Question

The rotating rod starts from rest and acquires a rotational speed n=600 revolution/minute in 2 seconds with constant angular acceleration. The angular acceleration of the rod is:

• A. $10\pi {rad/s}^2$
• B. $5\pi {rad/s}^2$
• C. $15\pi {rad/s}^2$
• D. None of these

Answer 1

The correct option is A $10\pi {rad/s}^2$

$\begin{array}{c}\text{Given, initial angular speed}=\text{0}\left({\omega }_0\right)\\ \text{and final argular speed}=600\frac{\text{revolution}}{\text{min.}}=10\text{revolution/sec.}\\ \text{It means, it covers}20\pi \text{rad. in}1\text{sec.}\end{array}$

$\text{Thus, angular acceleration}\left(\alpha \right)=\frac{{\omega }_t-{\omega }_0}{\Delta t}=\frac{20\pi }{2}=10\pi rad/s^2$