Circular Motion

When a particle moves in a circular path with uniform speed, it experiences centripetal acceleration. This acceleration is always directed towards the center of the circular path, which is along the radius. Even though the speed of the particle remains constant, the direction of motion changes continuously, and this change in direction requires acceleration. Thus, the acceleration is directed along the radius towards the center of the circle.

Step 1: Given mass , radius , and gravitational acceleration .
Step 2: The difference in kinetic energy between the bottom and the top of the vertical circle is equal to the change in potential energy:

In circular motion, centripetal acceleration always acts towards the center of the circle, while tangential acceleration acts along the tangent to the path at any instant.
Since these two directions are mutually perpendicular, the angle between centripetal and tangential acceleration is .