The bullet with horizontal velocity of $v_m =$ $m/s$ strikes the compound pendulum, which is initially at rest. The compound pendulum and the bullet have masses $M =$ $27.9$ $kg$ and $m = 23.6$ $g$, respectively. The height of the pendulum centre of gravity $G$ is $h_{pendulum} = 0.85 m$; the width of the pendulum, $w$ is $2 cm$; and the height at which the bullet strikes, $h_{bullet}$ is $1.1 m$.

Determine the angular velocity of the compound pendulum and the bullet immediately after the strike which causes the bullet to be embedded in the pendulum. The radius of gyration of the pendulum is $k_O =84.1$ $cm$ around point $O$. Also calculate the following parameters:

Angular momentum of the bullet before the strike about point $O$, $H_{bullet}$

Angular momentum of the pendulum before the strike about point $O$, $H_{pendulum}$

Mass moment of inertia of both of the bullet and pendulum about point $O$, $I_O$.

$H_{bullet,O}$ = $kg$-$m^2/s$, angular momentum of the bullet before the strike

$H_{pendulum,O}$ = $kg$-$m^2/s$, angular momentum of the pendulum before the strike

$I_O$ = $kg$-$m^2$, mass moment of inertia (Enter answer to three decimal points)

$\omega_{post-impact}$ = $rad/s$, angular velocity

# Pay attention to the unit of each answer