GATE ME 2023 Set 1 — Question 38
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Engineering Mechanics → Dynamics → Kinematics of Rigid Bodies
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Question
The figure shows a wheel rolling without slipping on a horizontal plane with angular velocity . A rigid bar PQ is pinned to the wheel at P while the end Q slides on the floor.What is the angular velocity of the bar PQ?
Correct answer
(D) ω₂ = 0.25ω₁
Solution
1.Let the contact point of the wheel with the floor be R. Since it rolls without slipping, R is the instantaneous center of rotation (ICR) of the wheel. .
2.Velocity of point P: . From the diagram, P is at relative to R at . So .
.3.Velocity of point Q: Since Q slides on the floor, .
4.Kinematics of bar PQ: .
From the diagram, . Let ..
5.Equating the components: .
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