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Question

Two thin planks are moving on four identical cylinders as shown. There is no slipping at any of the contact points. Calculate the ratio of angular speed of upper cylinders to lower cylinders


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Solution


Since there is no slipping between contact points, motion of the cylinders is as shown in the figure.
Let R be the radius of the cylinders.
For upper cylinder,
v1+Rω1=2v ........(1) [top]
ω1Rv1=v .......(2) [bottom]

For lower cylinders,
v2+Rω2=v ......(4) [top]
v2=Rω2 .........(3) [bottom]

From (1),(2),(3) and (4), we get

ω2=v2R and ω1=3v2R

ω1ω2=31

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