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Old Dec 4th 2008, 07:13 AM   #1
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Classical Mechanics: angular frequency

I take a book that is 30cm x 20 cm x 3 cm and is held shut by a rubber band, and I throw it into the air spinning about an axis that is close to the book's shortest symmetry axis at 180 rpm. What is the angular frequency of the small oscillations of its axis of rotation? What if I spin it about an axis close to the longest symmetry axis?

I'm having a lot of trouble just getting started with this problem. I can't seem to find the correct angular frequency formula. I don't know where to even start. Can any one please help me?
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Old Dec 4th 2008, 09:19 PM   #2
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Originally Posted by kala View Post
I take a book that is 30cm x 20 cm x 3 cm and is held shut by a rubber band, and I throw it into the air spinning about an axis that is close to the book's shortest symmetry axis at 180 rpm. What is the angular frequency of the small oscillations of its axis of rotation? What if I spin it about an axis close to the longest symmetry axis?

I'm having a lot of trouble just getting started with this problem. I can't seem to find the correct angular frequency formula. I don't know where to even start. Can any one please help me?
1 round = $\displaystyle 2\pi$
angular frequency=$\displaystyle \theta/t$ where theta is the angular displacement and t is the time(in second)

Hence the angular frequency of your book about the shortest symmetry axis is
$\displaystyle 180(2\pi)/60$
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