What is the condition for rolling without slipping?

Hi

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.

When an object is rolling on a plane without slipping, the point of contact of the object with the plane does not move. A rolling object`s velocity v is directly related to its angular velocity ω , and is mathematically expressed as v=ωR v = ω R , where R is the object`s radius and v is its linear velocity.