p0611 - 6.11. CHAPTER 6, PROBLEM 11 293 6.11 Chapter 6,...

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6.11. CHAPTER 6, PROBLEM 11 293 6.11 Chapter 6, Problem 11 Problem: Three identical spheres A, B and C of mass m are attached to a ring G with strings of length f . Initially, the spheres all rotate about the ring with rotation rate ω and the ring has velocity v G = v o i . Then, the ring breaks and the spheres are free to move in the xy plane, which is a frictionless surface. After the ring breaks, we observe that the velocities of spheres A and C are v A = 3 V j and v C =3 V i . Also, distances a and d are related by a = d 3 . Express your answers below in terms of V and d . (a) Determine the initial speed of the ring, v o . (b) Determine the string length, f . (c) Determine the initial rate, ω , at which the spheres were rotating about Point G. Solution: First, we compute the velocity of the center of mass by appealing to conservation of linear momentum. Then, we appeal to angular-momentum conservation in order to determine string length, f . Finally, we turn to total energy conservation to establish the initial value of the angular-rotation rate,
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This note was uploaded on 12/16/2010 for the course AME 301 at USC.

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p0611 - 6.11. CHAPTER 6, PROBLEM 11 293 6.11 Chapter 6,...

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