Formula Sheet

Motion, forces, and energy

Average speed

v = d/t

• v = speed (m/s)
• d = distance (m)
• t = total time (s)

Acceleration

a = change in speed / t or a = (v - u) / t

• a = acceleration (m/s²)
• v = final velocity (m/s)
• u - initial velocity (m/s)
• t = time taken (s)

Weight

W = mg

• W = weight (N)
• m = mass (kg)
• g = acceleration due to gravity (9.8m/s², or 10m/s²)

Density

p = m/V

• p = density (kg/m³, or g/cm³)
• m = mass (kg or g)
• V = volume (m³ or cm³)

Force

*F = ma

• F = resultant force (N)
• m = mass (kg)
• a = acceleration (m/s²)

Moment

Moment = Fd

• Moment = turning effect (Nm)
• F = force (N)
• d = perpendicular distance from pivot (m)

Momentum

p = mv

• p = momentum (kg m/s)
• m = mass (kg)
• v = velocity (m/s)

Impulse

Impulse = change in momentum or F x change in time or m(v - u)

• F = resultant force (N)
• v = final velocity (m/s)
• u = initial velocity (m/s)

Kinetic energy

Ek = 1/2mv²

• Ek = kinetic energy
• m = mass (kg)
• v = speed (m/s)

Gravitational potential energy

Ep = mgh

• Ep = gravitational potential energy
• m = mass (kg)
• g = gravitational field strength (N/kg)
• h = change in height (m)

Work done

W = change in energy or Fd

• W = work done (J)
• F = force (N)
• d = distance moved in direction of force (m)

Power

P = W/t or change in energy / t

• P = power (J/s or W)
• W = work done (J)
• t = time taken (s)

Efficiency

Efficiency = useful / total

• Expressed as % or decimal.

Pressure

p = F/A

• p = pressure (Pa or N/m²)
• F = force (N)
• A = surface area (m²)

Thermal physics

Boyle’s law (gas pressure)

P1V1 = P2V2

• P1, P2 = initial and final pressures (Pa or atm)
• V1, V2 = initial and final volumes (m³ or cm³)
• (Constant mass and temp.)

Specific heat capacity

c = change in energy / m x change in temperature

• c = specific heat capacity (J/(kg C°))
• m = mass (kg)

Waves

Wave equation

v = fλ

• v = wave speed (m/s)
• f = frequency (Hz)
• λ = wavelength (m)

Frequency and period

f = 1/T

• f = frequency (Hz)
• T = time period for one wave (s)

Refractive index (angles)

n = sin i / sin r

• n = refractive index
• i = angle of incidence
• r = angle of refraction

Refractive index (speed)

n = c/v

• n = refractive index
• c = speed of light in air/vaccum (3.0 x 10⁸ m/s)
• v = speed of light in medium (m/s)