292_Physics ProblemsTechnical Physics

292_Physics ProblemsTechnical Physics - 294 P10.22 Rotation...

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294 Rotation of a Rigid Object About a Fixed Axis P10.22 IM x m Lx =+ 2 2 a f dI dx Mx m L x =− = 22 0 af (for an extremum) ∴= + x mL Mm dI dx mM 2 2 ; therefore I is minimum when the axis of rotation passes through x mL = + which is also the center of mass of the system. The moment of inertia about an axis passing through x is mL m m L Mm LL CM = + L N M O Q P +− + L N M O Q P = + = 2 1 µ where = + Mm . x M m L L x x FIG. P10.22 Section 10.5 Calculation of Moments of Inertia P10.23 We assume the rods are thin, with radius much less than L . Call the junction of the rods the origin of coordinates, and the axis of rotation the z -axis. For the rod along the y -axis, Im L = 1 3 2 from the table. For the rod parallel to the z -axis, the parallel-axis theorem gives r m L mL F H G I K J 1 1 4 2 2 2 axis of rotation z x y FIG. P10.23
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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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