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'C' is a uniform cylinder to which a rod 'AB' is pinned at 'A' and the other end of the rod 'B' is moving along a vertical wall as shown in fig.
written 9.5 years ago by gravatar for teamques10 teamques10 ★ 70k •   modified 5.7 years ago

If the end 'B' of the rod is moving upward along the wall at the speed of 3.3 m/s find angular velocity of the cylinder assuming that it is rolling without slipping.

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engineering mechanics
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written 9.5 years ago by gravatar for teamques10 teamques10 ★ 70k

enter image description here

Considering rod AB

$WAB= VB/IB \\ = 3.3/1.3 \cos30 \\ = 2.93 rad/s $

Now, $VA = WAB . IA \\ = 2.93 * 1.3 \sin 30 = 1.905 m/s $

Now, As cylinder C is rolling without slipping, its ICR lies at point of contact between cylinder and ground

$WC = VA * 0.6 = 1.905 * 0.6 = 1.143 rad/s $

Angular velocity of cylinder is 1.143 rad/s

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