Unformatted text preview: r is its position vector. Now, we know that ˙ Ω = , v I = u e r , r = f e r where e r is a unit vector in the radial direction. Hence, a = 2 ω k × u e r + ω k × ( ω k × f e r ) = 2 ω u e θ + ω 2 f k × e θ = 2 ω u e θ − ω 2 f e r where e θ is a unit vector in the circumferential direction. Finally, we can express u as a function of ω and f from the given information. That is, we know that u = dr dt = dr d θ d θ dt = w f − 1 2 f π / 2 − W ω = ωf π Therefore, the collar’s acceleration is a = − ω 2 f e r + 2 π ω 2 f e θ...
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 '06
 Shiflett
 Acceleration, Angular Momentum, Angular velocity, Collar, constant angular velocity

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