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When one rolls without slipping, the point of contact must have exactly zero velocity. This implies a relationship between the velocity of the center of mass and the angular velocity of rotation to be

At each point on the wheel, the motion is the sum of the translation and the rotation. So the velocity vector at point P (from the first conceptual question on the previous page) is.

In rolling motion, the kinetic energy is a combination of translation and rotation.

K_{rolling} = \frac12 I_{cm}\omega^2 + \frac12 mv_{cm}^2 . Read carefully the section of the your textbook "The great downhill race" and here is a video displaying this race!

Yo-Yo Physics

Imagine you pull a yo-yo from underneath. The yo-yo is resting on a table.