exam

• Work

  W = m g h

  (Inclined plane) W = F d sin$\theta$
• Kinetic energy

  KE = $\frac{1}{2}$mv$^2$
• Potential energy


  PE = mgh
• Power

  P = w/t = Fv

  P = Fvcos0
• Momentum

  p = mv
• Centripetal acceleration

  a = v$^2$/r = r$\omega^2$
• Centripetal force

  F = mv$^2$/r = m$\omega^2$r
• Circular motion

  v = r$\omega$

  $\omega$ = $\theta$/t
• Inertia

  I = mr$^2$
• Torque

  $\tau$ = rFsin$\theta$

  $\tau$ = I$\alpha$
• Centre of gravity

  Xcg = $\frac{\sum_{ }^{ }XiAi}{\sum_{ }^{ }Ai}$
• Pressure

  P = $\rho$gh
• Gauge pressure

  Pgauge = Pabs - Patm
• Buoyant force

  Fb = $\rho$fluid gV
• Force against horizontal wall

  F = $\rho$ghA
• Force against vertical wall

  F = $\rho$gbh $\cdot$ h/2
• Vector magnitude

  $\left|V\right|\ =$$\ \sqrt{Vx^2\ +\ Vy^2}$
• Unit vector

  = V / $\left|V\right|$
• Angle of vector

  $\theta\ =$$\ \tan^{-1}\left(\frac{Y}{X}\right)$
• Cosine (inclined)

  R$^2$ = $a^2+$$b^2\ -\ 2ab\cos\left(180-\theta\right)$
• Sine (direction)

  $\alpha\ =$$\ \sin^{-1}\left(\frac{b\sin\left(180-\theta\right)}{R}\right)$
• Newton's 2nd law

  F = ma
• Friction

  f = $\mu R$
• Weight

  W = mg
• Friction (inclined plane)

  R = mgcos$\theta$

  f = mgcos$\theta\mu$
• Kinematics

  v = u + at

  s = ut + $\frac{1}{2}$at$^2$

  v$^2$ = u$^2$ + 2as
• Projectiles

  Horizontal

  V = Xcos$\theta$

  Vertical

  V = Xsin$\theta$
• Range (projectiles)

  R = $\frac{v^2\sin\left(2\theta\right)}{g}$
• Projectiles

  X = vtcos$\theta$

  Y = vtsin$\theta$ - $\frac{1}{2}$gt$^2$
• Max height of projectile

  h = u$^2$/2g

  v = u - gt
• Tension

  Body moving upwards

  T = W + F = mg + ma

  Body moving downwards

  T = W - F = mg - ma
• Distance an object falls under gravity

  s = $\frac{1}{2}$gt$^2$
• Coefficient of restitution

  e = $\frac{v2\ -\ v1}{u1\ -\ u2}$
• Conservation of momentum

  m1u1 + m2u2 = m1v1 + m2v2
• Magnitude of impulse (Ns)


  J = F$\Delta$t = $\Delta$p = m(v-u)

  (p = momentum)
• Centripetal force again

  tan$\theta$ = $\frac{v^2}{gR}$
• Centripetal force in horizontal (radial) direction

  $\frac{v^2}{R}$ = g(tan$\theta$ + $\mu\sec\theta$)
• Lami's theorem

  $\frac{P}{\sin\alpha}$=$\frac{Q}{\sin\beta}$=$\frac{R}{\sin\chi}$
• Projectiles time of flight

  T = $\frac{2V\sin\theta}{g}$
• Projectiles max range

  R = v$^2$/g