Centripetal Acceleration Equation

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Centripetal acceleration is experienced by a body when it undergoes a circular motion. Centripetal acceleration points toward the center of the circular path where the object is moving around. We feel centripetal acceleration when a train is moving in circular path and we are inside the that train, we feel a force pushing them to the outer edge of the circular path.  This feeling is often described as centrifugal force, although there is no real force pushing or pulling passengers away from the circle.


Centripetal acceleration of a body is expressed as ac. A body in a circular path of radius ‘r’ moving with uniform velocity ‘v’ has centripetal acceleration of
                                                                        ac = v2/r


Example 1: A wagon moving at 15 m/s takes a u-turn of radius 8m. What is the acceleration of the car?

Solution: As the wagon is taking u-turn it is undergoing circular motion. Hence, the wagon will experience centripetal acceleration. Radius (r) of the circular path is 8m and velocity (v) of the wagon is 15 m/s. Centripetal acceleration is given as
 ac = 152 /8

ac = 225/8

ac = 28.12 m/s2

Example 2: A stone is whirling around a circle of radius 0.4m with acceleration of 7 m/s2. What is the velocity of the stone?

Solution: As the stone is tracing a circular path hence, acceleration experienced by the stone is centripetal acceleration. Radius is given as 0.4 m and acceleration is 7 m/s2. Hence, from the expression of centripetal acceleration we can write

7 = v2/0.4 (v is the velocity of the stone)

v2 = 7x0.4

v2 = 2.8

v = sqrt (2.8)

v = 1.67 m/s

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