Rolling Without Slipping:
* If an object rolls without slipping, then the bottom of the rolling object (at the point of contact) must be momentarily at rest relative to a fixed observer.

* Rolling without slipping can be thought of as the motion of the center of mass (fixed observer) plus rotational motion about its center of mass (observer moving with the object).

* In the case for rolling without slipping, the distance, the velocity, and the acceleration of the center of mass is directly related to the angle of rotation, the angular velocity, and the angular acceleration about the center of mass.

Slipping and Rolling Disk
A disk on a horizontal surface is made to slip by a applied horizontal force. Friction between the surface and the disk eventually causes the disk to roll without slipping. When the disk rolls without slipping you can observe that the velocity of the center of mass is equal to the velocity of the rim of the disk.

Total Mechanical Energy for Linear and Rotational Motion of a Solid:

The total mechanical energy of an object is equal to the kinetic energy of its center of mass plus the rotational energy about its center of mass plus the gravitational potential energy of it center of mass.

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