p0709 - r is its position vector. Now, we know that = , v I...

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314 CHAPTER 7. RIGID-BODY KINEMATICS 7.9 Chapter 7, Problem 9 Problem: Rod AB is rotating in the counterclockwise direction with constant angular velocity ω . Collar P slides without friction as shown with constant relative speed u .I f r = 1 2 f when θ =0 o and the collar reaches Point B where r = f when θ =90 o , what is Collar P’s acceleration vector at the instant it reaches Point B? Express your answer as a function of ω and f . Solution: We know that in a coordinate frame rotating at angular velocity = ω k about Point A, the collar is not accelerating, i.e., a I = 0 where a I is the acceleration seen by a rotating observer. In general, the collar’s absolute acceleration is a = a I + ˙ × r +2 × v I + × ( × r ) where v I
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Unformatted text preview: r is its position vector. Now, we know that = , v I = u e r , r = f e r where e r is a unit vector in the radial direction. Hence, a = 2 k u e r + k ( k f e r ) = 2 u e + 2 f k e = 2 u e 2 f e r where e is a unit vector in the circumferential direction. Finally, we can express u as a function of and f from the given information. That is, we know that u = dr dt = dr d d dt = w f 1 2 f / 2 W = f Therefore, the collars acceleration is a = 2 f e r + 2 2 f e...
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This note was uploaded on 12/16/2010 for the course AME 301 at USC.

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