Non-uniform Circular Motion

Inuniform circular motion, the particle executing circular motion has a constant speed, and the circle is at a fixed radius. However, not all circular motion occurs at a constant speed. A particle can travel in a circle and speed up or slow down, showing an acceleration in the direction of motion. In that case, the motion is called non-uniform circular motion, and an additional acceleration is introduced, which is in the direction tangential to the circle.

For example, such accelerations occur at a point on a spinning top, which slows down after it has been spun, or any accelerating rotor. We know that centripetal acceleration is the time rate of change of the direction of the velocity vector. If the speed of the particle is changing too, then it has a tangential acceleration; this is the time rate of change of the magnitude of the velocity. The direction of tangential acceleration is tangent to the circle, whereas centripetal acceleration is radially inward, toward the center of the circle. Thus, a particle in a circular motion with a tangential acceleration has a total acceleration that is the vector sum of the centripetal and tangential accelerations.

This text is adapted from Openstax, University Physics Volume 1, Section 4.4: Uniform Circular Motion.