Hi everybody! I'm preparing myself for upcoming exams, and I struggle a little with conservation of angular momentum. Can anybody help me understand how to solve such problems? 1. The problem statement, all variables and given/known data (for a better comprehension, see the attached image) We have a wooden cylinder of mass mZ = 600g and of radius r0 = 5cm, which can rotate around its symmetry axis. Someone shoots on it, and the projectile has the mass mG = 5.0g and initial velocity v = 80m/s. The distance between the linear trajectory of the projectile and the rotation axis of the cylinder is r1 = 3.0cm. The projectile penetrates the cylinder and stays stuck at a distance of r2 = 3.5cm from the rotation axis of the cylinder. a) What is the frequency of rotation f of the cylinder after the impact? Where and how should you shoot the projectile in order to obtain maximum/minimum frequency? b) Which part of the kinetic energy is used to deform the wooden cylinder? c) If the cylinder was not fixed on a rotation axis but on a thread, what would be the differences to previous case when the projectile hits the cylinder? 2. Relevant equations So I imagine both conservation of linear momentum and of angular momentum are important. We also know that ω = 2πƒ. 3. The attempt at a solution Okay I give it a go: We know that the linear momentum is conserved, that the cylinder is not moving before the collision and that the two objects are moving together after the collision: mG ⋅ v = (mG + mZ) ⋅ v' Here I already see a problem: v' is supposed to be the tangential velocity of the system cylinder-projectile after the collision, but I believe a projectile located at r2 = 3.5cm does not have the same tangential velocity as a point located at r0 = 5.0cm. Is that correct? Then we would have mG ⋅ v = mG ⋅ vG' + mZ ⋅ vZ', which is also not so great. I encounter the same problem with the conservation of angular momentum: mG ⋅ v ⋅ r0 = (mG + mZ) ⋅ v' ⋅ r0 or mG ⋅ v ⋅ r0 = mG ⋅ vG' ⋅ r2 + mZ ⋅ vZ' ⋅ r0 ? I feel like I'm missing something, since none of those equations lead me anywhere :( Furthermore, I never manage to involve r1 in the equations, which obviously plays a role because of the 2nd part of the question. Can someone give me a clue so that I clarify my misunderstandings? Thank you very much in advance. Julien.