The velocity of an object moving in a circular path is continually changing in direction.

When an object follows a circular trajectory, it experiences a centripetal force that maintains its circular motion. This force is always directed towards the center of the circle and is perpendicular to the object’s velocity. As a result, while the direction of the object’s velocity is constantly changing, its magnitude remains constant.

The magnitude of the velocity of an object in circular motion can be calculated using the formula:

where:

• $v$ is the velocity of the object,
• $r$ is the radius of the circle, and
• $T$ is the period, or the time taken for one complete revolution.

This formula can be derived from the definition of velocity as the distance traveled per unit time. During one complete revolution, the object covers a distance equal to the circumference of the circle, which is given by $2\pi r$. Consequently, the time taken for one complete revolution can be expressed as:

Rearranging this equation to solve for $v$ yields the formula stated above.

It is essential to understand that although the magnitude of the velocity remains constant, the velocity itself is not constant due to the continuous change in direction. This variation in direction means the object is undergoing acceleration. The magnitude of this acceleration, known as centripetal acceleration, is expressed by the formula:

where:

• $a$ represents the centripetal acceleration,
• $v$ is the velocity of the object, and
• $r$ is the radius of the circular path.

This formula can also be derived from the definition of acceleration as the rate of change of velocity. The direction of the centripetal acceleration always points towards the center of the circle, which is crucial for keeping the object in its circular path.