Deep in the throes of revision for Mechanics 3. Here's an example of the sort of fun question I'm having to deal with:
"Using integration, show that the centre of mass of a uniform thin hemispherical bowl of radius a is at a distance a/2 from the centre C of the circular rim of the bowl.
"A lid is attached to the bowl to form a closed composite body B. The lid is a thin circular disc of radius a and centre C. The lid is made of the same uniform material as the bowl. Show that the centre of mass of B is at a distance a/3 from C.
"The body B has mass M. A particle P, also of mass M, is attached at a point on the circumference of the plane circular face of B. The body is placed with a point of its curved surface in contact with a horizontal plane and rests in equilibrium. Find, to the nearest half degree, the angle made by the line PC with the horizontal."