Physics

What is the moment of inertia of an object that rolls without slipping down a 2.00-m-high incline starting from rest, and has a final velocity of 6.00 m/s? Express the moment of inertia as a multiple of MR2, where M is the mass of the object and R is its radius.

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  1. PE=KE=KE(transl) + KE(rot).

    mgh = mv²/2 + I ω²/2=
    = mv²/2 + I v²/2R².

    I= (2R²/v²)(mgh- mv²/2)=
    =mR²(2gh/v² -1) =
    = mR²(2•9.8•2/36 -1)=
    =mR²(1.09-1)=0.09 mR²

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  2. The answer's actually 12.

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