A solid cylinder of mass M and radius R starts from rest and rolls down a hill without slipping. The cylinders center of mass drops a total distance h. The cylinder is subject to the downward gravitational force Fg of the Earth.
1. Find the potential energy U of the cylinder of the top the hill.
2. Find the total kinetic energy Ktot of the cylinder at the bottom of the hill, and express Ktot in terms of the transitional speed v of the cylinder.
3. Find the transitional speed v of the cylinder at the bottom of the hill.