# Uniform Circular Motion Formula

## Uniform Circular Motion Formula

A change in velocity direction is required for an object to travel in a curved circular path. It is because the tangent will provide the direction at each point along the circular path. The acceleration that results from a change in velocity will not be in the same direction as the velocity. Therefore, an acceleration that is always perpendicular to the velocity is required for an object to move in a circular path. The circular motion could either be uniform or non-uniform.

## Uniform Circular Motion

### Concept of Uniform Circular Motion:

The magnitude of the velocity will always be constant in a uniform circular motion. But from every point, the velocity’s direction will vary steadily. It implies that the object will travel in a circle. And the object will finish each of its numerous trips around the path in exactly the same amount of time.

The motion along a curved path can be described as circular. Uniform circular motion is the movement of any object along a circular path that travels the same distance around the circumference in the same amount of time. Any such motion has a constant speed and a continuously changing direction.

In a uniform circular motion, the tangential speed will be constant at every point along the circumference. Every point along the circumference of this tangential velocity vector is tangent.

Additionally, the acceleration vector is always pointed in the direction of the centre of the circle the object’s motion creates. Due to its distance from the center, this acceleration is either referred to as “radial acceleration” or “centripetal acceleration,” which denotes that it is “center seeking.”

The formula for Uniform Circular Motion

Numerous Indian educational boards include the Uniform Circular Motion Formula in their physics curricula. It is also covered in several Physics classes’ curricula. You can learn the Uniform Circular Motion Formula with the aid of textbooks. The recommended textbooks are the easiest for students to use as learning resources for the uniform circular motion formula.

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### Solved Examples

Q.1: A player is moving with a constant tangential speed of 50 m per second. He takes one lap around a circular track in 40 seconds. Calculate the magnitude of the acceleration of the player.

Solution:

Given parameters:

The magnitude of Velocity, V = 50 m per second

Time period, T = 40 seconds.

We know that,

V=2πRT

Therefore,R=T×V2π

Putting values,

R=40×502×3.14

R = 31.84

Now,