles

a, b, c

— side lengths

For any triangle.

Cosine rule

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

A

— angle opposite side a

a, b, c

— side lengths

For any triangle.

Speed

speed = \frac{distance}{time}

t im e

— time (s)

s p ee d

— speed (m s^-1)

d i s t an ce

— distance (m)

Scalar quantity.

Kinetic Energy

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

m

— mass (kg)

v

— speed (m s^-1)

K E

— kinetic energy (J)

Scalar quantity.

Gravitational Potential Energy

GP E = m g h

g

— acceleration of free fall (m s^-2)

h

— height (m)

m

— mass (kg)

GP E

— gravitational potential energy (J)

Scalar quantity.

Work Done

W = F d

F

— force (N)

W

— work done (J)

d

— distance moved in direction of force (m)

Scalar quantity.

Volume of a cylinder

V = \frac{π d ^{2} l}{4}

V

— volume (m^3)

d

— diameter (m)

l

— length (m)

Also V = πr^2l where r is radius.

Acceleration of free fall (pendulum)

g = \frac{4 π ^{2} l}{T ^{2}}

T

— period of oscillation (s)

g

— acceleration of free fall (m s^-2)

l

— length of pendulum (m)

Derived from the formula for the period of a simple pendulum.

⚠ Common Misconceptions

Confusing a number alone with a physical quantity; units are essential for meaning.

Believing the scientific method is linear rather than cyclical and iterative.

Confusing base units with derived units, or thinking derived units are arbitrary.

Assuming homogeneity guarantees an equation's correctness; it only confirms dimensional consistency.

Confusing uncertainty with a mistake; uncertainty is inherent in all measurements.

Confusing accuracy (closeness to true value) with precision (consistency of readings).

Thinking systematic errors can be reduced by averaging; averaging only reduces random errors.

Adding vectors algebraically like scalars, rather than considering their directions.

Forgetting that components of a resolved vector must be perpendicular for simple trigonometric relations.

Cheat Sheet

Physics · Physical quantities and units

Key Facts

Understand that all physical quantities consist of a numerical magnitude and a unit.

Make reasonable estimates of physical quantities included within the syllabus.

Recall the SI base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K).

Express derived units as products or quotients of SI base units and use them appropriately.

Use SI base units to check the homogeneity of physical equations.

Recall and use prefixes and their symbols for decimal submultiples or multiples of units.

Understand and explain the effects of systematic and random errors in measurements.

Understand the distinction between precision and accuracy.

Formulas

Uncertainty in sum/difference

Δ x = Δ y + Δ z

Δ x

— absolute uncertainty in x

Δ y

— absolute uncertainty in y

Δ z

— absolute uncertainty in z

For quantities added or subtracted (x = y + z or x = y - z).

Fractional uncertainty in product/quotient

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

Δ x / x

— fractional uncertainty in x

Δ y / y

— fractional uncertainty in y

Δ z / z

— fractional uncertainty in z

For quantities multiplied or divided (x = Ayz or x = Ay/z, where A is a constant).

Percentage uncertainty in product/quotient

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

(Δ x / x) \times 100

— percentage uncertainty in x

(Δ y / y) \times 100

— percentage uncertainty in y

(Δ z / z) \times 100

— percentage uncertainty in z

For quantities multiplied or divided (x = Ayz or x = Ay/z, where A is a constant).

Fractional uncertainty with powers

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

a

— power of y

b

— power of z

Δ x / x

— fractional uncertainty in x

Δ y / y

— fractional uncertainty in y

Δ z / z

— fractional uncertainty in z

For quantities raised to a power (x = Ay^a z^b, where A is a constant).

Percentage uncertainty with powers

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

a

— power of y

b

— power of z

(Δ x / x) \times 100

— percentage uncertainty in x

(Δ y / y) \times 100

— percentage uncertainty in y

(Δ z / z) \times 100

— percentage uncertainty in z

For quantities raised to a power (x = Ay^a z^b, where A is a constant).

Horizontal component of vector

F_{H} = F cos θ

F

— magnitude of force (N)

F H

— horizontal component of force (N)

θ

— angle to the horizontal (degrees or radians)

Applies to any vector quantity, not just force.

Vertical component of vector

F_{V} = F sin θ

F

— magnitude of force (N)

F V

— vertical component of force (N)

θ

— angle to the horizontal (degrees or radians)

Applies to any vector quantity, not just force.

Pythagoras' theorem

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

a

— adjacent side

h

— hypotenuse

o

— opposite side

For right-angled triangles.

Sine rule

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

A, B, C

— opposite angles

a, b, c

— side lengths

For any triangle.

Cosine rule

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

A

— angle opposite side a

a, b, c

— side lengths

For any triangle.

Speed

speed = \frac{distance}{time}

t im e

— time (s)

s p ee d

— speed (m s^-1)

d i s t an ce

— distance (m)

Scalar quantity.

Kinetic Energy

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

m

— mass (kg)

v

— speed (m s^-1)

K E

— kinetic energy (J)

Scalar quantity.

Gravitational Potential Energy

GP E = m g h

g

— acceleration of free fall (m s^-2)

h

— height (m)

m

— mass (kg)

GP E

— gravitational potential energy (J)

Scalar quantity.

Work Done

W = F d

F

— force (N)

W

— work done (J)

d

— distance moved in direction of force (m)

Scalar quantity.

Volume of a cylinder

V = \frac{π d ^{2} l}{4}

V

— volume (m^3)

d

— diameter (m)

l

— length (m)

Also V = πr^2l where r is radius.

Acceleration of free fall (pendulum)

g = \frac{4 π ^{2} l}{T ^{2}}

T

— period of oscillation (s)

g

— acceleration of free fall (m s^-2)

l