# Uniform Circular Motion Formula

## Formula of Uniform Circular Motion

When the radius of the circular path is R, and the magnitude of the velocity of the object is V. Then, the radial acceleration of the object is:

Similarly, this radial acceleration is always perpendicular to the velocity direction. Its SI unit is m2s−2.

The radial acceleration can be mathematically written using the period of the motion i.e. T. This period T is the volume of time taken to complete a revolution. Its unit is measurable in seconds.

### Circular Motion Formulas

Of an object, if the magnitude of the velocity travelling in uniform circular motion is v, then the velocity is equivalent to the circumference C of the circle divided by the time period. Thus,

V = C/T

The circumference of the circle will be equivalent to pi (π) multiplied by the radius R.

Thus, C = 2πR

At any point in the motion, thus the velocity is,

V = 2πR/T

Using this value in the equation for radial acceleration, we will get,

Where,

R = The radius of the circular path

T = Period of time

V = The Velocity

C = The Circumference

### Solved Examples for Uniform Circular Motion Problems

Example:

A cricket player is moving at a constant tangential speed of 80 m per second. He takes one lap around a circular track in 60 seconds. Find out the magnitude of the acceleration of the player.

Solution:

Known parameters:

The magnitude of Velocity, V = 80 m/second

Time period, T = 60 seconds.

V = 2πR/T

Thus, R = T × V/2π

Plugging in the values,

R = 60×80/2×3.14

R = 75.40

Now,

put R = T × V/2π, we get

= 4π2R

= 4π2×T×V/2π

= 2×π×V

= 2 × 3.14 × 80/60

= 8.38

Acceleration will be 8.38ms-2