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I did this problem and have gotten it wrong-- but my math is right. Maybe I'm missing something? Here's the question:

We want to support a thin hoop by a horizontal nail and have the hoop make one complete small-angle oscillation each 2.0 s. What must the hoop's radius be?

So this is a physical pendulum, and in order to find the radius, I need to know the period. The period is found by:

[tex]T=2\pi\sqrt{\displaystyle{\frac{I}{mgd}}}[/tex]

Where I is the moment of inertia, g is the acceleration due to gravity, and d is the distance from the pivot point to the center of gravity.

For a hoop, the moment of inertia is: [tex]I=MR^2[/tex]

And the center of gravity is in the center of the hoop, so d is the radius.

So with that information, I set up the following:

[tex]T=2\pi\sqrt{\displaystyle{\frac{MR^2}{MgR}}}[/tex]

[tex]T=2\pi\sqrt{\displaystyle{\frac{R}{g}}}[/tex]

And in plugging in the values, I get:

[tex]2=2\pi\sqrt{\displaystyle{\frac{R}{9.8}}}[/tex]

Solving for R, I get .9929475

Which, when I plug into my equation, I get very close to 2 for my period. However, this is incorrect...

Any ideas as to why?

Thanks!!!!

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# Homework Help: Could Someone Check This Answer?

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