# Tangential Velocity Formula

Tangential velocity is the linear speed of any object moving along a circular path. A point on the outside edge of a turntable moves a greater distance in one complete rotation than a point near to the center.Â When a body moves in a circular path at a distance r from the center, the bodyâ€™s velocity is directed tangentially at any instant. This is known as tangential velocity. In other words, the linear velocity is its tangential velocity at any instant.

## Formula of Tangential Velocity

The tangential velocity formula is given by,

$V_{r}=r\omega$

Where,

• r is theÂ radius of the circular path and
• Ï‰Â is the angular velocity

The tangential velocity formula is applied in calculating the tangential velocity of any object moving in a circular path.

It is expressed in meter per second (m/s).

### Solved Examples

Example 1

If the angular velocity of a wheel is 40 rad/s, and the wheel diameter is 60 cm, calculate the tangential velocity.

Solution:

Given:

Radius, r = Â½ of diameter of 60 cm

r = 30 cm = 0.30 m

Angular velocity, Ï‰ = 40 rad/s.

The tangential velocity formula is given by,

$V_{r}=r\omega$

Â Â = 40 x 0.30

Â  VrÂ = 12 m/s

Example 2

If a wheel moves at 10 m/sec, and its angular velocity is 5 radians/sec, calculate the radius of the wheel.

Solution:

Given:

Tangential velocity, Vr= 10 m/sec

Angular velocity, Ï‰, = 5 radians/sec.

the formula for tangential velocity is given by,

Vr = Ï‰ r

Vr / Ï‰ = r

10/5= r

r = 2 m