Angular Speed (AQA A Level Physics): Revision Note

Angular speed

• Any object travelling in a uniform circular motion at the same speed travels with a constantly changing velocity

• This is because it is constantly changing direction, and is therefore accelerating

• The angular speed (⍵) of a body in circular motion is defined as:

  The rate of change in angular displacement with respect to time

• Angular speed is a scalar quantity and is measured in rad s^-1

• It can be calculated using:

$\omega =\frac{∆\theta }{∆t}$

• Where:

  • $\omega$ = angular speed (rad s^-1)

  • $∆\theta$ = change in angular displacement (radians)

  • $∆t$ = time interval (s)

• Taking the angular displacement of a complete cycle as 2π, the angular speed $\omega$ can be calculated using the equation:

$\omega =\frac{v}{r}=2\pi f=\frac{2\pi }{T}$

• Where:

  • $v$ = linear speed (m s^-1)

  • $r$ = radius of orbit (m)

  • $f$ = frequency (Hz)

  • $T$ = time period (s)

• Angular velocity is the same as angular speed, but it is a vector quantity

• This equation shows that:

  • The greater the rotation angle θ in a given amount of time, the greater the angular velocity ⍵

  • An object rotating further from the centre of the circle (larger r) moves with a smaller angular velocity (smaller ⍵)