Concept #1: Conservation of Energy with Rotation
Example #1: Work to accelerate cylinder
Practice: How much work is needed to stop a hollow sphere of mass 2 kg and radius 3 m that spins at 40 rad/s around an axis through its center?
Example #2: Which shape reaches bottom first?
Example #3: Cylinders racing down: rolling vs. sliding
Practice: Two solid cylinders of same mass and radius roll on a horizontal surface just before going up an inclined plane. Cylinder A rolls without slipping, but cylinder B moves along a slippery path, so it moves without rotating at all times. At the bottom of the incline, both have the same speed at their center of mass. Which will go higher on the inclined plane? (Why?)