Thursday, September 4, 2014
Pencil rolling down the plane
Inspired by IPhO 1998. A pencil that's made of homogeneous wood is shaped like a regular hexagonal prism, with hexagon side $s$ and mass $M$. The pencil rolls down an inclined plane. Find the moment of inertia. Assume that the sides are slightly concave so that only the vertices of the hexagons are touching the plane at any given moment.