A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s2. In a 4.0-s interval the wheel turns through an angle

Question

A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s2. In a 4.0-s interval the wheel turns through an angle of 80 radians. Assuming the wheel started from rest, how long had it been in motion at the start of the 4.0-s interval?
a. 3 s.
b. 6 s.
c. 9 s.
d. 12 s.

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Vân Khánh 5 years 2021-08-03T23:45:25+00:00 1 Answers 62 views 0

Answers ( )

  1. Nem
    0
    2021-08-03T23:46:56+00:00
    Reply

    Answer:

    a. 3 s.

    Explanation:

    Given;

    angular acceleration of the wheel, α = 4 rad/s²

    time of wheel rotation, t = 4 s

    angle of rotation, θ = 80 radians

    Apply the kinematic equation below,

    \theta = \omega_1 t \ + \ \frac{1}{2} \alpha t^2\\\\80 = 4\omega_1 + \frac{1}{2}*4*4^2\\\\80 = 4\omega_1 + 32\\\\ 4\omega_1 = 48\\\\ \omega_1 = \frac{48}{4}\\\\ \omega_1 = 12 \ rad/s

    Given initial angular velocity, ω₀ = 0

    Apply the kinematic equation below;

    \omega_1 = \omega_o + \alpha t_1\\\\12 = 0 + 4t\\\\4t = 12\\\\t = \frac{12}{4}\\\\t = 3 \ s

    Therefore, the wheel had been in motion for 3 seconds.

    a. 3 s.

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