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Question

# A flywheel (I = 50 kg-m²) starting from rest acquires an angular velocity of 200.0 rad/s while subject to a constant torque from a motor for 5 s. (a) What is the angular acceleration of the flywheel? (b) What is the magnitude of the torque?

Solution

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a) From $\textbf{the kinematics of the rotational motion}$ we knw that :

$\omega_{f} = \omega_{i} + \alpha t$

where:

• $\omega_{i}$ is the initial angular velocity .
• $\omega_{f}$ is the final angular velocity .
• $\alpha$ is the angular acceleration .
• $t$ is the time .

From $\textbf{givens}$ we know that : $\omega_{f} = 200\ \; \mathrm{rad/s}$ , $\omega_{i} = 0\ \; \mathrm{rad/s}$ and $t = 5 \ \; \mathrm{s}$ .

$\textbf{Plugging}$ known information into our equation we get :

\begin{align*} \omega_{f}& = \omega_{i} + \alpha t \\ \alpha t &=\omega_{f} - \omega_{i} \\ \alpha&=\dfrac{\omega_{f} - \omega_{i}}{t}\\ &= \dfrac{200 - 0}{5}\\ &=40 \end{align*}

$\boxed{\omega_{f} = 40\ \; \mathrm{rad/s}}$

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