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Page 1 of 2 Circular motion Angle in radians = arc length radius Convert degrees to radians 180 Linear velocity Velocity = r s r radians = Angular velocity displacement time angular velocity = v = s t = = = angle traced out time t Relationship between linear velocity and angular velocity = v v = r Proof : linear velocity = radius x angular velocity (v = r) Suppose the moving particle traces out an angle in time t seconds as it moves a distance s From the definition of the radian t = s rt = t = = r = v = s r s x 1 t r v x 1 r v r divide both sides by t but = / t v = s/t Page 2 of 2 Note : A body travelling in a circular path with a constant speed has a changing velocity (due to the change in direction) and is therefore accelerating Centripetal acceleration: the acceleration towards the centre of a circle of a body moving in a circular path. Linear centripetal acceleration a = v2 r Angular centripetal accelaration a = r 2 (page 40 tables) Centripetal force : the force towards the centre needed to keep a body moving in a circular path. Note Force = mass x acceleration Linear centripetal force F = m v2 r F = mxa Angular centripetal force F = m r 2