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Teach: Circular motion

Aims

  • Understand why the force needed for constant speed circular motion is towards the centre.
  • Define quantities.
  • The small angle approximation.
  • Derive the equation for centripetal acceleration.
  • Apply theory to common examples.

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Considerations

There are several ways of introducing this but creating a simple example with gravity is problematic, the conical pendulum is good but analysing the forces involves taking components. Simplest is to use Algodoo without gravity.

By considering energy you can deduce that since KE is constant no work is done but velocity is changing so there is an unbalanced force, this must therefore be perpendicular to the velocity.

The flying pig experiment is always popular.

Timing

Probably two lessons

Apparatus and software

String and pigs, plus Algodoo of course.

Observations and common pitfalls

In the derivation of centripetal acceleration the change in velocity is found vectorially, students always find this step difficult. It is important to separate the vectors from the diagram of the ball otherwise students get confused between the displacement and the vector representing Δv.

Examiners like to ask about vertical circular motion so students have to think about the loss of KE as the object rises, there are several examples, mass on string, roller coaster, hump back bridge. I like to mime a loop the loop fairground ride with facial expressions squashing my face at the bottom and elongating it at the top, always gets a laugh.

The pendulum describes an arc so is travelling in a circle, however when we derive the equation we assume the amplitude is small so the displacement is horizontal. This confuses students and examiners like to prey on the confusion. A bit unfair I think. In questions where the y want students to consider the motion to be circular it should be clearly stated that the amplitude is large.

Cars travelling around flat and backed tracks are nice examples as is the wall of death.

The most common mistake in the flying pig experiment is students measuring the length of the string instead of the vertical distance.

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