a wheel has a constant angular acceleration of 3.0 rad/s2. during a certain 4.0s interval it turns through an angle of 120 rad. assuming tha

Question

a wheel has a constant angular acceleration of 3.0 rad/s2. during a certain 4.0s interval it turns through an angle of 120 rad. assuming that the wheel started from rest, how long has it been in motion at the start of this 4 s interval

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bonexptip 3 years 2021-08-23T13:22:24+00:00 1 Answers 0 views 0

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    2021-08-23T13:24:14+00:00

    Answer:

    8 s

    Explanation:

    We are given that

    Acceleration=\alpha=3 rad/s^2

    Time, t=4 s

    Angle,\theta=120 rad

    Initial angular velocity,\omega_0=0 rad/s

    Let \omega be the velocity at the start of this 4 s interval

    We know that

    \theta=\omega_0t+\frac{1}{2}\alpha t^2

    Using the formula

    120=4\omega+\frac{1}{2}(3)(4)^2

    120=4\omega+24

    120-24=4\omega

    4\omega=96

    \omega=\frac{96}{4}=24rad/s

    t=\frac{\omega-\omega_0}{\alpha}=\frac{24-0}{3}=8 s

    t=8 s

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