Project ForgeFor an inline slider-crank mechanism, the lengths of the crank and connecting rod are 3 m and 4 m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 1 m/s, the magnitude of angular velocity (upto 3 decimal points accuracy) of the crank is __________ radian/s.
Explanation
With crank r=3, rod l=4, and the rod perpendicular to the crank, geometry gives tanθ=l/r=4/3 (sinθ=4/5, cosθ=3/5). Since OC⊥CP, the crank-pin velocity V_C (always ⊥OC, magnitude ωr) is entirely directed along CP. Equating the rigid-rod-preserving component of velocity along CP for both C and the slider P: V_P·(CP unit vector) = V_C. Working out CP direction (0.8,-0.6) and V_C=ω(-2.4,1.8) gives V_P×0.8 = -3.0ω, so with |V_P|=1: |ω| = 1/3.75 ≈ 0.267 rad/s.
Source: GATE ME 2017 Session 1 (ME-1) (2017)
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