Question

A uniform solid cylinder of mass $5kg$ and radius $30cm$, and free to rotate about its axis, receives an angular impulse of $3kg{m}^2{s}^{-1}$ initially followed by a similar impulse after every $4s$. What is the angular speed of the cylinder $30s$ after the initial impulse? The cylinder is at rest initially.

• A. $100$
• B. $200$
• C. $300$
• D. $500$

Answer 1

The correct option is A $100$

$AngularImpulse=Changeinangularmomentum-------\left(1\right)Changeinangularmomentum=I\omega -I{\omega }_{0}WhereI=Momentofinertiaofthecylinder{\omega }_0=Initialangularimpluseand\omega =anugularimpulseafter4secondsPuttingthevaluesinequation1weget3=\frac{1}{2}m{r}^2\{\omega -0\}\omega =\frac{6}{5\times {0.3}^2}=13.33radianpersecondAlsoweknow\omega ={\omega }_0+\alpha t\alpha =\frac{13.33}{4}=3.33Nowangularspeedafter30seconds=3.33\times 30=100radianspersecond$