Question
A body rotates about a fixed axis with an angular acceleration of one radian/ second/ second. Through what angle does it rotate during the time in which its angular velocity increases from 5rad/s to 15rad/s.
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Answer
$\alpha=1\text{rad/s}^2,\ \omega_0=5\text{rad/s};\ \omega=15\text{rad/s}$
$\therefore\text{w}=\text{w}_0+\alpha\text{t}$
$\Rightarrow\text{t}=\frac{(\omega-\omega_0)}{\alpha}=\frac{(15-5)}{1}=10\text{sec}$
Also, $\theta=\omega_0\text{t}+\frac{1}{2}\alpha\text{t}^2$
$=5\times10+\frac{1}{2}\times1\times100=100\text{rad}$
$\therefore\text{w}=\text{w}_0+\alpha\text{t}$
$\Rightarrow\text{t}=\frac{(\omega-\omega_0)}{\alpha}=\frac{(15-5)}{1}=10\text{sec}$
Also, $\theta=\omega_0\text{t}+\frac{1}{2}\alpha\text{t}^2$
$=5\times10+\frac{1}{2}\times1\times100=100\text{rad}$
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