Moment of inertia and angular momentum
Why one tucks to spin fast: moment of inertia and conservation of angular momentum.
- 11 cards
- 5 topics
- Free
The outline, topic by topic
Each topic is weighted the way the exam weighs it.
- Concepts
- The numbers
- Predict, then see
- Scenarios
- Understand
A few cards from the deck
Moment of inertia: what is it?
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A body's resistance to rotation, depending on its mass and how far that mass is from the axis.
Arms out, it is large; tucked, it is small.
Why is a double somersault done tucked rather than straight?
- Tucked, the moment of inertia is smaller and rotation faster
- Tucked, angular momentum increases and rotation speeds up
- Tucked, one jumps higher and stays longer in the air
- Straight, the moment of inertia is smaller and rotation faster
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Tucked, the moment of inertia is smaller and rotation faster
Flight time and angular momentum are set at take-off: only a smaller moment of inertia makes one spin faster. The straight double somersault exists, but it needs far more angular momentum at take-off.
Angular momentum: what is it?
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The quantity of rotation, equal to moment of inertia times angular velocity.
In the air, it stays constant about the centre of mass: weight acts through that point and creates no torque.
Once in the air, can a gymnast create rotation?
- Yes, tucking gives him extra angular momentum
- No, he can only share out his angular momentum among his body segments
- Yes, swinging his arms gives him extra angular momentum
- No, and he cannot change his rotation speed either
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No, he can only share out his angular momentum among his body segments
Total angular momentum is created on the ground, at take-off: in the air, weight acts through the centre of mass and does not change it. The gymnast can still share it out differently: tucking speeds up the rotation, circling arms turn the rest of the body the other way, and asymmetric arm movements tilt the body to start a twist in the air.