Rotational Kinetic Energy?

A homogeneous solid cylinder rolls without slipping on a horizontal surface. The total kinetic energy is K. The kinetic energy due to rotation about its center of mass is...

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  • Ash
    Lv 7
    2 months ago
    Favorite Answer

    Total KE = KE(linear) + KE(rotational) 

    K = ½mv² + ½Iω²

    For solid cylinder, with axis along the length, I = ½mr²

    Also we know ω = v/r

    K = ½mv² + ½(½mr²)(v/r)²

    K = ½mv² + ¼mv²

    K = ¾mv²  ............(1)

    KE(rotational) = ¼mv² ....(2)

    (2) divided by (1) gives

    KE(rotational)/K = (¼mv²)/¾mv²

    KE(rotational)/K = 

    from (1)

    KE(rotational)/K = ⅓

    KE(rotational) = ⅓ K

    Answer (b)

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