Non-uniform Circular Motion

In a non-uniform circular motion, the object moves in a circular path with varying speed. The velocity vector arrows of varying sizes indicate the change in speed.

As the speed is not constant, the magnitude of the radial acceleration varies with speed. The greater the speed, the greater the radial acceleration and vice versa.

Since the velocity is changing, there is a tangential acceleration in addition to radial acceleration.

If the object is speeding up, the tangential acceleration is in the same direction as the velocity vector. When the object is slowing down, the direction of tangential acceleration is opposite to the velocity vector.

At any given point, the tangential acceleration is the rate of change of speed. Hence, at points of minimum or maximum speeds, the tangential acceleration is zero.

The magnitude and direction of the total acceleration varies with speed. At the fastest and at the slowest speeds, the acceleration is equal to radial acceleration. In non-uniform circular motion, the total acceleration is the sum of radial and tangential accelerations.