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The cylinder of the radius R is confined to roll without slipping at A and B. If the plates have the velocities as shown, determine the angular velocity of the cylinder.

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$\frac{3 V}{2 R}$

$\frac{6 V}{R}$

$\frac{7 V}{R}$

$\frac{9 V}{R}$

answer is A.

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Detailed Solution

No slip condition at $A, v_{cm} + Rω = ν \dots \dots \dots . (1)$

No slip condition at $B, v_{cm} - Rω = - 2 ν \dots \dots \dots . (2)$

$(1) - (2) \Rightarrow 2 Rω = 3 v \Rightarrow ω = \frac{3 v}{2 R}$

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