A spinning disc with a mass of 2.5kg and a radius of 0.80m is rotating with an angular velocity of 1.5 rad/s. A ball of clay with unknown ma

Question

A spinning disc with a mass of 2.5kg and a radius of 0.80m is rotating with an angular velocity of 1.5 rad/s. A ball of clay with unknown mass is dropped onto the disk and sticks to the very edge causing the angular velocity of the disk to slow to 1.13 rad/s. What is the mass of the ball of clay

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Cherry 2 months 2021-07-31T08:08:04+00:00 1 Answers 1 views 0

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    2021-07-31T08:09:31+00:00

    Answer:

    M = 1.90 Kg

    Explanation:

    Given data: mass = 2.5 Kg

    radius R = 0.8 m

    angular velocity ω = 1.5 rad/s

    Angular momentum L =0.5×Iω^2

    Where, I  is the moment of inertia of the spinning disc.

    I = 0.5MR^2

    I = 0.5×2.5×0.8^2

    I = 0.8 Kg/m^2

    Then L = 0.5×0.8×1.5^2 = 0.8×2.25 = 0.9 Kg-m^2/sec

    Let unknown mass be M

    New mass of disc = (2.5+M) Kg, R = 0.8 m

    New I = 0.5(2.5+M)(0.8)^2

    Since, angular momentum is conserved

    Angular momentum before = angular momentum after

    0.5×0.5(2.5+M)(0.8)^2×(1.13)^2 = 0.9

    Solving for M we get

    0.204304(2.5+M)=0.9

    M = 1.90 Kg

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