Angular momentum
Rotational momentum, L = I omega. It stays constant when no outside torque acts.
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Analogy
A skater pulls her arms in and spins faster.
Example
L = I omega4 x 2 = 8 kg m^2/s2 x omega = 8omega = 4 rad/s
In practice
If I halves from 4 to 2 kg m squared, omega doubles from 2 to 4 rad/s.
Practice
Flashcards
- When is angular momentum conserved?When no net outside torque acts.
Interview questions
- A figure skater pulls her arms in. Explain the change in spin rate and kinetic energy.
- Angular momentum is conserved
- Moment of inertia falls so omega rises
- Kinetic energy increases because the skater does work
Questions people ask
Why does a spinning top stay upright?
Its spin gives it large angular momentum. Changing the direction of that angular momentum needs a torque, and gravity's torque only makes the top slowly circle round, which is called precession. As friction slows the spin, the top finally falls over.
Why do cats land on their feet?
A falling cat has no outside torque, so total angular momentum stays near zero. It tucks one half of its body in and stretches the other, then swaps, so the front and back halves turn in turn. The whole cat flips over with no net angular momentum, so it lands feet first.