Question

A body rotates about fixed axis with an angular acceleration of $3{\text{rad/s}}^2$. Through what angle does it rotate during the time in which its angular velocity increases from $15\text{rad/s}$ to $45\text{rad/s}$ ?

Answer 1

It is given that the body rotates with constant angular acceleration $\alpha =3{\text{rad/s}}^2$ and initial angular velocity ${\omega }_0=15\text{rad/s}$ and final angular velocity $\omega =45\text{rad/s}$

Using equation of motion under constant angular acceleration

${\omega }^2={\omega }_0^2+2\alpha \theta$
$\Rightarrow \theta =\frac{{\omega }^2-{\omega }_0^2}{2\alpha }=\frac{{45}^2-{15}^2}{2\times 3}$

$\theta =\frac{2025-225}{2\times 3}$

$\theta =300\text{rad}$
Hence option A is the correct answer.