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Conservation of momentum on merry-go-round

  1. Jan 13, 2004 #1
    A playground merry-go-round has a disk-shaped platform that rotates with negligible friction about a vertical axis. The disk has a mass of 200kg and a radius of 1.8 m. A 36-kg child rides at the center of the merry-g-round while a playmate sets it turning at 0.25 rev/sec. If the child then walks along a radius to the outer edge of the disk, how fast will the disk be turning.

    [tex]\omega_0 = 0.5\pi [/tex] rad/sec.
    [tex] I_0 = \frac{1}{2} m r^2 [/tex] (MOI for disk).
    [tex] L = I_0\omega_0 = \frac{1}{2} m r^2 \omega_0 [/tex]
    So, if angular momentum is conserved, [tex] L = I_f\omega_f [/tex]
    My only problem is figuring out the MOI for a disk with an object spinning around the outer edge. Anyone know?
  2. jcsd
  3. Jan 21, 2004 #2

    Doc Al

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    Staff: Mentor

    Treat the child as a point mass. Its moment of inertia is [itex]mr^2[/itex]. The total MOI is that of the disk plus that of the child.
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