Refer to the video clip for this experiment (see Assignments Page).

1. What is the angular acceleration of the wheel coasting with its axis on your fingers after you spin it?

2. What are the final velocity and the angular acceleration of the wheel while the washer is falling, based on the number of revolutions during the fall and the time of fall?

3. What are the final velocity and the acceleration of the falling washer, based on time of fall and distance fallen?

4. What is the radius of the wheel?

5. Do your results confirm that angular velocity is equal to velocity divided by radius?

6. Do your results confirm that angular acceleration is equal to acceleration divided by radius?

7. What is the total of the m r^2 contributions of the bolts and nuts?

8. What is the total moment of inertia of the system?

9.  Find the following torques and explain how the three should be related:

10.  Do your results confirm that net torque = moment of inertia * angular acceleration, and if so how do you draw this conclusion?

11.  What is the PE change of the falling mass?

12. What is the KE of each bolt at the instant the end of the thread has reached the paper clip?

13. What is the KE of the falling mass at the instant the end of the thread has reached the paper clip?

14. What is the KE of the styrofoam at the instant the end of the thread has reached the paper clip?

15. What is the KE of the system after the mass has fallen, and by how much does the PE of the system change as the mass falls?

16.  What is the torque exerted by the friction between the axle and your fingers, and how much energy is lost to this friction as the washer falls?

17. What are the details of energy conservation as the washer falls? Account for everything.

Do all calculations in kg and meters, not grams and cm.

M = mass of styrofoam disk (22 g), R = radius of that disk (11 cm). It contributes .5 M R^2 to the moment of inertia I.

Each bolt (11 g or 13.3 g, depending on which wheel) contributes m r^2 to the moment of inertia I, where r is its distance from the axis of rotation.

The torque on the system comes from the force exerted by gravity on the washer, which is exerted along a line 11 cm from the axis of rotation.

Torque is designated by the Greek `tau, angular acceleration by Greek `alpha.

Newton's Second Law says the F = m a. An equivalent statement is `tau = I `alpha.

The angular momentum of a rotating system is L = I * `omega.

The kinetic energy of a rotating system is KE = .5 I * `omega^2.