Physics formulae

g (gravitational field strength)

g = 9.81 N kg^-1

speed (with time)

speed (m s^-1) = distance (m) / time (s)

$$v=\dfrac{d}{t}$$

velocity

velocity (m s^-1) = displacement (m) / time (s)

$$\bm{v}=\dfrac{\Delta\bm{s}}{\Delta t}$$

acceleration

acceleration (m s^-2) = change in velocity (m s^-1) / time taken to change the velocity (s)

$$\bm{a}=\dfrac{\Delta\bm{v}}{\Delta t}$$

moment of a force

moment (Nm) = force (N) × perpendicular distance from the pivot to the line of action of the force (m)

moment = $\bm{F}x$

resultant force needed to give an acceleration

resultant force (N) = mass (kg) × acceleration (m s^-2)

$$\sum\bm{F}=m\bm{a}$$

final velocity

final velocity (m s^-1) = initial velocity (m s^-1) + acceleration (m s^-2) × time (s)

$$\bm{v}=\bm{u}+\bm{a}t$$

displacement (with final velocity)

displacement (m) = time (s) × (initial velocity (m s^-1) + final velocity (m s^-1)) / 2

$$\bm{s}=t\times\dfrac{\bm{u}+\bm{v}}{2}$$

displacement (with acceleration)

displacement (m) = initial velocity (m s^-1) × time (s) + ½ × acceleration (m s^-2) × time (s)²

$\bm{s}=\bm{u}t + \frac{1}{2}\bm{a}t^{2}$ 

final velocity² (with displacement)

final velocity (m s^-1)² = initial velocity (m s^-1)² + 2 × acceleration (m s^-2) × displacement (m)

$$\bm{v}^{2}=\bm{u}^{2}+2\bm{as}$$

gravitational potential energy

gpe (J) = mass (kg) × gravitational field strength (N kg^-1) × height (m)

$$E_{grav}=m\bm{g}h$$

$$E_{grav}=m\bm{g}\Delta h$$

kinetic energy

kinetic energy (J) = ½ × mass (kg) × (speed)² (m²s^-2)

$E_{k}=\frac{1}{2}mv^2$ 

speed (after falling a certain distance from rest)

$$v=\sqrt{2\bm{g}\Delta h}$$

how high an object could rise if projected upwards at a certain speed

$$\Delta h = \dfrac{v^2}{2\bm{g}}$$

work done

work done (J) = force (N) × distance moved in direction of force (m)

$$\Delta W = \bm{F}\Delta\bm{s}$$

work done by a force at an angle

$$\Delta W = \bm{F}\Delta \bm{s}\cos\theta$$

power

power (W) = energy transferred (J) / time for the energy transfer (s)

$P=\dfrac{E}{t}$ 

power (W) = work done (J) / time for the work to be done (s)

$P=\dfrac{\Delta W}{t}$ 
power (W) = [force (N) × distance moved (m)] / time for the force to move (s)
$P=\dfrac{\bm{F}\Delta \bm{s}}{t}$ 

efficiency

efficiency = useful work done / total energy input

momentum

momentum (kg m s^-1) = mass (kg) × velocity (m s^-1)

$\bm{p} = m \times \bm{v}$ 

applied force

applied force (N) = change in momentum (kg m s^-1) / time (s)

$\bm{F} = \dfrac{\text{d}\bm{p}}{\text{d}t} = \dfrac{\text{d}(m\bm{v})}{\text{d}t}$ 

$\bm{F} = \dfrac{\Delta\bm{p}}{\Delta t}$ 

density

density (kg m³) = mass (kg) / volume (m³)

$$\rho = \dfrac{m}{V}$$

upthrust

upthrust (N) = weight of fluid displaced (N) = volume of fluid displaced (m³) × density of fluid (kg m^-3) × g (N kg^-1)

$$W = V\rho g$$

acceleration (with resultant force)

acceleration (m s^-2) = resultant force (N) / mass (kg)

$$\bm{a}=\dfrac{\sum\bm{F}}{m}$$

Stokes’ Law

viscous drag (N) = 6π × radius of sphere (m) × coefficient of viscosity of fluid (Pa s) × velocity of sphere (m s^-1)

$\bm{F}=6 \pi r \eta \bm{v}$ 

Terminal velocity of a small sphere moving at low speeds

$\bm{v_\text{term}}=\dfrac{2r^2\bm{g}(\rho_s - \rho_f)}{9\eta}$  

Hooke’s law

force applied (N) = stiffness constant (N m^-1) × extension (m)

$$\Delta F = k\Delta x$$

Work done in deforming a material

area under graph

OR

$$\Delta E_{el} = \frac{1}{2}F\Delta x$$

Tensile or compressive stress

stress (Pa or N m^-2) = force (N) / cross-sectional area (m²)

$$\sigma = \dfrac{F}{A}$$

Tensile or compressive strain

strain (no units) = extension (m) / original length (m)

$$\varepsilon = \dfrac{\Delta x}{x}$$

Young modulus

Young modulus (Pa) = stress (Pa) / strain (no units)

$$E = \dfrac{\sigma}{\varepsilon}$$

Wave equation

wave speed (m s^-1) = frequency (Hz) × wavelength (m)

v = fλ

Speed of a wave on a string

wave speed (m s^-1) = sqrt[ tension (N) / mass per unit length of string (km m^-1) ]

$$v=\sqrt{\dfrac{T}{\mu}}$$

Frequency of string vibrations

frequency (Hz) = [1 / wavelength (m)] × sqrt[ tension (N) / mass per unit length of string (km m^-1) ]

$$v=\dfrac{1}{\lambda}\sqrt{\dfrac{T}{\mu}}$$

Diffraction grating spacing

$$d=\dfrac{1}{\text{number per metre}}$$

OR:

$$d=\dfrac{1\times 10^{-3}}{\text{number per millimetre}}$$

Diffraction grating

$$n\lambda = d\sin{\theta}$$

n = order

λ = wavelength

d = spacing between slits

θ = angle between original direction of waves and direction of bright spot