Question

A cylinder having moment of inertia $I$, which is free to rotate about its axis, receives an angular impulse of $J$ kg $m^2/s$ initially, followed by similar impulse after every $4$ s. What is the angular speed of the cylinder $30$ s after the initial impulse?

• A. $\frac{7J}{I}$
• B. $\frac{8J}{I}$
• C. $\frac{J}{I}$
• D. $0$

Answer 1

The correct option is B $\frac{8J}{I}$

There can be a total of eight impulses given to the cylinder in 30 s.
Using $\overrightarrow{J}={\overrightarrow{L}}_f-{\overrightarrow{L}}_i$ for every impulse, we get
$(8\cdot J)=I\cdot \omega -0\Rightarrow \omega =\frac{8J}{I}$