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16 February, 22:39

A 0.35-kg turntable of radius 0.30 m spins about a vertical axis through its center. A constant rotational acceleration causes the turntable to accelerate from 0 to 24 revolutions per second in 8.0 s. Part A

Calculate the rotational acceleration.

/alpha = ?

Part B

Calculate the torque required to cause this acceleration.

torque = ?

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Answers (1)
  1. 16 February, 22:47
    0
    (a) ∝ = 18.84 rad/s^2

    (b) 0.297 N m

    Explanation:

    m = 0.35 kg

    r = 0.3 m

    fo = 0 rps

    f = 24 rps

    t = 8 s

    (A)

    ωo = 2 x π x fo = 0

    ω = 2 π f = 2 x 3.14 x 24 = 150.72 rad/s

    Use first equation of motion for rotational motion

    ω = ωo + ∝ t

    Where, ∝ is the rotational acceleration

    150.72 = 0 + 8 ∝

    ∝ = 18.84 rad/s^2

    (B) Torque = Moment of inertia x rotational acceleration

    Moment of inertia of turn table = 0.5 x mass x radius²

    I = 0.5 x 0.35 x 0.3 x 0.3 = 0.01575 kg m²

    Torque = 0.01575 x 18.84 = 0.297 N m
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