Angular Momentum

Total $13$pt

$3.$ A projectile of mass $m=2kg$ moves to the right with a speed $v_i=10\frac{m}{s}.$ The projectile strikes and sticks to the end of a stationary rod of mass $M=8kg,$ length $L=2m,$ pivoted about a frictionless axle perpendicular to the page through $O$ at the end of the rod. Consider the system is including both ball and rod. a$)$ What is the angular momentum of the system before the collision about an axis through $O?($b$)$ What is the kinetic energy of the system before the collision? $($c$)$ There is no external torque applied on the system, what is the moment of inertia of the system about an axis through $O$ after the projectile sticks to the rod? $($d$)$ What should be the angular momentum of the system after collision about the axis through $O?($Is it same as the initial?$)($e$)$ What is the angular speed of the ball and bar together? $($ f $)$ What is the kinetic energy of the system after the collision? $($ g $)$ What is the energy lost? $($Hint: this is same as the example in class, a baseball is caught by an arm$)(6$ p $)$

$vi=10\frac{m}{s}$

$l=I$

$m*v*r*sin+Iw$

$mv*d+0=Iw$

$mvd=(I$ proj $+$Irod$)w$

$mv*d=(m{r}^2+\frac{1}{3}{m}_e^2)w$