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p0711 - 320 CHAPTER 7 RIGID-BODY KINEMATICS 7.11 Chapter 7...

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320 CHAPTER 7. RIGID-BODY KINEMATICS 7.11 Chapter 7, Problem 11 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 ,a re d β /dt = and d γ /dt = 1 3 .D e t e rm i n et h e 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 i = 1 3 i 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., α = d I ω dt + × ω = 0 + k × w 1 3 i + k W = 1 3 2 j The absolute velocity of Point P is given by v P = ω × r P where r P is given by r P = f cos γ j + f sin γ k Thus, taking the indicated cross product, Point P’s absolute velocity is v P

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p0711 - 320 CHAPTER 7 RIGID-BODY KINEMATICS 7.11 Chapter 7...

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