Analytical Mech Homework Solutions 113

Analytical Mech Homework Solutions 113 - 11 l 3R xcm = = 2...

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11 3 2 cm lR x m ω == ±± ± 3 3 R mg R m R m  −= =   4 mg R = 66 4 end R mg xll ml m = ± 3 2 end x g = 8.14 For a solid sphere: 3 4 3 s M a π ρ = and 2 2 5 ss I Ma = () 22 2 5 cm s ka = For subscript c representing a solid sphere the size of the cavity, from eqn. 8.3.2: s c I II =+ 32 5 24 243 1 53 2 2 533 2 aa I a ρπ  =   =− 3 33 44 4 7 23 8 a a ma = 18 3 1 27 7 0 cm I m = 2 a From eqn. 8.6.11, for a sphere rolling down a rough inclined plane: 2 2 sin 1 cm cm g k
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