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Unformatted text preview: Problem Set 8: Problem 1.
Problem: A gun with barrel OP of length is mounted on a turret as shown. The rates of change of the barrel's azimuth and elevation angles, and , are d/dt = and d/dt = 1 . Determine the 3 angular velocity of the barrel, , the angular acceleration of the barrel, , the absolute velocity of Point P, vP , and the absolute acceleration of Point P, aP . Solution: We are given d/dt = and d/dt = 1 . Both rotations are in the counterclockwise direction, 3 so that d 1 d k = k and = = = dt dt 3 thus, the angular velocity of the barrel is ~ =+ = 1 i+k 3 The barrel's angular acceleration is given by the Coriolis Theorem, viz., = d + = 0 + k dt 1 i+k 3 = 1 2 j 3 The absolute velocity of Point P is given by ~ vP = rP where rP is given by rP = sin j + cos k Thus, taking the indicated cross product, Point P's absolute velocity is i vP =
1 3 j 0 sin k cos = - sin i + 1 1 cos j - sin k 3 3 0 Similarly, Point P's absolute acceleration is ~ ~ ~ aP = rP + ( rP ) = rP + vP ...
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This note was uploaded on 05/12/2010 for the course AME 301 taught by Professor Shiflett during the Spring '06 term at USC.
- Spring '06