6. **Tippy top. A tippy top is a nearly spherical top that turns itself upside-down when spun on a smooth table. The torque that causes the top to flip is due to a small frictional force at the point of contact with the table. This frictional force is parallel to the table, opposing the velocity of slipping, as illustrated in the figure. The top itself consists of a sphere with a portion removed to expose the "stem." The stem is used to spin the top. Initially the stem points up. When the top is released, the angle A between the stem and the vertical steadily increases until the top flips over. (a) Order the moments of inertia along your three principal axes. (Which is larger, which is smaller, which is equal?) Select es as your symmetry axis. Select the other axes so initially @ = wo(sin 0, 0, cos 0). Sketch these principal axes on top of the figure. (b) Use Euler's equation for one of your axes to show that 0 ~ I/(Iwo). [Hint: differentiate w to get something that depends upon 0.] (c) Show that the top takes approximately t ~ 2x Rwo/(5ug) to flip over. (d) Estimate numbers for the video that comes up first in a google search for "tippe top SMU", and show that the calculated flipping time is on the same order of magnitude as the observed time