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- Homework Statement
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- Relevant Equations
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**a**inside a fixed cylinder of radius

**b,**the cylinder that rolls rotate about its own axis in such way that it does not skid/slip.

Now, the thing that is making myself confused is the constraint condition: I know the answer is ##(b-a) \dot \theta = a \dot \phi##, but i can't understand it! Aat least to me, the condition of non slipping is equivalent to say the circunference traced by a point initially at the contact with the rough surface is equal to the distance traced by the body itself. So, the cylinder moved ##b \theta## while it rotates ##a \phi##. So the condition, to me, could be written as ##(b) \dot \theta = a \dot \phi##. I don't understand why it is being used (b-a) instead! That is, this is the distance traveled by the CG, but shouldn't we seek for the distance traveled by the point of contact?