Problem $4$

Two plastic pucks $($solid cylinders$)$ of equal mass $m=0\mathrm{.}032kg$ and radius $r=0\mathrm{.}014m$ are placed on an air hockey table. The left puck is thrown while spinning and collides with the right stationary puck. When they collide, the puck stick together and rotate around their center of mass. The left puck is thrown a height $h=\frac{3}{2}r$ above the center of the stationary disk. The incoming speed of the left puck is vec$(v)=2\mathrm{.}30\frac{m}{s}$hat$(x)$ and its angular speed is $=1\mathrm{.}74ra\frac{d}{s}$hat$(z).$

a$)$ Calculate the center of mass of the using the center of the lower puck as your origin $($show your work$).$

b$)$ Calculate the angular momentum of the system relative to the center of mass before the collision.

c$)$ Calculate the moment of inertia $($about the center of mass$)$ of the two mass system.

d$)$ Calculate the angular velocity about the center of mass after the collision $($specify both magnitude and direction$).$

e$)$ Calculate the linear velocity of the two disks after the collision.

before collision

after collision

$h=R$

Variable Type Data$/$Info

$\backslash$table$[[$Li$,$float,$-0\mathrm{.}00050974336],[$Li$1,$float,$-0\mathrm{.}0005152],[$Li$2,$float,$5\mathrm{.}45664e-06$