Analytical Mech Homework Solutions 107

Analytical Mech Homework Solutions 107 - 5 8.5 Consider the...

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5 8.5 Consider the sphere with the cavity to be made of a (i) solid sphere of radius and and mass a s M , with its center of mass at 0 z = , and (ii) a solid sphere the size of the cavity, with mass c M and center of mass at 2 a z = − . The actual sphere with the cavity has a mass s c M mM =− and center of mass . cm z 3 33 44 7 4 28 3 sc a mM M a a π ρπ ρ  =−= =   8 7 s M m = and 1 7 c M m = From eqn. 8.3.2, I II = + 2 2 22 55 2 a M aM I = + 2 21 3 1 57 4 7 0 a I ma m m a =− = 8.6 The moment of inertia about one of the straight edges is 2 z I Rd v = where 222 R xy =+ . From Appendix F … 2 sin dv r dr d d θ θφ = φ θ r R y x z 22222
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