# Tangential Speed

What is tangential speed ? Calculate tangential speed for radius r.

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Tangential speed is the speed at which the particle which is moving in a circular path would move in if the force acting on the particle towards the center were to be eliminated. This could be the gravitational force, the force exerted by a string or any other similar force.

For a body rotating in a circle of radius r the time period or the time taken to complete one rotation is T. The tangential speed in this case at any point is given as v = 2*pi*r / T.

So if the force acting towards the center were to be eliminated the particle would move in a tangential direction to the circle it was moving in, at a speed equal to 2*pi*r / T.

Tangential speed occurs in rotaional motion and it is the spped of a point located at a radius r.

The vector v is perpendicular to the radius and it has a magnitude and a direction.

The tangential speed could be calculated when the angular speed is given

The angular speed is omega and the tangential speed is v.

**v = r*omega**

We can connect the velocity with the angular speed in this way:

- we'll link the distance s, covered by the point along the circle, with the angle measured in radians:

s = r*theta (1)

theta - the angle measured in radians

r - the radius of the circle

But v = s/t (2)

s - displacement

t - time

We'll substitute (1) in (2):

v = r*theta/t

But the ratio theta/t is the angular speed omega.

**v = r*omega**