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11 March, 06:52

A gyroscope slows from an initial rate of 49.3 rad/s at a rate of 0.731 rad/s^2. (a) How long does it take (in s) to come to rest? (b) How many revolutions does it make before stopping?

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  1. 11 March, 09:23
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    (a) 67.44 second

    (b) 529.5 revolutions

    Explanation:

    ωo = 49.3 rad/s

    α = 0.731 rad/s^2

    (a) Let it takes t time to come to rest.

    ω = 0

    Use first equation of motion for rotational motion

    ω = ωo + α t

    0 = 49.3 - 0.731 x t

    t = 67.44 second

    (b) Let it turns an angle θ rad before coming to rest. use third equation of motion for rotational motion.

    ω^2 = ωo^2 + 2 α θ

    0 = 49.3 x 49.3 - 2 x 0.731 x θ

    2430.49 = 1.462 θ

    θ = 1662.44 rad

    Number of revolutions = θ / 2π = 1662.44 / 3.14 = 529.5 revolutions
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