Solve the following :

Question:

A wheel rotating at a speed of 600 rpm (revolutions per minute) about its axis is brought to rest by applying a constant torque for 10 seconds. Find the angular deceleration and the angular velocity 5 seconds after the application of the torque.

Solution:

$\omega_{0}=600 \mathrm{rpm}=\frac{600}{60} \frac{\mathrm{rev}}{\mathrm{sec}}$

$\omega_{0}=10 \frac{\mathrm{rev}}{\mathrm{sec}} ; \omega=0 ; t=10 \mathrm{sec}$

$\omega=\omega_{0}+\alpha t$

$\alpha=-1 \mathrm{rev} / \mathrm{sec}^{2}$

For $\mathrm{t}=5 \mathrm{sec}$,

$\omega=\omega_{0}+\alpha t$

$=10+(-1)(5)$

$\omega=5 \mathrm{rev} / \mathrm{sec}$

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