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Activity: Angular momentum

Short and sweet. You'll learn how to define angular momentum and then how to apply conservation of angular momentum.

Theory

The angular momentum of a point mass, m moving in a circle of radius r at speed v is given 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.
Examples

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.

    Summary

    A clip from One Minute Physics with a more sophisticated version of angular momentum:

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

    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.

    Assess yourself

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

    and some more...

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