Turntable Apparatus
April 1st, 2010
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Turntable Apparatus
Physics help, inertia?
No clue where to start! Any help would be great!
This problem describes one experimental method for determining the
moment of inertia of an irregularly shaped object such as the payload for a
satellite. Figure below shows a counterweight of mass m suspended by a cord
wound around a spool of radius r, forming part of a turntable supporting the
object. The turntable can rotate without friction. When the counterweight is
released from rest, it descends through a distance h, acquiring a speed v. Show
that the moment of inertia I of the rotating apparatus (including the turntable) is
mr2(2gh/v2 – 1).
Once you realize that this is a conservation of energy problem, it turns into an algebra exercise.
PE = KE
m*g*h = 1/2*m*v**2 + 1/2*I*ω**2
Recall that v = r*ω so that ω**2 = v**2/r**2
m*g*h = 1/2*m*v**2 + 1/2*I*v**2/r**2
Now solve for I to get
I = m*r**2(2*g*h/(v**2) - 1)
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