## Uniformly Varied Circular Motion

When a body, which describes a circular path, and undergoes a change in its angular velocity, then this body has angular acceleration (α).

The angular forms of the Uniformly Varied Curvilinear Motion equations are obtained when divided by the radius R of the trajectory to which the body moves.

Like this:

MUV | MCUV | |

Linear quantities | Angular quantities | |

And, resulting acceleration is given by the vector sum of tangential acceleration and centipetal acceleration:

Example:

A circular steering wheel with radius 0.4 meters rotates from rest with angular acceleration equal to 2rad / s².

(a) What will be your angular velocity after 10 seconds?

(b) What will be the angle described at this time?

(c) What will be the resulting acceleration vector?

*(a) By the hourly function of angular velocity*:

*(b) By the angular displacement time function:*

*(c) By the established tangential and centripetal acceleration relations:*