6.6 Rolling

Rolling Without Slipping

Rolling without Slipping When a body is rolling, it will have a translational kinetic energy and rotational kinetic energy. When an object is rolling without slipping, the point on the body that is touching the ground will not move. At that point, static friction exerts a torque on the body, making the body rotate forward and repeat this process all over again. Since at the point in contact with the ground is stationary, the static friction will not do work onto the body, meaning that the body’s total energy will be constant.

In order to relate the body’s linear motion to its rotational motion, we can use the equations derived in lesson 5.2, which can be used to describe the motion of the center of mass of the body. These equations are: ${\Delta x_{cm}=r \Delta \theta}$, ${v_{cm}=r \omega}$, and ${a_{cm}=r \alpha}$.