Okay, so my previous calculations were wrong because the moment of inertia for the rod changes after collision? Meaning I(combined object) doesn't equal Irod? To find the new moment of inertia i have to find the new center of mass for the combined object, which is (0*1/9*M +1/2*L*M)/10/9*m...
Okay, so instead of m*r*v=m*r*v ill use I*ω = m*r*v?
Substituting v=ω*L gives me I*ω = m*L^2*ω
That gives me i*ω = 10/9*M *L*v v=ω*L
i*ω1 =10/9*M*L^2 * ω2 , i=1/3*M*L^2, ω1 = sqrt (29.43/L), I=Irod
I rod*sqrt (29.43/L) = 10/9 *M*L^2*w
solving for w using symbolab gives me w = (1.627*sqrt...
Assuming no friction anywhere, no drag and perfect inelastic collision
Using conservation of mechanical energy i can determine the rotational speed of the rod right before collision occurs.
mgh=1/2*i*w^2
center of mass falls 1/2*L so we have:
M*g*1/2*L = 1/2*(1/3*M*L^2)*w^2
Solving for w...