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Motion of Rolling Cylinder in Fixed Cylinder: Confusing Constraint Condition
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[QUOTE="haruspex, post: 6527275, member: 334404"] No. Start by imagining the small cylinder rotating through dϕ but its centre remaining fixed (so it is slipping). adϕ of its perimeter skids across a fixed point on the outer cylinder. Call the point on its perimeter in contact with the outer cylinder P. Now move the small cylinder, without further rotation, to where it would have been had it rolled instead. If it was rotating clockwise then this involves moving it anticlockwise. Note that the point of contact is no longer P. Instead, it is adθ anticlockwise around from P. So length of perimeter of the small cylinder that would have come into contact during rolling is adϕ+adθ. Thus adϕ+adθ=bdθ, or adϕ=(b-a)dθ. (I assume you know that the easy way is to consider the small cylinder rotating about its point of contact, so its centre moves through an arc length (b-a)dθ.) [/QUOTE]
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Motion of Rolling Cylinder in Fixed Cylinder: Confusing Constraint Condition
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