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A cylindrical body is pure rolling, what will be the degree of freedom for it? I am confused between 2 and 1 if slipping occurs than it has 2 but in pure rolling there's no slipping so what will it be then?

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    $\begingroup$ If there is no slipping, then there is one. You are on the right track. $\endgroup$ – garyp Jun 21 '16 at 12:11
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if the body is rolling on a plane, then its degree of freedom is 2: one for rotation about the body's axis and one for translation of its center of gravity in forward and backward direction.

if there is no slipping, the translation can be calculated from the rotation and the radius of the block. Thus the degree of freedom is degenerated to 1.

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