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Dynamics_Part56

Dynamics_Part56 - Problem Set 8 Problem 1 Problem A gun...

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Problem Set 8: Problem 1. Problem: A gun with barrel OP of length f is mounted on a turret as shown. The rates of change of the barrel’s azimuth and elevation angles, β and γ , are d β /dt = and d γ /dt = 1 3 . Determine the angular velocity of the barrel, ω , the angular acceleration of the barrel, α , the absolute velocity of Point P, v P , and the absolute acceleration of Point P, a P . Solution: We are given d β /dt = and d γ /dt = 1 3 . Both rotations are in the counterclockwise direction, so that = d β dt k = k and ω = d γ dt = 1 3 thus, the angular velocity of the barrel is ˜ ω = + ω = w 1 3 i + k W The barrel’s angular acceleration is given by the Coriolis Theorem, viz.,
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