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Angular momentum of turntable problem

  1. Mar 28, 2013 #1
    1. The problem statement, all variables and given/known data

    A 1.9kg , 20 cm-diameter turntable rotates at 150rpm on frictionless bearings. Two 480g blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick.

    what is the objects angular velocity in rpm right after this event?

    2. Relevant equations

    L=Iω where L is angular momentum, I is the moment of inertia and ω is the angular velocity
    moment of inertia for a disk rotating about it's center 1/2*m*r^2

    3. The attempt at a solution

    Ok, so it seems like a simple conservation problem, so I tried to solve it like one.

    I final*ω final = I initial * ω initial
    ergo
    ω final = (I initial * ω initial)/ I final

    convert 150 rpm in rad/s, (150/60)*2[itex]\pi[/itex] =15.71

    since the formula for the moment of inertia "I" for a disk rotating about the center is 1/2*m*r^2
    I just plug in the values

    (.5*1.9kg*.1^2m*15.71 rad/s)/ (.5*(1.9+.96kg)*.1^2m) = 10.44 rad/s

    converting back to rpm (10.44/ 2[itex]\pi[/itex] )*60 = 99.66 rpm rounded to 100 rpm.

    But this solution is incorrect. What have I done wrong?
     
    Last edited: Mar 28, 2013
  2. jcsd
  3. Mar 28, 2013 #2
    You seem to believe that the final moment of inertia is that of a more massive disk, but that is not write. You should treat the system as a disk with two additional masses at its rim.
     
  4. Mar 28, 2013 #3
    I see what you're saying, but I have no idea how to account for that in the math. Another hint please?
     
  5. Mar 28, 2013 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Do you know the moment of inertia for a point-mass at a radius r? Just use this (for both masses).
     
  6. Mar 28, 2013 #5
    You can consider the disk and the masses separately, and sum their ang. mom.
     
  7. Mar 28, 2013 #6
    Thank you much guys, those tips got me to where I needed to go!

    Edit: Oh yeah, I made "I final" equal the sum of the moments of inertia of the disk, and the two point masses. Thanks a bunch.
     
    Last edited: Mar 28, 2013
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