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Homework Help: Angular momentum of particle problem

  1. Oct 18, 2009 #1
    1. The problem statement, all variables and given/known data

    A 3-lb collar can slide on a horizontal rod which is free to rotate about a vertical shaft. The collar is initially held at A= 0.5 ft by a cord attached to the shaft. A spring constant of 2 lb/ft is attached to the collar and to the shaft and is undeformed when the collar is at A=0.5 ft. As the rod rotates at the rate of (theta dot)= 16 rad/s, hte dord is cut and the collar moves out along the rod. Neglecting friction and the mass of the rod, determine (a) the radial and transverse components of the acceleration of the collar at A, (b) the acceleration of the collar relative to the rod at A, (c) the transverse component of the velocity of the collar at B = 1.5 ft.


    2. Relevant equations

    r' = transverse velocity r'' = transverse acceleration
    (theta)' = radial velocity (theta)'' = radial acceleration

    h=rvsin(phi)


    3. The attempt at a solution

    (a) Spring Force, Fs=kx=mar= 0
    (mar = mass * transverse acceleration)

    (b) m[ r'' - r (theta)'squared]

    (c) h0=hf (initial = final)
    r0v0sin(phi)=rvBsin(phi)
    r(r0 theta') = rvB
    vB= [r0(squared) * theta]/ rf
     
  2. jcsd
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