Tangential Velocity

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Tangential velocity of an object travelling in a circular motion is the instantaneous velocity of the object at a particular instant of time on the circular path. In order to travel in a circular path, the object needs to change its direction at every instant and hence tangential velocity is a vector quantity as it has both magnitude and direction. The magnitude of the tangential velocity is the speed of the object with which it’smoving in a circle, and its direction is along the tangent drawn at that particular point on the circle.

Example 1: Roger drives the car on a circular track of radius 6m. What is the tangential velocity of Roger’s car if it takes 4secs to complete one circular rotation around the track?

Tangential velocity, vt = (Distance travelled)/ (Time taken)
Distance travelled on a circular track = Circumference of the circle = 2πr
This implies: Distance, d = 2 * π * 6 = 12π meters.
Time, t = 4secs
Tangential velocity, vt = 12π/4 = 9.42m/sec
 
Example 2: An object moves on a circular path of radius 4m. What is the time taken by the object to cover one circular rotation when its tangential velocity is 8.6m/sec?

Tangential velocity, vt = (Distance travelled)/ (Time taken)
Distance travelled on a circular track = Circumference of the circle = 2πr
This implies: Distance, d = 2 * π * 4 = 8π meters.
Tangential velocity, vt = 8.6m/sec
Time taken = (distance)/ (tangential velocity) ==> time= 8π/8.6 = 2.92secs
This implies time taken to complete one circular rotation = 2.92secs

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