The speed of an object in uniform circular motion is determined by dividing the total distance traveled by the time taken.

To elaborate, uniform circular motion refers to the movement of an object along a circular path at a constant speed. While the speed remains unchanged, the direction of the velocity vector constantly varies, resulting in an inward acceleration directed towards the center of the circle. This inward acceleration is known as centripetal acceleration.

The speed of an object in uniform circular motion can be calculated using the formula:

For an object moving in a circle, the distance traveled in one complete revolution is the circumference of the circle, which can be calculated using the formula:

where $r$ is the radius of the circle. The time taken for one complete revolution is usually provided or can be inferred from the context.

For instance, consider an object moving in a circle with a radius of $5$ meters, completing one full revolution in $10$ seconds. The speed of the object can be calculated as follows:

It is crucial to understand that while the speed (the magnitude of the velocity) remains constant in uniform circular motion, the velocity itself is not constant, as it continuously changes direction. This distinction is fundamental to grasping the principles of circular motion and the associated forces.

Furthermore, centripetal acceleration, which describes the acceleration of an object moving along a circular path, can be calculated using the formula:

where $v$ represents the speed of the object and $r$ is the radius of the circle. This equation illustrates that centripetal acceleration is directly proportional to the square of the speed and inversely proportional to the radius. Therefore, an increase in speed or a decrease in the radius will result in a greater centripetal acceleration.