# Problems

- Author:
- Timo Budarz

1. Given a car driving around a turn of radius 40m at 20m/s, what is the car's angular velocity?
2. If a 1/2 inch diameter drill bit spins at 3000 rotations per minute, how fast is the outer edge moving as it contacts a piece of metal while drilling a machine part?
3. Find the inertia of a rod of length L that has a non-uniform density given by when it's rotated about the end where x=0. Hint: Just replace the constant with this function and follow the steps of the integral in the chapter.
4. Find the inertia of a cylinder of mass 2.0kg, length 0.4m and radius 0.1m when it's rotated about its symmetry axis. You may use the tabulated formulas given in the link.
5. Find the inertia of the same cylinder in question 4, except when rotated about a parallel axis that is located 0.1m from the central axis (at the radius of the cylinder).
6. What is the maximum magnitude of torque that can be produced on a bolt by applying a force of 100N on a wrench that is 0.5m long?
7. What is the torque (vector) produced by a force acting with a lever arm given by
8. How much angular momentum is associated with a solid, spinning ball of mass 0.050kg and radius 0.075m that is rotating at a rate of 20rad/s?
9. For how long does a torque of 50Nm need to act to make a disk of mass 4.0kg and radius 0.50m to go from rest up to a rotation speed of 100 rad/s about its symmetry axis?
10. Explain why a spinning top on a table doesn't fall in the direction gravity is pulling it.

Answers:
1. 0.5 rad/s
2. 2 m/s
3.
4.
5.
6. 50 Nm
7.
8.
9. 1.0s
10. See precession discussion.