# Tangential Velocity Formula

Tangential velocity is the linear speed of any object moving along a circular path. A point on the outside the edge of a turntable moves greater distance in one complete rotation than a point near to the center. When a body moves in a circular path at a distance r from the center, the body’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.

Tangential Velocity Formula is given by,

$V_{t}\,&space;=\,&space;r\frac{d\Theta&space;}{dt}$

Where,

r = radius of circular path and

ω = angular velocity

Hence the Tangential Velocity Formula can also be given by,

$V_{t}\,&space;=\,&space;r\omega$

If time t is only given, then

Tangential Velocity is determined using formula,

$V_{t}\,&space;=\,&space;\frac{2\pi&space;r&space;}{t}$

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).

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 = ½ of diameter of 60 cm

= 30 cm = 0.30 m.

Angular velocity, ω = 40 rad/s.

Tangential velocity formula is given by,

Vt = ω r

= 40 x 0.30

= 12 m/s

Example 2

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

Solution:

Given:

Tangential velocity, Vt = 10 m/sec

Angular velocity, ω, = 5 radians/sec.

the formula for tangential velocity is given by,

Vt = ω r

Vt / ω = r

10/5= r

r = 2 m