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Unformatted text preview: Problem Set 8: Problem 5.
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: We know that in a coordinate frame rotating at angular velocity = k about Point A, the collar is not accelerating, i.e., a =0 where a is the acceleration seen by a rotating observer. In general, the collar's absolute acceleration is a = a + r + 2 v + ( r) where v is the collar's velocity as seen by the rotating observer and r is its position vector. Now, we know that = 0, v = u er , r = er where er is a unit vector in the radial direction. Hence, a = 2 k u er + k ( k er ) = 2u e + 2 k e = 2u e - 2 er where e is a unit vector in the circumferential direction. Finally, we can express u as a function of and from the given information. That is, we know that u= Therefore, the collar's acceleration is a = - 2 er + 2 2 e dr d dr = = dt d dt -1 2 /2 - 0 = ...
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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