Hello again, got some rather interesting questions for those who have been kind enough to put up with my ridiculous free response questions over the past 3 weeks. Here it goes:(adsbygoogle = window.adsbygoogle || []).push({});

A solid disk (of Radius R) has four holes cut out of it, each of which are centered at R/2. The holes have a radius of R/4 and are equidistance from the center of the disk, which has a mass M. I wish I had a picture but just imagine 4 holes of the size given. The center of the disk lies in the origin of the x-y plane, and the holes (at least the center of each) lie on the x and y axis, two in the positive and one in the negative. Very symmetrical indeed.

The Moment of inertia of the disk is CMR^2, where C is some constant.

a) The disk rolls down an incline of height H. In terms of C and H, what is the velocity at the bottom of the incline?

b) A small pin is mounted at the top of the disk at (0,R) and is pointed in the z plane. The disk is displaced by a small angle and begins to oscillate. What is the period, in terms of C and R?

c) What is the value of C?

Okay, so part a and b are rather simple. Conservation of energy and the formula for a physical Pendelum are totally at hand here. The problem lay in part c.

I know that some hidden math is involved. The use of the parallel axis theorem and "negative densities". That's not the issue. The only issue that I have is what do I need to equal each other in order to solve for C and what is the right setup to determine the "missing" mass of each of the holes in terms of M.

ANY HELP WOULD BE SUPER APPRECIATED!!! If y'all need my work, just let me know.

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# Homework Help: Yet another moment of intertia problem and such

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