Physics

Circular motion


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: