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27 May, 01:51

A 2.1 kg, 20-cm-diameter turntable rotates at 70 rpm on frictionless bearings. Two 520 g blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick. What is the turntable's angular velocity, in rpm, just after this event

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  1. 27 May, 05:38
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    There is change in moment of inertia of turntable due to which its angular velocity changes. We shall apply law of conservation of angular momentum

    initial moment of inertia = 1 / 2 M r², M is mass and r is radius of table

    I₁ = 1/2 x 2.1 x. 10²

    =.0105 kg m²

    final moment of inertia

    I₂ = I₁ + 2 x m r², m is mass of fallen blocks on the table

    =.0105 + 2 x. 52 x. 1²

    =.0105 +.0104

    =.0209 kg m²

    initial angular velocity ω₁ = 2π n, n is revolution per second

    = 2π x 70 / 60

    = 2.3333 π rad / s

    Final angular velocity ω₂ = ?

    Applying law of conservation of angular momentum

    I₁ ω₁ = I₂ ω₂

    .0105 x 2.3333 π =.0209 x ω₂

    ω₂ = 1.172 π

    =.586 x 2 π rad / s

    no of revolution per sec =.586

    no of revolution per minute =.586 x 60

    = 35.16 rpm.
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