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Let us consider a rolling whithout slipping cylinder. We can work in two different ways. First considering the motion as a pure translation of the cm plus a rotation about the cm. Second, considering the motion as a pure rotation about the instantaneous axis from the contact point with the ground.

The cylinder is moving with constant velocity. In the first way, the cm has no acceleration. But in the second way, the cm has a centripetal acceleration vcm^2/R.

What is going wrong here?

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# Cm acceleration

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