Centripetal Acceleration (SL IB Physics)

• 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

Centripetal acceleration is always directed toward the centre of the circle, and is perpendicular to the object’s velocity

• It is directed towards the centre of the circle as it is in the same direction as the centripetal force
• It can be defined using the radius r and linear speed v:

• 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:

• Where:
  • ω = angular speed (rad s^–1)

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

• Alternatively, since we know angular velocity is:

• Where:
  • f = frequency (Hz)
  • T = time period (s)
• This means the centripetal acceleration can also be written as:

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