## Exploration 10.3: Torque and Moment of Inertia

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A mass (between 0.01 kg and 1 kg) is hung by a string from the edge of a massive (between 0 kg and 2 kg) disk-shaped pulley (with a radius between 0.1 and 4 meters) as shown **(position is given in meters, time is given in seconds, and angular velocity is given in radians/second)**. Restart.

Set the hanging mass to 0.25 kg, the radius of the pulley to 2 m, and vary the mass of the pulley.

- How does the magnitude of the angular acceleration of the pulley depend on the mass (and therefore moment of inertia) of the pulley?
- How does the magnitude of the acceleration of the hanging mass depend on the mass (and therefore moment of inertia) of the pulley?
- How are your answers to (a) and (b) related?

Set the mass of the pulley to 0.5 kg, the radius of the pulley to 2 m, and vary the hanging mass.

- How does the magnitude of the angular acceleration of the pulley depend on the hanging mass?
- How does the magnitude of the acceleration of the hanging mass depend on the hanging mass?
- How are your answers to (d) and (e) related?

Set the hanging mass to 0.25 kg, the mass of the pulley to 0.5 kg, and vary the radius of the pulley.

- How does the magnitude of the angular acceleration of the pulley depend on the radius of the pulley?
- How does the magnitude of acceleration of the hanging mass depend on the radius of the pulley?
- How are your answers to (g) and (h) related?

Set the mass of the pulley to 0.5 kg, the hanging mass to 0.25 kg, and the radius of the pulley to 2 m.

- Determine the acceleration of the hanging mass and the angular acceleration of the pulley.
- From Newton's second law, determine the tension in the string.
- How much torque does this tension provide to the pulley?

Exploration by Chuck Niederriter and Mario Belloni.