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Physics Equations - GCSE Physics

The relationships listed below will not be provided for students in the examination, either in the form given or in rearranged form. Students must recall and be able to use these equations.

1. Motion & Forces

(1) Average Speed
average speed=distance movedtime taken\text{average speed} = \frac{\text{distance moved}}{\text{time taken}}
(2) Force, Mass and Acceleration
force=mass×acceleration(F=m×a)\text{force} = \text{mass} \times \text{acceleration} \quad (F = m \times a)
(3) Acceleration
acceleration=change in velocitytime taken(a=v−ut)\text{acceleration} = \frac{\text{change in velocity}}{\text{time taken}} \quad \left(a = \frac{v - u}{t}\right)
(4) Momentum
momentum=mass×velocity(p=m×v)\text{momentum} = \text{mass} \times \text{velocity} \quad (p = m \times v)
(8) Weight
weight=mass×gravitational field strength(W=m×g)\text{weight} = \text{mass} \times \text{gravitational field strength} \quad (W = m \times g)
(10) Moment of a Force
moment=force×perpendicular distance from the pivot\text{moment} = \text{force} \times \text{perpendicular distance from the pivot}

2. Energy & Work

(6) Work Done
work done=force×distance moved(W=F×d)\text{work done} = \text{force} \times \text{distance moved} \quad (W = F \times d)
(7) Energy Transferred (Work Done)
energy transferred=work done\text{energy transferred} = \text{work done}
(7) Kinetic Energy
kinetic energy=12×mass×speed2(KE=12mv2)\text{kinetic energy} = \frac{1}{2} \times \text{mass} \times \text{speed}^2 \quad \left(KE = \frac{1}{2} m v^2\right)
(7) Gravitational Potential Energy
gravitational potential energy=mass×g×height(GPE=m×g×h)\text{gravitational potential energy} = \text{mass} \times g \times \text{height} \quad (GPE = m \times g \times h)
(16) Efficiency
efficiency=useful energy outputtotal energy output×100%\text{efficiency} = \frac{\text{useful energy output}}{\text{total energy output}} \times 100\%

3. Electricity & Electromagnetism

(11) Charge
charge=current×time(Q=I×t)\text{charge} = \text{current} \times \text{time} \quad (Q = I \times t)
(11) Voltage
voltage=current×resistance(V=I×R)\text{voltage} = \text{current} \times \text{resistance} \quad (V = I \times R)
(11) Electrical Power
electrical power=voltage×current(P=V×I)\text{electrical power} = \text{voltage} \times \text{current} \quad (P = V \times I)
(11) Energy Transferred
energy transferred=charge×voltage(E=Q×V)\text{energy transferred} = \text{charge} \times \text{voltage} \quad (E = Q \times V)
(13) Transformer Turns Ratio
input (primary) voltageoutput (secondary) voltage=primary turnssecondary turns(VpVs=NpNs)\frac{\text{input (primary) voltage}}{\text{output (secondary) voltage}} = \frac{\text{primary turns}}{\text{secondary turns}} \quad \left(\frac{V_p}{V_s} = \frac{N_p}{N_s}\right)
(18) Input Power and Output Power (100% Efficiency)
VpIp=VsIsV_p I_p = V_s I_s

4. Waves & Optics

(12) Wave Speed
wave speed=frequency×wavelength(v=f×λ)\text{wave speed} = \text{frequency} \times \text{wavelength} \quad (v = f \times \lambda)
(14) Refractive Index (Snell's Law)
n=sin⁡isin⁡rn = \frac{\sin i}{\sin r}
(15) Critical Angle
sin⁡c=1n\sin c = \frac{1}{n}

5. States of Matter & Pressure

(5) Density
density=massvolume(ρ=mV)\text{density} = \frac{\text{mass}}{\text{volume}} \quad \left(\rho = \frac{m}{V}\right)
(9) Pressure
pressure=forcearea(p=FA)\text{pressure} = \frac{\text{force}}{\text{area}} \quad \left(p = \frac{F}{A}\right)
(17) Pressure Difference
pressure difference=height×density×gravitational field strength(p=h×ρ×g)\text{pressure difference} = \text{height} \times \text{density} \times \text{gravitational field strength} \quad (p = h \times \rho \times g)