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Angular Momentum Problem

  1. Dec 1, 2008 #1
    1. The problem statement, all variables and given/known data
    The problem asks to calculate the angular momentum for a metallic bob that is suspended from the ceiling by a thread of negligible mass. The angle between the thread and the vertical is 30degrees. It is also given that the mass of the bob is 7 kg and the length of the thread is 2.4m.

    2. Relevant equations
    I used the equations:mv^2/r=Tsin(theta)

    3. The attempt at a solution
    I first rearranged mg=Tcos(theta) to solve for T=mg/cos(theta)
    Next I substituted this into mv^2/r =Tsin(theta) and got mv^2/r=mgtan(theta)
    I found r by using the length of the thread and the angle with the vertical:
    sin30= r/2.4 r=1.2
    Next I solved for v. v=2.6m/s.
    My problem after this was applying it to the equation L=Iw
    I knew that L=(2/5)mr^2w or L=2mrv/5 but I wasn't sure what to put for the radius since it was not given.

    Am I even on the right track???
    Thanks in advance!
  2. jcsd
  3. Dec 1, 2008 #2
    These should be correct...

    L = I(omega) is correct, but you are using the wrong I. 2/5mr^2 is the moment of inertia of a sphere about an axis through its centre. However, the bob is not rotating about its centre, but rather about a vertical axis at the centre of its circular motion.

    Hence I = mr^2, where r is the radius of its circular motion.
  4. Dec 1, 2008 #3
    Thanks a lot! yea that makes sense. so i guess you can kind of think of it as the moment of inertia of a hollow cylinder?
  5. Dec 1, 2008 #4
    Not really, we are treating the bob as having the moment of inertia of a single point particle rotating about an axis
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