# Circular Velocity Formula

The movement of an object along the circumference of a circle or rotation along its circular path is known as circular motion. It may be uniform and exhibit a constant angular rate of rotation and speed, or non-uniform with changing rate of rotation.

Rotating around a fixed axis of a three-dimensional body involves circular motion of its parts. The motion equation describes the movement of the center of mass of a body. Objects moving in circles possess a speed which is equal to the distance traveled per time of travel. By multiplying the rotational frequency with the circumference we can determine the average speed of the object.

The circular velocity formula is expressed as,

**vc = 2 πr / T**

Where in,

r denotes the radius of the circular orbit

T is time period.

In terms of angular velocity ω, the circular velocity is described as

(FORMULA NEEDS TO BE CREATED)

**vc = ω r**

Where in,

ω denotes the angular velocity,

r indicates the radius of circular path

**Example 1**

Determine the circular velocity of a pebble tied to a thread of 0.75 m when swirled is rotating with angular velocity of 45 radians /s

**Solution**

Given parameters are,

Angular velocity ω = 45 rad/s

radius = 0.75 m

The circular velocity formula is given by

vc = ω r

vc = 45 × 0.75

= 33.75 m/s.

**Example 2**

Determine the circular velocity of the earth if the distance from sun to earth is 149500000 km and

period of earth revolution is 365.25 days.

**Solution**

Given parameters are,

radius r = 1495 × 108 m

Period T = 365.25 days

The circular velocity is expressed by

vc = 2πr / T

vc = 2×π×1495×108 / 365.25

= 2.571 × 109 m/s.