Activity: Angular momentum

Aims

  • Define angular momentum.
  • Apply conservation of angular momentum.

Angular momentum

The angular momentum of a point mass, m moving in a circle of radius r at speed v is give by

Angular momentum = mvr = mr2ω

For a rigid body with moment of inertia, I spinning with angular velocity ω

Angular momentum = Iω

According to Newton's second law

T space equals space I alpha space equals I fraction numerator capital delta omega over denominator capital delta t end fraction equals fraction numerator capital delta I omega over denominator capital delta t end fraction

So if there are no external torques acting (T = 0) then there is no change in angular momentum which means that it is conserved.

Principle of conservation of angular momentum

If no external torques act on a system of isolated bodies the total angular momentum is constant.

In the following animation the two spinning balls are pulled together by shortening the spring joining them.

  • Explain why they rotate faster when the spring gets shorter.

The next one shows a car in space. Watch what happens as the motor starts to make the front wheels rotate.

  • Why does the whole car start to rotate?
  • Why doesn't the centre move?

Here is a real example

  • Explain why the ice skater spins fastest at when her leg is up straight.

You can experiment with Algodoo yourself, here are some instructions Conservation of angular momentum (Algodoo)

There are also some problems to solve in the book (exercises 25 to 28).

Angular momentum multiple choice quiz

Use what you have learnt to explain how some of the following spins work.

and some more

A clip from one minute physics with a more sophisticated version of angular momentum.

Angular momentum practical

Using the PASCO apparatus in the photo, find out if angular momentum is conserved when a lump of Plasticine is dropped onto the spinning beam.

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