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Linear and Angular Motion

Conservation of angular momentum

  • 3 things to know
  • Component 1

Overview

Angular momentum and its conservation in flight, contact with the ground, moment of inertia against angular velocity, the diver tucking and opening out, worked diver and skater calculations, and the trampolinist's tuck and pike.

What you need to know

Answer each one before you reveal it.

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Key term

Why does angular momentum stay constant while a performer is in the air?

Key term

Describe how angular momentum, moment of inertia and angular velocity change during a diver's tucked somersault.

Key term

Define angular momentum and give its equation.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Define angular momentum and give its equation.

    Model answer

    Angular momentum is the quantity of rotation a body possesses. Angular momentum = moment of inertia × angular velocity, measured in kg m²/s.

  2. 2

    State the principle of conservation of angular momentum.

    Model answer

    Angular momentum stays constant unless an external torque acts on the body. Once a performer leaves the ground, angular momentum is fixed for the whole flight.

  3. 3

    Why does angular momentum stay constant while a performer is in the air?

    Model answer

    Gravity acts through the centre of mass, so it creates no turning effect on a performer in flight. Air resistance is usually too small to matter. Angular momentum cannot change without an external torque.

  4. 4

    Why can angular momentum change while a performer is in contact with the ground?

    Model answer

    Contact with the ground lets reaction forces create an external torque on the body. Angular momentum can therefore be gained or lost, as when a gymnast punches into a round-off.

  5. 5

    Describe the relationship between moment of inertia and angular velocity during flight.

    Model answer

    Moment of inertia and angular velocity are inversely proportional when angular momentum is conserved. A halved moment of inertia gives double the angular velocity.

  6. 6

    How does a diver increase the speed of rotation during a somersault?

    Model answer

    The diver tucks tightly, bringing mass closer to the transverse axis and cutting the moment of inertia. Angular momentum is conserved, so the angular velocity increases.

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