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Spring Angular Momentum Problem

  1. Jan 19, 2015 #1
    1. The problem statement, all variables and given/known data
    Capture.PNG
    2. Relevant equations
    PE spring = .5 kx^2
    KE rotation = .5 I w^2

    3. The attempt at a solution
    I tried to do a conservation of energy
    (Note: I = moment of inertia, L = length)
    3*.5*k L^2 = .5 I w^2

    I =3 M R^2 ---> a^2 = b^2 + c^2 -2bc cos(a) (the reason why I am using law of cosines is to find the radius from the center to each point mass)

    R = L / sqrt(3)

    I = ML^2

    3*.5*k*L^2 = .5*M*L^2 *w^2

    k = 1/3 * Mw^2 which is wrong. The answer is C. How do you do this?
     
  2. jcsd
  3. Jan 19, 2015 #2

    Quantum Defect

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    This is an equilibrium problem. The effective restoring force of the springs, acting on the masses, provides the centripetal force.
     
  4. Jan 19, 2015 #3
    I see, Let me try. So the mass is 3m, and the Radius is calculated by law of cosines to be 4L/rad(3). so:

    3*k*cos(30)* L = m*w^2 * 4L/rad(3)
    k = m*w^2 * 2/9

    I'm still messing up. What am I doing?
     
  5. Jan 19, 2015 #4

    Quantum Defect

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    Draw a vector diagram for the forces acting on one of the balls.
     
  6. Jan 19, 2015 #5
    Capture.PNG
     
  7. Jan 19, 2015 #6

    Quantum Defect

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    Set the net inward force provided by the springs equal to the centripetal force, to maintain uniform circular motion.
     
  8. Jan 19, 2015 #7
    OK

    2 * f spring* cos(30) = f centripetal = rad(3) * f spring

    k*L* rad(3) = m w^2 * 2L/rad(3)

    k = 2/3 * m w^2

    Thank you!
     
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