# 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. The object may be moving in uniform motion and has a constant angular rate of rotation and speed or non-uniform motion with changing rate of rotation. Objects moving in circles possess a speed which is equal to the distance travelled 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

$V_{c}=2\pi r/T$

Where,

r denotes the radius of the circular orbit

T is the time period

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

$V_{c}=\omega r$

Where,

ω denotes the angular velocity ($\omega =2 \pi /T$)

r is the radius of the circular path

### Solved Examples

Example 1

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

Solution

Given parameters are,

Angular velocity ω = 45 rad/s

The circular velocity formula is given by

$V_{c}=\omega r$

Vc = 45 × 0.75

Vc = 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 ×$10^{8}$ m

Period T = 365.25 days

The circular velocity is expressed by

$V_{c}=2\pi r/T$

$V_{c}=(2)(3.14)(1495*10^{8})/365.25$
Vc = 2.571 × 109 m/s.

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