## Overview of Non-Uniform Circular Motion

Non-uniform circular motion denotes a change in the speed of a particle moving along a circular path.

### Learning Objectives

Explain when a particle undergoes non-uniform circular motion

### Key Takeaways

#### Key Points

• In non- uniform circular motion, the size of the velocity vector (speed) changes, denoting change in the magnitude of velocity.
• The change in speed has implications for radial ( centripetal ) acceleration. There are two possibilities: 1) the radius of the circle is constant; or 2) the radial (centripetal) force is constant.
• In either case, the angular velocity in non-uniform circular motion is not constant, as $\omega = \frac{\text{v}}{\text{r}}$, and $\text{v}$ varies.

#### Key Terms

The change in direction is accounted by radial acceleration ( centripetal acceleration ), which is given by following relation: $\text{a}_\text{r} = \frac{\text{v}^2}{\text{r}}$. The change in speed has implications for radial (centripetal) acceleration. There are two possibilities:
1: The radius of circle is constant (like in the motion along a circular rail or motor track). A change in $\text{v}$ will change the magnitude of radial acceleration. This means that the centripetal acceleration is not constant, as is the case with uniform circular motion. The greater the speed, the greater the radial acceleration. A particle moving at higher speed will need a greater radial force to change direction and vice-versa when the radius of the circular path is constant.
In either case, the angular velocity in non-uniform circular motion is not constant as $\omega = \frac{\text{v}}{\text{r}}$ and $\text{v}$ is varying.