Moment of inertia and conservation of angular momentum

Overview

Moment of inertia and the radius of gyration, angular momentum and its conservation, the diver and skater changing spin with a worked example, body shape and opening out before entry.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   What is moment of inertia?

   Model answer

   Moment of inertia is the resistance of a rotating body to a change in its angular motion. The unit is kilogram metres squared (kg m²).

2. 2

   What factors affect moment of inertia?

   Model answer

   Moment of inertia depends on the mass of the body and how the mass is distributed about the axis. Mass further from the axis increases it.

3. 3

   What is the radius of gyration?

   Model answer

   The radius of gyration describes how far the mass is spread from the axis of rotation. A larger radius gives a larger moment of inertia.

4. 4

   What is angular momentum?

   Model answer

   Angular momentum is the quantity of rotation a body has. Angular momentum equals moment of inertia multiplied by angular velocity.

5. 5

   What is the conservation of angular momentum?

   Model answer

   Angular momentum stays constant during flight unless an external torque acts. Changes in body shape change the spin rate, not the angular momentum.

6. 6

   How does a diver speed up a somersault?

   Model answer

   The diver tucks, bringing mass closer to the axis and reducing moment of inertia. Angular velocity increases to keep angular momentum constant.

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