A pulley, with a rotational inertia of \( 1.0 \times 10^{-3} \mathrm{~kg} \cdot \mathrm{m}^{2} \...

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A pulley, with a rotational inertia of \( 1.0 \times 10^{-3} \mathrm{~kg} \cdot \mathrm{m}^{2} \) about its axle and a radius of \( 10 \mathrm{~cm} \), is acted on by a force applied tangentially at its rim. The force magnitude varies in time as \( F=0.50 t+0.30 t^{2} \), with \( F \) in newtons and \( t \) in seconds. The pulley is initially at rest. At \( t=3.0 \mathrm{~s} \) what are its angular acceleration
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