A flat circular platform is mounted on a fixed base via a low-friction air bearing. A reaction wheel is mounted at the centre of the platform. The reaction wheel and the platform have a common vertical axis of rotation.

Initially, both the platform and the reaction wheel are at rest. The reaction wheel motor is switched on, and the wheel quickly accelerates to a high constant angular speed in a counter-clockwise direction (when viewed from above).

Compare, with reference to angular momentum, the subsequent motions of the platform and the reaction wheel.

To determine the moment of inertia of the platform, a small brass weight is suspended by a thread directly above the rotating platform at a distance $r$ from the axis of rotation. The platform is spinning freely at an initial angular speed ${\omega }_i$.

The thread is cut, allowing the weight to fall and land on a patch of adhesive tape on the platform so that it immediately sticks and rotates with the platform. The new angular speed of the platform is ${\omega }_f$.

The brass weight can be modeled as a point mass.

Describe how to determine the moment of inertia of the platform using measurements of ${\omega }_i$ and ${\omega }_f$.

In your answer you should:

• suggest how ${\omega }_i$ and ${\omega }_f$ are measured
• state any other measurements needed and name the equipment used to make them
• explain how the moment of inertia of the platform is determined from the measurements.