Final answer:
The speed of the center of a rolling object without slipping is given by the equation v = ωr, where v is the linear velocity of the center, ω is the angular velocity, and r is the radius of the object.
Step-by-step explanation:
If an object is rolling without slipping, the speed of its center (v) is directly related to its angular velocity (ω) by the equation v = ωr, where r is the radius of the object. This relationship means that the linear velocity at the center of mass is the product of the angular velocity around its axis and the radius of the object. This is because the point on the edge of the rolling object that is in contact with the surface is momentarily at rest while the entire object continues to move forward, hence the linear speed of the center of mass is equivalent to the tangential speed at the rim of the object.