4.9:
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.
4.9:
Non-uniform Circular Motion
In uniform 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.