Shown is a top view of a pulley on a table. The massive disk-shaped pulley can rotate about a fixed axle located at the origin. The pulley is subjected to two forces in the plane of the table, the tension in each rope (each between 0 N and 10 N), that can create a net torque and cause it to rotate as shown (position is given in meters, time is given in seconds, and angular velocity is given in radians/second). Restart. Also shown is the "extended" free-body diagram for the pulley. In this diagram the forces in the plane of the table are drawn where they act, including the force of the axle.

Set the mass of the pulley to 1 kg, the radius of the pulley to 2 m, vary the forces, and look at the "extended" free-body diagram.

1. How is the force of the axle related to the force applied by the two tensions?
2. How do you know that this must be the case?

Set the mass of the pulley to 1 kg, the radius of the pulley to 2 m, and vary the forces.

3. What is the relationship between F₁ and F₂ that ensures that the pulley will not rotate?
4. For F₁ > F₂, does the pulley rotate? In what direction?
5. For F₁ < F₂, does the pulley rotate? In what direction?
6. What is the general form for the net torque on the pulley in terms of F₁, F₂, and r_pulley?

Set the mass of the pulley to 1 kg, F₁ to 10 N, F₂ to 5 N, and vary the radius of the pulley.

7. How does the angular acceleration of the pulley depend on the radius of the pulley?

Set the radius of the pulley to 2 m, F₁ to 10 N, F₂ to 5 N, and vary the mass of the pulley.

8. How does the angular acceleration of the pulley depend on the mass of the pulley?
9. Given that the pulley is a disk, find the general expression for the angular acceleration in terms of F₁, F₂, m_pulley, and r_pulley.