The period of circular motion remains independent of the mass of the object in motion.

The period of circular motion is influenced solely by the radius of the circular path and the speed at which the object travels. This relationship is governed by the concept of centripetal force, which is the force necessary to maintain an object’s circular trajectory. The formula that describes the period of circular motion is given by:

where $T$ represents the period, $r$ denotes the radius of the circular path, and $v$ indicates the speed of the object.

Notably, the mass of the object does not appear in this equation, signifying that it does not have an effect on the period of circular motion. The reason for this is that the centripetal force required to keep an object moving in a circular path is proportional to the square of its speed and inversely proportional to the radius of the circular path. Consequently, if the mass of the object increases, the centripetal force needed to sustain its circular motion will also rise, while the speed and radius will remain constant. As a result, the period of circular motion will remain unchanged.

It is crucial to understand that while the mass of the object does not impact the period, it can influence other aspects of circular motion. For instance, it affects the amount of force needed to initiate the circular motion or the energy required to maintain it. However, these considerations do not directly influence the period of circular motion.