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Circular Motion 2

Physics: AQA A Level, topic 6.1.2

Centripetal Acceleration

Acceleration is a change in the direction or magnitude of the velocity. In a circle, the velocity is always changing. This means that the object is always accelerating.

Change in velocity

Change in velocity

  • We can use vectors to find the change in velocity of an object between two points.
  • If we make a triangle of vectors with the initial and final velocity we see that the change in velocity is always pointing towards the centre.
  • In circular motion, the acceleration always points towards the centre of the circle.
Centripetal acceleration

Centripetal acceleration

  • The acceleration in circular motion is always directed towards the centre of the circle, this is because the change in velocity is directed towards the centre.
  • Acceleration = change in velocity ÷ change in time
  • ac=Δv  ÷  Δt a{_c}={\Delta}v\;{\div}\;{\Delta}t
  • This is called centripetal acceleration.
Calculating acceleration

Calculating acceleration

  • Centripetal acceleration can be found using linear or angular quantities:
  • ac=Δv  ÷  Δt a{_c}={\Delta}v\;{\div}\;{\Delta}t
  • ac=v2÷r a{_c}=v^2 {\div} r
  • ac=rω2 a{_c}=r{\omega}^2

Centripetal Force

Any force which causes circular motion is known as a centripetal force. The larger the centripetal force, the smaller the circle.

Forces towards the centre

Forces towards the centre

  • The direction of centripetal force is always towards the centre of the circle.
  • Any combination of forces can cause a centripetal force, for example, the earth's gravity on the moon.
  • Centripetal force is always perpendicular to the instantaneous velocity.
Calculating centripetal force

Calculating centripetal force

  • According to Newton's second law of motion, the net force is mass times acceleration.
  • Fc=macF{_c}=ma{_c}
  • By substituting in the equation ac=v2/r a{_c}=v^2/r
  • Fc=mv2/r F{_c}=mv^2/r
    • Where m is the mass of the object.

Test yourself on Circular Motion 2

  • What direction is the centripetal acceleration of circular motion in?

  • What is the equation for centripetal acceleration?

  • In what direction does centripetal force act?

  • What is the correct form of the equation for centripetal force?

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