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The math of a 'moment of inertia' in application

  1. Apr 13, 2005 #1
    I am trying to detemine the moment of interia of an object, not too accurately.

    I have the object mounted in bearings, and on the shaft of the object I have a ring (radius of 2.5in) which I have a filament wrapped around which drops to a weight of 5lbs (mass of .1554 slug). I can release the weight and time the travel over a known distance (approx 24in in 5sec, an acceleration 'a' of 9.6in/sec^2). Angular acceration is 'a'/'r' or 3.84rad/sec^2. I have determined the tension in the filament to be 4.88lbf by F=ma, m=.1554slug * (subtracting 'a'(conv. to ft/sec^2) from g(ft/sec^2)). The torque would then be 4.88lbf * 2.5in or 12.2in.lbf.

    My problem has come down to the math. I have seen moment of inertia defined in both lb.in^2 and in.lb.sec^2. I cannot seem to figure out how torque (in.lbf) / angular acceleration (rad/sec^2) can be conveyed to MOI of either version, the units don't seem to cancel out right.

    Any input would be greatly appreciated, until then I will have fun putting a sharp stick in my eye.

    Last edited: Apr 13, 2005
  2. jcsd
  3. Apr 13, 2005 #2


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    Moment of inertia has units [M]*[L]2 (mass times length squared)
    When you see inch*pound*second^2, the "pound" is pound-force.
    When you see pound*inch^2. the "pound" is pound-mass.
    Also note that radians are unitless dimensions.
    I hope that helps.
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