294_Physics ProblemsTechnical Physics

# 294_Physics ProblemsTechnical Physics - 296 P10.27 Rotation...

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296 Rotation of a Rigid Object About a Fixed Axis P10.27 For a spherical shell dI dmr r dr r == 2 3 2 3 4 22 2 πρ ej Id I r rr d r Ir r R dr RR IR Md m r r R dr R R =− F H G I K J = F H G I K J ×− F H G I K J × F H G I K J F H G I K J F H G I K J zz z 2 3 4 2 3 41 4 2 1 1 6 1 0 2 3 4 21 0 5 2 3 1 61 0 6 8 3 10 14 2 5 11 6 6 4 2 1 1 6 1 0 0 14 2 3 11 6 4 43 0 3 5 3 5 35 23 0 3 π ππ af e j .. kg m 3 R I MR R IM R 3 2 332 2 8 3 10 14 2 5 11 6 6 0 1 4 2 3 1 1 6 4 2 3 907 183 0330 = = F H G I K J = ∴= bg . . . . *P10.28 (a) By similar triangles, y x h L = , y hx L = . The area of the front face is 1 2 hL . The volume of the plate is 1 2 hLw . Its density is ρ = M V M hLw M hLw 1 2 2 . The mass of the ribbon is dm dV ywdx Mywdx hLw Mhx hLL dx Mxdx L = = = ρρ 2 2 . The moment of inertia is y x h L FIG. P10.28 d m x Mxdx L M L xdx M L LM L x LL = = = z = 2 0 2 3 0 2 42 2 all mass . (b) From the parallel axis theorem II M L I ML =+ F H G I K J
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## This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .

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