n electric turntable 0.750 m in diameter is rotating about a fixed axis with an initial angular velocity of 0.250 rev/s and a constant angul

Question

n electric turntable 0.750 m in diameter is rotating about a fixed axis with an initial angular velocity of 0.250 rev/s and a constant angular acceleration of 0.900 rev/s2. (a) Compute the angular velocity of the turntable after 0.200 s. (b) Through how many revolutions has the turntable spun in this time interval

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Thiên Thanh 3 years 2021-08-27T16:21:18+00:00 1 Answers 69 views 0

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  1. linhdan
    0
    2021-08-27T16:22:56+00:00
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    Answer:

    a) \omega_f=2.7018\ rad.s^{-1}

    b) n=0.068\ rev

    Explanation:

    Given:

    diameter of the table, d=0.75\ m

    initial angular velocity of the table, \omega_i=0.25\ rev.s^{-1}=0.5\pi\ rad.s^{-1}

    angular acceleration of the table, \alpha=0.9\ rev.s^{-2}=0.9\times2\pi=1.8\pi\ rad.s^{-2}

    a)

    time of observation, t=0.2\ s

    Now the angular velocity after the given time:

    using equation of motion

    \omega_f=\omega_i+\alpha.t

    where:

    \omega_f= final angular velocity

    \omega_f=0.5\pi\times +1.8\pi\times 0.2

    \omega_f=2.7018\ rad.s^{-1}

    b)

    No. of revolutions made in the given time:

    n=N_i.t+\frac{1}{2}\times \alpha.t^2

    where:

    N_i= initial revolution speed

    n=0.25\times0.2+\frac{1}{2}\times 0.9\times 0.2^2

    n=0.068\ rev

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