OCR A Level Physics

Revision Notes

5.4.6 Centripetal Acceleration

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Centripetal Acceleration

  • 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:

Calculating Centripetal Acceleration equation 1

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

 v = r⍵

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

Calculating Centripetal Acceleration equation 2

  • This equation shows that centripetal acceleration is equal to the radius times the square of the angular speed
  • Alternatively, rearrange for r:

Calculating Centripetal Acceleration equation 3

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

Calculating Centripetal Acceleration equation 4

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

Centripetal acceleration diagram, downloadable AS & A Level Physics revision notes

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

 
  • Where:
    • a = centripetal acceleration (m s−2)
    • v = linear speed (m s1)
    • ⍵ = angular speed (rad s−1)
    • r = radius of the orbit (m)

Worked example

A ball tied to a string is rotating in a horizontal circle with a radius of 1.5 m and an angular speed of 3.5 rad s−1.

Calculate its centripetal acceleration if the radius was twice as large and angular speed was twice as fast.

WE - Centripetal acceleration answer image, downloadable AS & A Level Physics revision notes

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