If you place a cylinder such as this chocolate roll on an inclined plane, it could get to the bottom in one of two ways: 1. It could slide down 2. It could roll down. If you ran these two modes side by side, the one that slid would reach the bottom first. To explain why needs an energy analysis. At the top of the slope, the cylinder has gravitational potential energy and as it falls this turns into kinetic energy. The problem is that if it rolls, there are two types of kinetic energy to consider. There is the familiar linear kinetic energy based on its straight line speed and calculated by 1/2 m.v^2. But there is also the rotational kinetic energy. That is calculated by 1/2 I.omega-squared. I is the moment of inertia which has been on display at the Winter Olympics. When a skater holds her arms out wide, she spins slowly. When she pulls them in, she spins fast. Ease of motion depends on how far away the mass is so it is "moment of inertia". Omega is the angular speed in radians per second. So anyway, if the same gravitational potential energy is shared out between two types of kinetic energy, a smaller share goes to the normal linear kinetic energy so the cylinder goes down the slope slower. If the cylinder rolls it takes longer to reach the bottom than if it slides.
