The generalisation of Newton’s second law to circular dynamics states that the angular acceleration of an object α is proportional to the applied torque τ and inversely proportional to its moment of inertia, I. That is

In this experiment you will attempt to verify this expression by measuring the angular acceleration of a disc subject to an applied torque. You should then be able to determine the moment of inertia and confirm that it agrees with the calculated value.

1. For this experiment you will be using the Pasco Rotational Dynamics Apparatus. This is a sensitive piece of equipment which makes use of precisely ground disks which rotate on a cushion of air to minimise friction. It is therefore essential that you handle these discs carefully and avoid touching their surface. Do not allow them to rotate unless the compressed air is connected. Please listen carefully to Peter or David at the start of the lab so that you know how to set up the equipment.
2. Tie the mass which is to be use to supply the torque to one end of the string and attach the other end to the thread anchor washer.
3. Fit the anchor washer into the recess of the pulley and secure the pulley to centre of the top disc. The thread should run from the pulley over the air bearing so that the mass is hanging just above the ground
4. When the air is on slowly wind the thread around the pulley until the accelerating mass is just below the air bearing. Hold the top disc stationary than release it and allow the accelerating mass to do its work!
5. As soon as the top disc is released start recording the frequency from the frequency meter. This displays the number of black lines on the edge of the disc which pass by per second. It gives a new reading every two seconds. You should convert this frequency to angular velocity. You should be able to make enough measurements so that you can plot angular velocity vs time and hence determine the angular acceleration of the disc.
6. Measure the radius of the pulley, weigh the accelerating mass and hence determine the torque acting on the disc. Hence use to find the moment of inertia of the disc (with uncertainty).
7. Compare your answer with the calculated value and quantitatively account for any discrepancy (It may be useful for you to know that the rotating part of the air bearing has inner radius 0.77 cm and outer radius 1.35 cm and mass 26 g).

Attach some of the accessories to the top disc and measure their moments of inertia. Compare to calculated values: