A physical pendulum is made from a solid sphere. The moment of inertia of a soli

Question

A physical pendulum is made from a solid sphere. The moment of inertia of a solid sphere is (2/5)mr2, the mass is 3 kg, and the radius is 0.03m. The pendulum is suspended through a hole drilled 0.01m from the top of the sphere: a)find the period of this pendulum b)if the amplitude of oscillation is .01m, what is the angular frequency? c)how long would a simple pendulum have to be to have the same frequency? I need help starting the problem by choosing the right formula. So far I have gotten .22s for the period, 28.56 rad/s for angular frequency, and .3m for the simple pendulum length. I have a test tomorrow and this is on the review so I would really appreciate a quick response. Thanks! A physical pendulum is made from a solid sphere. The moment of inertia of a solid sphere is (2/5)mr2, the mass is 3 kg, and the radius is 0.03m. The pendulum is suspended through a hole drilled 0.01m from the top of the sphere: a)find the period of this pendulum b)if the amplitude of oscillation is .01m, what is the angular frequency? c)how long would a simple pendulum have to be to have the same frequency? I need help starting the problem by choosing the right formula. So far I have gotten .22s for the period, 28.56 rad/s for angular frequency, and .3m for the simple pendulum length. I have a test tomorrow and this is on the review so I would really appreciate a quick response. Thanks!

Explanation / Answer

The moment of inertia of a solid sphere is I = (2/5)mr2 where m = mass = 3 kg radius r = 0.03m plug the values we get I = 1.08*10^-3 kg m^ 2 height from the from the top of the sphere L = 0.01 center mass position from suspended point L ' = L + r = 0.04 m a)the period of this pendulum T = 2(pi) sqrt [ I / (mgL ')] = 0.1904 s b)the amplitude of oscillation A = 0 .01m the angular frequency w= 2(pi) / T = 33 rad / s c)frequency of simple pendulum f = 1 / T = 5.25 Hz we know f = [1/ 2(pi) ] sqrt ( g / L ") [2(pi) f ]^2 = g / L" 1089 = g / L " from this required length L " = g / 1089 = 9 * 10 ^ -3 m

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