If a trapeze artist rotates 1 each second while sailing through the air, and contracts to reduce her rotational inertia to 0.40 of what it w

Question

If a trapeze artist rotates 1 each second while sailing through the air, and contracts to reduce her rotational inertia to 0.40 of what it was, how many rotations per second will result?

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Doris 4 years 2021-09-04T05:53:41+00:00 1 Answers 9 views 0

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  1. Amity
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    2021-09-04T05:54:53+00:00
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    Thus the number of rotations per second are 2.5

    Explanation:

    A trapeze is rotating with 1 rotation per second .

    Thus its angular velocity ω = 2π n

    here n is the number of rotations per second

    Thus ω = 2π b because n = 1 in this case

    Suppose the moment of inertia of his is = I

    Then angular momentum L₁ = I  ω = 2 I π

    In the second case , the moment of inertia becomes = 0.4 I

    Let his angular velocity is  ω₀

    Thus angular momentum L₂ = 0.4 I  ω₀

    Because no external torque is applied , therefore angular momentum will remain constant .

    Thus L₁ = L₂

    Therefore  2 I π = 0.4 I x 2 n₀ π

    here n₀ is the number of rotations per second

    n₀ = \frac{1}{0.4} = \frac{5}{2} = 2.5

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