308_Physics ProblemsTechnical Physics

308_Physics ProblemsTechnical Physics - 310 P10.66 Rotation...

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310 Rotation of a Rigid Object About a Fixed Axis P10.66 (a) EM R = F H G I K J 1 2 2 5 22 ω ej E =⋅ × × F H G I K J 1 2 2 5 5 98 10 6 37 10 2 86 400 257 10 24 6 2 2 29 .. . e j π J (b) dE dt d dt MR T = F H G I K J F H G I K J L N M M O Q P P 1 2 2 5 2 2 2 =− = F H G I K J F H G I K J F H G I K J × × F H G I K J × 1 5 1 5 2 86 400 10 10 86 400 163 10 2 2 3 2 2 29 6 17 MR T dT dt MR TT dT dt dE dt a f bg . . J s s 3.16 10 s sday Jday 7 *P10.67 (a) ωω α fi t =+ ππ = = = F H G I K J × F H G I K J −− if tt TT t 32 22 2 2 21 0 1 1 1 10 di ~ s d 1 d 100 yr d 86 400 s yr 3.156 10 s s 7 (b) The Earth, assumed uniform, has moment of inertia IM R I ==× × = ×⋅ × = 2 5 2 5 5 98 10 6 37 10 9 71 10 9 71 10 2 67 10 10 46 2 37 37 22 2 16 . ~. . kg m kg m kg m s N m 2 2 e j τα The negative sign indicates clockwise, to slow the planet’s counterclockwise rotation.
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