Physics

A solid disk rotates in the horizontal plane at an angular velocity of 0.0684 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.190 kg·m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.418 m from the axis. The sand in the ring has a mass of 0.486 kg. After all the sand is in place, what is the angular velocity of the disk?

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  1. angular momentum before
    =I w=.19 * .0684 + .486(.418)^2*0
    = .013

    new I w = (.19 +.085)w

    so
    .013 = .275 w

    w = .047 rad/s

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