derive the expression for centripetal acceleration
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Explanation:
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 .
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It is also useful to express ac in terms of angular velocity. Substituting v = rω into the above expression, we find ac=(rω)2r=rω2 a c = ( r ω ) 2 r = r ω 2 . We can express the magnitude of centripetal acceleration using either of two equations: ac=v2r;ac=rω2 a c = v 2 r ; a c = r ω 2 .
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