Centripetal Acceleration (AQA A Level Physics): Revision Note

Centripetal acceleration formula

• Centripetal acceleration is defined as:

  The acceleration of an object towards the centre of a circle when an object is in motion (rotating) around a circle at a constant speed

• It can be defined using the radius r and linear speed v:

$a=\frac{v^2}{r}$

• Where:

  • $a$ = centripetal acceleration (m s^–2)

  • $v$ = linear speed (m s^–1)

  • $r$ = radius of the circular orbit (m)

• Using the equation relating angular speed ω and linear speed v:

$v=r\omega$

• Where:

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

• These equations can be combined to give another form of the centripetal acceleration equation:

$a=\frac{{\left(r\omega \right)}^2}{r}$

$a=r{\omega }^2$

• This equation shows that centripetal acceleration is equal to the radius times the square of the angular speed

• This equation can be combined with the first one to give another form of the centripetal acceleration equation:

$a=\frac{v^2}{\left({\displaystyle \frac{v}{\omega }}\right)}$

$a=v\omega$

• This equation shows how the centripetal acceleration relates to the linear speed and the angular speed

• Where:

  • $a$ = centripetal acceleration (m s⁻²)

  • $v$ = linear speed (m s⁻¹)

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

  • $r$ = radius of the orbit (m)