How do you relate the angular acceleration of the object to the linear acceleration of a particular point? There are actually two perpendicular components to the linear acceleration. One is due to the change in direction of a rotating object. It is inward directed along the radius and is therefore called the radial component of the linear acceleration. This is simply the inward directed centripetal acceleration of an object moving in UCM This is the component of the linear acceleration that is due to changes in direction.

The other component is due to any changes in speed of the rotating object. It acts tangent to the circle and is therefore known as the tangential component of the linear acceleration. This is the component of the linear acceleration that is due to changes in speed.

Rolling with Uniform Acceleration Consider a disk rolling without slipping with a Uniform Acceleration. While most points both rotate and move linearly, the center of mass is moving linearly with a constant acceleration

Rolling with Uniform Acceleration Both a point on the outside of the disk and the center of mass must move the same distance with the same linear velocity for the disk to roll without slipping!

Rolling with Uniform Acceleration Both a point on the outside of the disk and the center of mass must move the same linear distance, with the same linear velocity and the same linear acceleration for the disk to roll without slipping! Rolling Condition – must hold for an object to roll without slipping. Radian measure