Question

A flywheel rotates with a uniform angular acceleration. its angular velocity increase from $20\pi$ rad/sec to $40\pi$ rad/sec in 10 seconds. How many rotation did it make it period :-

• A. 150
• B. 100
• C. 125
• D. 175

Answer 1

The correct option is A 150

$\begin{array}{cc}\text{Given,}{\omega }_0& =20\pi \text{rad/s}\\ {\omega }_t& =40\pi \text{rad}/s\\ \text{and,}& \Delta t=10sec.\end{array}$

$\text{Thus,}\begin{array}{cc}\alpha & =\frac{{\omega }_t-{\omega }_0}{\Delta t}\\ & =\frac{40\pi -20\pi }{10}rad/s^2\\ & =\left(2\pi \right)rad/s^2\end{array}$

$\begin{array}{c}\text{Now, total angle covered during time t}\left(\Delta \theta \right)={\omega }_{0}t+\frac{1}{2}\alpha t^2\\ \therefore \Delta \theta =20\pi \times 10+\frac{1}{2}\times \left(2\pi \right)\times 100\\ =300\pi \\ \text{Hence, total rotation made during this time}=\frac{300\pi }{2\pi }=150\end{array}$