GATE 2017 ME (ME1) – Question 57
An inline slider-crank has crank length 3 m and connecting-rod length 4 m. At an instant when the crank and rod are perpendicular, slider speed is 1 m/s. Find the crank angular-speed magnitude in rad/s, to three decimal places.
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Correct answer: 0.26 to 0.29
Explanation
The 3 m and 4 m links form the legs of a right triangle, so the crank-centre-to-slider distance is 5 m. The connecting rod makes cosine $4/5$ with the slider direction. The crank-pin velocity is perpendicular to the crank and hence parallel to the rod. Equating velocity projections along the rod gives $v_{pin}=v_{slider}(4/5)=0.8$ m/s. Therefore $|\omega|=v_{pin}/3=0.266667$ rad/s, or 0.267.