AQA A Level Physics

Revision Notes

6.1.4 Centripetal Acceleration

Calculating 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 that centripetal acceleration is equal to the linear speed times 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 s-1)
    • ⍵ = 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 radius 1.5 m and angular speed 3.5 rad s-1.

Calculate its’s centripetal acceleration with a radius twice as large and angular speed twice as fast.

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

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