Physics Question, Help!?

In the figure the lower disk, of mass 450g and radius 3.1 cm , is rotating at 180 rpm on a frictionless shaft of negligible radius. The upper disk, of mass 270 g and radius 2.0 cm , is initially not rotating. It drops freely down onto the lower disk, and frictional forces bring the two disks to a common rotational speed.

A. Find the common speed.

B. Find the fraction of the initial kinetic energy lost to friction.

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  • Whome
    Lv 7
    9 months ago
    Favourite answer

    A. Find the common speed.

    Conservation of angular momentum L = Iω

    for a uniform disc, moment of inertia is

    I = ½mr²

    initial angular momentum

    L = ½(0.450)(0.031²)180(2π/60) + ½(0.270)(0.020²)0.0 = 1.811 x 10^-5‬

    final angular momentum

    1.811 x 10^-5‬‬ = (½(0.450)(0.031²) + ½(0.270)(0.020²))ω(2π/60)

    ω = 144 rpm

    B. Find the fraction of the initial kinetic energy lost to friction.

    angular kinetic energy is KEr = ½Iω²

    KEi = ½(½(0.450)(0.031²))(180(2π/60))² = 0.0384 J

    KEf = ½(½(0.450)(0.031²) + ½(0.270)(0.020²))(144(2π/60))² = 0.0307 J

    fraction of KE lost to friction

    R = (KEi - KEf) / KEi

    R = 0.2001...

    or almost exactly 20%

    I hope this helps.

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