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Tangential Acceleration

# Tangential Acceleration

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Tangential acceleration of an object travelling in circular motion is the acceleration caused due to change in the magnitude of the object’s velocity. Since in a circular paththe object continuously changes its direction to move in a circle, tangential acceleration is calculated by finding the change in the velocity at a particular instant of time.Tangential acceleration is a vector quantity and therefore the direction of the tangential acceleration at a particular point on the path is always in direction of the tangent drawn at that point on the circle.

Example 1: An object with an initial speed of 25m/sec travels in a circular path and accelerates uniformlychanging its speed to 40msec in 5secs. What is the object’s tangential acceleration?

Given: Initial speed, vi = 25m/sec/

Final speed, vf = 40m/sec

Time, t = 5secs

Tangential acceleration, at = |dv/dt|

Here, dv = change in speed = (vf – vi) and dt = time interval

This gives: at = (40 – 25)/5 ==> at = 15/5 = 3m/sec2

Example 2: A car starts from rest and travels on a circular road with a uniform acceleration. If in a time period of 2secs, it changes its velocity to 12m/sec, then calculate its tangential acceleration.

Given: Car starts from rest ==> Initial speed, vi = 0m/sec

Final speed, vf = 12m/sec

Time, t = 2secs

Tangential acceleration, at = |dv/dt|

This gives: at = (12 – 0)/2 ==> at = 12/2 = 6m/sec2