## 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:

arad = v2/R

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,

arad = 4π^{2}R/T^{2}

Where,

arad= The Radial acceleration

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.

We are already known that,

V = 2πR/T

Thus, R = T × V/2π

Plugging in the values,

R = 60×80/2×3.14

R = 75.40

Now,

arad = 4π^{2}R/T^{2}

put R = T × V/2π, we get

= 4π^{2}R

= 4π^{2}×T×V/2π

= 2×π×V

= 2 × 3.14 × 80/60

= 8.38

Acceleration will be 8.38ms^{-2}

Q1. What is the Use of Uniform Circular Motion Formula (Circular Motion Formula)?

Answer: For an object moving along a curved circular path, the direction of its velocity should change. It is owing to the fact that at each point on the circular motion equations tangent will provide the direction. A change in velocity induces acceleration which will not be in a similar direction as the velocity. Thus, for an object moving along a circular path, there should be an acceleration, which will always be perpendicular to the velocity. The circular motion could either be uniform or non-uniform.

Q2. What is the Concept of Uniform Circular Motion?

Answer: Uniform circular motion indicates that the magnitude of the velocity of an object will invariably be constant. However, the direction of the velocity will alter at a constant rate from each point. It implies that the path of the object will create a circle. And the object will accomplish the repeated trips around the path in the same amount of time every time.

Q3. Why is the Term Circular Used in Circular Motion Equations?

Answer: The circular term is applicable to explain the motion in a curved path. The motion of any object throughout some circular path, covering equal distance along the circumference in the same time period is called the uniform circular motion. In any such motion, the speed remains constant, with continually changing direction. In a uniform circular motion, the tangential speed at each point on the circumference will be constant.