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Rotational Motion

Physics: AQA A Level, topic 11.1.3

Rotational Motion

Rotational motion is described in a very similar way to linear motion.

Angular displacement

Angular displacement

  • Angular displacement is the change in angle, θ, usually measured in radians.
Angular velocity

Angular velocity

  • Angular velocity is the rate of change of angle with time, usually measured in radians per second.
  • ω=ΔθΔt\omega = \frac{\Delta \theta}{\Delta t}
Angular acceleration

Angular acceleration

  • Angular acceleration is the rate of change of angular velocity, measured in radians per second per second.
  • α=ΔωΔt\alpha = \frac{\Delta \omega}{\Delta t}

Angular acceleration

There is a set equations to find quantities under constant angular acceleration.

Angular velocity

Angular velocity

  • The equation for angular velocity is:
  • ω=ΔθΔt\omega = \frac{\Delta\theta}{{\Delta}t}
  • Angular velocity can also be expressed in terms of linear velocity:
  • ω=vr\omega = \frac{v}{r}
Angular acceleration

Angular acceleration

  • Angular acceleration is the rate of change of angular velocity. The equation for angular acceleration is:
  • Angular acceleration = change in angular velocity ÷ change in time
  • α=ΔωΔt\alpha = \frac{\Delta\omega}{{\Delta}t}
  • Where α\alpha is the angular acceleration.
Angular SUVAT equations

Angular SUVAT equations

  • There are angular versions of SUVAT equations which have the form:
  • ω2=ω1+αt{\omega_2}={\omega_1}+{\alpha}t
  • θ=ω1t+αt22\theta = {\omega_1}t+\frac{{\alpha}t^2}{2}
  • θ=(ω1+ω2)2t\theta = \frac{({\omega_1}+{\omega_2})}{2}t
  • ω22=ω12+2αθ{\omega_2}^2= {\omega_1}^2 + 2\alpha\theta
  • Where θ\theta is the angular displacement.

Test yourself on Rotational Motion

  • What is the correct equation for angular velocity?

  • Which of these statements are true about rotational motion?

  • Which equations for constant angular acceleration are correct?

  • Which equation does not include the angular displacement?

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