Homework #10

Due by 5 pm Friday December 12^th.

• 10-6) Consider the equilibrium of a small masslet on the surface of the water.
• 10-14) Hint, we looked at the tunnel through the earth problem earlier. What is different about gravity if you are insie the earth instead of outside it?
• 10-19) Drill.
• 11-13) A full inertia tensor.
• 11-16) Refresh your minds with the details of a rotation matrix in chapter 1 and this should be quite straightforward.
• One from Seth. A frisbee is thrown into the air with a definite wobble. If air friction exerts a frictional torque -cω on the rotation of the frisbee, show that the component of ω in the direction of the symmetry axis decreases exponentially in time. Show also that the angle between the symmetry axis and the angular velocity vector ω decreases in time if the moment of inertia around the symmetry axis is larger than the other moment of inertia. (A frisbee is a symmetric top.) Thus, the amount of wobble steadily diminishes if there is air friction. Demo?