In the given arrangement, the rod is free to rotate about the hinge and it is in constant contact with the equilateral triangular block of base length 2 a 3 . If the block is moving horizontally with a speed v = 20 ms - 1 , then find the magnitude of the angular velocity of the rod (in rad . s - 1 ) at the instant when θ = 30 o . [Given that a = 1 m ]

Question

In the given arrangement, the rod is free to rotate about the hinge and it is in constant contact with the equilateral triangular block of base length 2 a 3 . If the block is moving horizontally with a speed v = 20 ms - 1 , then find the magnitude of the angular velocity of the rod (in rad . s - 1 ) at the instant when θ = 30 o . [Given that a = 1 m ],

MARKS App · Accepted Answer

h x = tan θ x = h cot θ d x d t = − h cosec 2 θ d θ d t ω = v h sin 2 θ = 20 1 × 1 4 = 5 rad/s

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