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Glob on the Table

  1. Nov 30, 2011 #1
    1. The problem statement, all variables and given/known data
    On a frictionless table, a glob of clay of mass 0.72 kg strikes a bar of mass 1.34 kg perpendicularly at a point 0.23 m from the center of the bar and sticks to it.

    If the bar is 1.22 m long and the clay is moving at 8.3 m/s before striking the bar, what is the final speed of the center of mass?

    At what angular speed does the bar/clay system rotate about its center of mass after the impact?

    2. The attempt at a solution

    Here is what I did

    Vcm = sum(mi*vi) / total mass

    in this case just one body has velocity:
    Mclay = .72 kg
    Mbr = 1.34 Kg
    Mtotal = 2.06 kg
    Vclay = 8.3 m/s

    Vcm = 2.901 m/s

    which is correct, I got the first part, but here is the second part that I got wrong

    now calculate the angular speed:

    angular speed - omega

    omega = v /r

    v - is the linear velocity on the trajectory of the body (tangential velocity)
    r - is the distance between the body which rotate and the center of rotation

    in your case the centre of rotation is the center of mass and r is the distance of the clay to the centre of mass

    D = 1.22 m
    d = 0.23 m

    the centre of the bar related to one end is D/2
    the position of the clay related to the same end is d+D/2

    Xcm = [Mclay *(d+D/2)+Mbr*(D/2) ]/Mtotal

    Xcm = .6904 m position of the center of mass

    the angular velocit of the clay:

    omega clay = Vclay / D1

    D1=(d+D/2)-Xcm = .1496 m

    omega clay = 55.477 rad/s

    now about the bar:

    the center of the bar is situated related to the center of mass at:

    Dbar = Xcm - D/2 = .0804 m

    If you assume that the bar when it rotate has the same tangential velocity v = 8.3 m/s

    omega bar = 8.3 / 0.0804 = 103.249 rad/s

    the question is asking about At what angular speed does the bar/clay system rotate about its center of mass after the impact?

    and so I add up both the omega of the bar and the clay and got 158.726 rad/s
    but it's wrong

    Can anyone tell me where my mistake is?
     
  2. jcsd
  3. Dec 1, 2011 #2

    Simon Bridge

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