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(D) Let the initial angular velocity at the start of the observation be $\omega_0$. Given angular acceleration $\alpha = 3.0 \ rad/s^2$,time interval

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$8$

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(D) Let the initial angular velocity at the start of the observation be $\omega_0$. Given angular acceleration $\alpha = 3.0 \ rad/s^2$,time interval $t = 4.0 \ s$,and angular displacement $	heta = 120 \ rad$.Using the kinematic equation $	heta = \omega_0 t + \frac{1}{2} \alpha t^2$:$120 = \omega_0(4) + \frac{1}{2}(3)(4)^2$$120 = 4\omega_0 + 24$$4\omega_0 = 96 \implies \omega_0 = 24 \ rad/s$.The wheel started from rest $(\omega_{initial} = 0)$ with constant acceleration $\alpha = 3.0 \ rad/s^2$. Let $T$ be the time elapsed before the observation started.Using $\omega_0 = \omega_{initial} + \alpha T$:$24 = 0 + 3T$$T = \frac{24}{3} = 8 \ s$.

$A$ flywheel starts from rest and rotates with a constant angular acceleration of $3.0 \ rad/s^2$. An observer notes that it covers an angle of $120 \ rad$ in a time interval of $4.0 \ s$. How long had the wheel been rotating before the observer started the observation?

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