Question

Uniform Copper Cone

Height: 3cm

Diameter: 2cm

Center of Mass: H/4

Moment of Inertia: 8.445 x 10-7

We are going to discuss spinning the cone like a top. Assume that the cone is place on its tip and is perfectly vertical and initially at rest. It is grabbed by two fingers at the very top on both sides that exert the same constant 5 N frictional force to the base of the cone for 0.1 seconds. The normal forces from each finger also have the same magnitude and point towards the center of the base.

1. Draw a free body diagram for the cone while being spun by the fingers. Make sure to include all forces acting on the cone.

2. Calculate the net torque on the cone while the fingers are spinning the top.

3. Calculate the angular acceleration of the cone while the fingers are spinning the top.

4. Calculate the final angular velocity of the cone when the fingers release.

5. Calculate the final angular frequency of rotation when the fingers release.

6. Calculate the final frequency of rotation when the fingers release.

7. Calculate the final period of rotation when the fingers release.

8. Calculate the angular momentum of the cone when the fingers release.

We then stop the cone and pick it up and put it into a furnace. The furnace is set at 1000 oC. Noting that room temperature is on average 23 oC, answer the following.

9. Describe what happens to the cone while heating. Discuss both the microscale and the macroscale.

10. Calculate any changes to the cone on the macroscale during this process.

Answer 1