Equations

• Absolute uncertainty


  Uncertainty of measuring instrument or half the range of readings, use the largest value, same units as the quantity
• Fractional uncertainty


  Absolute uncertainty / measured or mean value
• Percentage uncertainty


  (Absolute uncertainty / measured or mean value) x 100%
• Percentage uncertainty in y

  (Δy/y) x 100%
• Horizontal force component


  FH = Fcosθ
• Vertical force component


  FV = Fsinθ
• Pythagoras' theorem


  F = √(FH^2 + FV^2)
• Average velocity


  v = (s2 - s1) / (t2 - t1) = (Δs) / (Δt) = (u + v) / 2
• Average acceleration


  a = (v - u) / (t2 - t1) = (Δv) / (Δt)
• Suvat equation 1


  a = (v - u) / t
• Suvat equation 2


  s = (u + v)t / 2
• Suvat equation 3


  s = ut + (1/2)at^2
• Suvat equation 4


  v^2 = u^2 + 2as
• Suvat equation 5


  s = (v^2 - u^2) / (2a)
• Newton's second law: Force


  F = Δp/Δt = ma
• Linear momentum


  p = mv
• Conservation of linear momentum between two objects


  m1u1 + m2u2 = m1v1 + m2v2
• Perfectly elastic collision


  Relative speed of approach = Relative speed of separation
• Moment of a force

  T = Fx
• Torque due to a couple


  τc = Fd
• Principle of moments: Sum of clockwise moments = Sum of anticlockwise moments
• Conditions of equilibrium: Σ Fnet = 0, Σ Tnet = 0
• Density


  ρ = m/V
• Pressure


  p = F/A
• Pressure in fluids


  p = ρgh
• Upthrust (buoyancy force)


  Fb = ρgV
• Work done


  W = Fs cosθ
• Principle of conservation of mechanical energy
• Efficiency of a machine

  η = (useful work out) / (total work in) = (useful power out) / (total power in)
• Mechanical power


  P = W/t = Fv
• Change in gravitational potential energy


  ΔEp = mgh
• Work done = force x distance moved = weight x change in height
• Translational kinetic energy


  Ek = (1/2)mv^2 = p^2/(2m)
• Effective spring constant in series

  1/ktot = 1/k1 + 1/k2 + ... + 1/kN
• Effective spring constant in parallel

  ktot = k1 + k2 + ... + kN
• Applied spring load


  F = kx
• Strain


  ε = Δx/L0
• Stress


  σ = F/A
• Young's modulus


  E = σ/ε = (FL0)/(AΔx)
• Springs in series


  ktot = 1 / (1/k1 + 1/k2 + ... + 1/kN)