Unformatted text preview: Problem Set 8: Problem 2.
Problem: Rod AB is rotating in the counterclockwise direction with constant angular velocity . Collar P slides without friction as shown with constant relative speed u. If r = 1 when = 0o and the 2 collar reaches Point B where r = when = 90o , what is collar P's acceleration vector at the instant it reaches Point B? Express your answer as a function of and . Solution: An observer in a coordinate frame rotating with angular velocity = k about Point D sees the motion of Point B as pure rotation with angular velocity = i about the center of the disk (Point C). Thus, the relative velocity and acceleration vectors are vB aB = rB/C = i (-R k) = R j = vB = i R j = 2 R k vB = vB + rB/D The absolute velocity of Point B is given by where rB/D is given by 1 rB/D = -2R i + R j - R k 2 Thus, substituting for vB and taking the indicated cross product, we find vB = R j + R -2 j - Point B's absolute acceleration is where vB is the collar's velocity as seen by the rotating observer and rB/D is its position vector relative to the collar. Now, we know that = 0, while vB and aB are as given above. Thus, the absolute acceleration of Point B is 1 aB = 2 R k + 2 k R j + k k -2R i + R j - R k 2 1 = 2 R k - 2 R i + k R -2 j - i 2 1 = 2 R k - 2 R i + 2 R 2 i + j 2 1 = 2( - )R i + 2 R j + 2 R k 2 aB = aB + rB/D + 2 vB + ( rB/D ) 1 i 2 1 = - R i + ( - 2)R j 2 ...
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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