Look at the figure below, which shows a possible design for a child's toy. The designer wants to build a "weeble" (which wobbles, but doesn't fall down :-) It is a single, solid object, the shape is a perfect hemisphere (radius a) on the bottom, glued to a solid cylinder on top. The CM is shown, it is "h" above the base. (You don't need to compute it - it's given)
Come up with a formula for the gravitational potential energy U(theta) when the whole toy is tipped to an angle theta. (Sorry, but you
will need to pull out a paper and pencil if you want to get this right! It is not identical to Taylor's example above) Fill in your answer for U(theta) in the space below the figure.
(Note: on an upcoming homework, you will finish this problem, and thus decide what the criterion is on h and a to make this toy stable)