A merry-go-round on a playground consists of a horizontal solid disk with a weight of 795 N and a radius of 1.49 m. A child applies

Question

A merry-go-round on a playground consists of a horizontal solid disk with a weight
of 795 N and a radius of 1.49 m. A child applies force tangentially to the edge of the
disk to start it from rest and rotate at 47.79 rmp (revolution per minute) in 5.00 s.
(a) Calculate the angular acceleration
(b) Calculate the net torque required for such motion.
(c) Calculate the rotational kinetic energy for such motion.

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Doris 4 years 2021-09-05T08:06:07+00:00 1 Answers 17 views 0

Answers ( )

  1. Farah
    0
    2021-09-05T08:07:51+00:00
    Reply

    Answer:α = 1.00 rad/s², τ = 90.0 N•m, KEr = 1.12 kJ

    Explanation:

    m = 795/9.81 = 81.0 kg

    ω₁ = 47.79 rev/min(2π rad/rev) / (60 s/min) = 5.00 rad/s

    α = (ω₁ – ω₀)/τ = (5.00 – 0.00)/5.00 = 1.00 rad/s²

    I = ½mR² = ½(81.0)(1.49²) = 90.0 kg•m²

    τ = Iα = 90.0(1.00) = 90.0 N•m

    KEr = ½Iω² = ½(90.0)5.00² = 1,124.477 ≈ 1.12 kJ

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