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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 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=v…….(1)

No slip condition at B
Vcm - R𝝎=-2v…….(2)
(1) –(2) $\Rightarrow$ 2R𝝎=3v $\Rightarrow$ 𝝎=𝟑𝒗/𝟐𝑹

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