Question

A ring of mass 10 kg and radius 4 m, initially at rest, suddenly gain an angular velocity of 10 rad/s in 2 milli-seconds. The applied angular impulse is .

• A. 800 $\frac{Kg-m^2}{s}$
• B. 1500 $\frac{Kg-m^2}{s}$
• C. 1600 $\frac{Kg-m^2}{s}$
• D. 1000 $\frac{Kg-m^2}{s}$

Answer 1

The correct option is C 1600 $\frac{Kg-m^2}{s}$

Initial angular momentum, $\left|\overrightarrow{L_i}\right|=0$
Final angular momentum, $\left|\overrightarrow{L_f}\right|=I{\omega }_f$
$=M{r}^2\omega$
$=10\times (4{)}^2\times 10$
$=1600\frac{Kg-m^2}{s}$
$\left|\overrightarrow{J_a}\right|=\left|\overrightarrow{L_f}\right|-\left|\overrightarrow{L_i}\right|=1600\frac{Kg-m^2}{s}$