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Angular Rotation

  1. Apr 21, 2008 #1
    [SOLVED] Angular Rotation

    1. The problem statement, all variables and given/known data

    A cockroach of mass m lies on the rim of a uniform disk of mass 7.50 m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.250 rad/s. Then the cockroach walks half way to the center of the disk.
    (a) What then is the angular velocity of the cockroach-disk system?
    _______ rad/s

    (b) What is the ratio K/K0 of the new kinetic energy of the system to its initial kinetic energy?
    ______


    (c) What accounts for the change in the kinetic energy?
    centrifugal force
    friction
    cockroach does negative work on the disc
    cockroach does positive work on the disc
    gravity
    centripetal force



    3. The attempt at a solution

    Ok so Rotational Inertia of the Disk at all times would be (1/2)MR^2
    Then the Rotational Inertia of the Bug would be mR initially and then (1/2)mR finally.

    Since momentum is conserved Iw = Iw

    Therefore,

    (1/2)MR^2(.25) + (m)(R)(.25) = (1/2)MR^2(w) + (1/2)mR(w)

    I have the mass of the uniform disk so I can plug that into M giving me

    3.75R^2(.25) + (m)(R)(.25) = 3.75R^2(w) + (1/2)mR(w)

    Now I'm lost, can anyone point me in the right direction? Thanks
     
  2. jcsd
  3. Apr 22, 2008 #2

    alphysicist

    User Avatar
    Homework Helper

    Hi Nanuven,


    The rotational inertia of the bug would be mR^2. After you have that, what would be the final value of its rotational inertia?
     
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