Why are the contact points of the surface of | vedclass

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(C) In pure rolling motion,a circular body rotates about its center of mass while the center of mass moves linearly. Let $v_{cm}$ be the linear veloci

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Because the velocity of the point of contact relative to the surface is zero.

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(C) In pure rolling motion,a circular body rotates about its center of mass while the center of mass moves linearly. Let $v_{cm}$ be the linear velocity of the center of mass and $\omega$ be the angular velocity of the body. The velocity of any point on the rim of the body at a distance $R$ from the center is the vector sum of the linear velocity of the center and the tangential velocity due to rotation. For the point of contact with the ground,the linear velocity is $v_{cm}$ (forward) and the tangential velocity due to rotation is $v_{rot} = R\omega$ (backward). In pure rolling,the condition is $v_{cm} = R\omega$. Therefore,the net velocity of the point of contact is $v_{net} = v_{cm} - R\omega = 0$. Since the net velocity is zero,the point of contact is instantaneously at rest relative to the surface.

Why are the contact points of the surface of a circular body stationary during pure rolling motion?

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