PLEASE PROVIDE A FULL EXPLANATION AND STEP BY STEP ON HOW TO APPROACH AND DO EVE

Question

PLEASE PROVIDE A FULL EXPLANATION AND STEP BY STEP ON HOW TO APPROACH AND DO EVERYTHINg.
As I completely got this question wrong.

Question if unclear: A wad of sticky clay with mass m and velocity v_i is fired at a solid cylinder of mass M and radius R. The cylinder is initially at rest and is mounted on a fixed horizontal axle that runs through its center of mass. The line of motion of the projectile is perpendicular to the axle and at a distance d < R from the center.
a.) Find the angular speed of the system just after the clay strikes and sticks to the surface of the cylinder.
b.) How much mechanical energy is lost due to friction in this process? (The rotational inertial of the cylinder about its center axle is 1/2 MR^2)

** also on a side note, how would you find the angular momentum for this problem?

Explanation / Answer

conserve angular momentum of the system about the center axis of cylinder...........
inertia after sticking, Itotal = 0.5MR2 + mR2
mVid = Itotal x
= mVid/ Itotal
= mVid/(0.5MR2 + mR2 )

loss in mechanical energy lost = K.Einitial - K.E final
  = 0.5mVi2 - 0.5Itotal2
= 0.5mVi2 - 0.5[0.5MR2 + mR2]{mVid/(0.5MR2 + mR2 )}2
= 0.5mVi2 - 0.5mVid/(0.5MR2 + mR2 )

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