5.1 Uniform Circular Motion Rolling Without Slipping

 

Explanation: The applet canvas is divided into four sections. The top section illustrates the concept of uniform circular motion as discussed in Section 5.1. The animation on the left shows the position and velocity vectors of an object in uniform circular motion. Note that like the position vector, the velocity has a constant magnitude and continually changes direction. This similarity is illustrated in the middle animation. The middle animation is there only to illustrate this similarity; it does not show the actual velocity of the rotating object. The velocity of the rotating object is tangential, not radial. The last animation shows the acceleration (centripetal) of the rotating object. The second section is an animation  of an object rolling without slipping. It shows the velocity and the position vector of a  point on the rim relative to the center of rotation. Relationships between the linear quantities and their rotational counterparts are discussed in Sections 5.1 and 9.1. The third section shows the overall velocity vector of a point on the rim of the rolling body. The white vector represents the velocity of the center with respect to the ground, and the red vector represents the velocity of the point with respect to the center. The sum of these two vectors is the cyan (blue) vector. It represents the velocity of the point relative to the ground. The fourth section draws the trajectory followed by a point on the rim.

Source: Fu-Kwun Hwang