Question

Derive the expressions for the centripetal acceleration.​

Answer 1

Centripetal acceleration ac is the acceleration experienced while in uniform circular motion. It always points toward the center of rotation. It is perpendicular to the linear velocity v and has the magnitude ac=v2r;ac=rω2 a c = v 2 r ; a c = r ω 2 .

Hence, vector form of centripetal acceleration is: →a=−ωR2(sinωt ˆi+cosωt ˆj) which shows that it's direction is towards the centre and along the string at every point of circular track. Expression for centripetal acceleration of a body undergoing circular motion: As we derived →a=−ωR2(sinωt ˆi+cosωt ˆj)

a force which acts on a body moving in a circular path and is directed towards the center of the circular path. The expression for it is. F=mv2/r=mrw2=mwv. Directed towards the center.

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