450_Physics ProblemsTechnical Physics

450_Physics ProblemsTechnical Physics - 452 P15.36...

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452 Oscillatory Motion P15.36 (a) The parallel-axis theorem: I I Md ML Md M M M T I Mgd M Mg =+ = + = + = F H G I K J == = = CM 2 2 2 m m m m m m 12 9.80 m s s 22 2 1 12 1 12 100 13 12 13 12 1 00 2 13 209 .. . . a f a f ej a f ππ π (b) For the simple pendulum FIG. P15.36 T 2 201 . . m 9.80 m s s 2 difference = = 408% . s s 2.01 s P15.37 (a) The parallel axis theorem says directly II m d CM 2 so T I mgd Im d mgd + 2 CM (b) When d is very large T d g 2 gets large. When d is very small T I mgd 2 CM gets large. So there must be a minimum, found by dT dd d dd dm g d I md mgd mg mgd I md md d m g g d md mgd g d + F H G I K J + F H G I K J + = −+ + + + = −− 02 2 1 2 2 1 2 2 2 0 2 12 2 32 2 2 2 2 CM CM CM CM CM CM bg This requires + = d CM 20 or d CM = 2 . P15.38 We suppose the stick moves in a horizontal plane. Then,
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