1. Given a car driving around a turn of radius 40m at 20m/s, what is the car's angular velocity?[br]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?[br]3. Find the inertia of a rod of length L that has a non-uniform density given by [math]\lambda(x) = ax+b.[/math] when it's rotated about the end where x=0. Hint: Just replace the constant [math]\lambda[/math] with this function and follow the steps of the integral in the chapter.[br]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.[br]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).[br]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?[br]7. What is the torque (vector) produced by a force [math]\vec{F}=10N\hat{i}+20N\hat{j}[/math] acting with a lever arm given by [math]\vec{r}=0.40m\hat{i}?[/math] [br]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?[br]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?[br]10. Explain why a spinning top on a table doesn't fall in the direction gravity is pulling it.[br]

Answers:[br]1. 0.5 rad/s[br]2. 2 m/s[br]3. [math]\frac{aL^4}{4}+\frac{bL^3}{3}[/math][br]4. [math] 0.01 kg\cdot m^2[/math][br]5. [math] 0.03 kg\cdot m^2[/math][br]6. 50 Nm[br]7. [math] 8N\cdot m\hat{k}[/math][br]8. [math] 0.00225\frac{kg m^2}{s}[/math][br]9. 1.0s[br]10. See precession discussion.