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Homework Statement
I have a disk that can rotate about an axis at a radial distance h from the center of the disk. I am given a graph showing the the rotational inertia I of the disk as a function of the distance h from the center of the disk out to the edge of the disk. From the graph (see attached picture) I can see that the ends of the graph are as follows: when h is zero (i.e. the axis is right on the center of the disk) I = 0.03 kg*m^2 and when h = 0.2m, I = 0.63 kg*m^2.
I am asked to determine the mass of the disk from these data.
Homework Equations
##I_p = I_{cm} + Md^2## (parallel axis theorem)
##I_{disk} = 1/2Mr^2## (the moment of inertia of a disk about its CM)
The Attempt at a Solution
Let point A be when h = 0, i.e. the axis is right on the CM. Let point B be when h = 0.2, i.e. on the edge of the disk. Applying the parallel axis theorem to both locations and given the values from the problem:
##I_B = I_{disk} + M(0.2)^2 = 0.63##
##I_A = I_{disk} + M(0)^2 = 0.03##
Subtracting the second equation from the first gives
##I_B  I_A = 0.63  0.03 = 0.60 = M[(0.2)^2  0^2]##
and so M = 15kg, which is the correct answer. But if I actually try to use this to recalculate the moment of inertia of the disk I get
##I_{disk} = 1/2Mr^2 = 1/2(15)(0.2^2) = 0.3 \not= I_A = 0.03##
and similarly I get the "wrong" answer for I_B using the parallel axis theorem. Is the problem just written poorly, or am I missing something really obvious here?
Thanks for any help... first time using Tex... hope I did okay.
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