Ok, so as far as I understand it, it is impossible to turn linear momentum (p) into rotational momentum (L), but I don't quite understand why. The main thought experiment I have in my head is this: A ball in space is traveling with a momentum mbVb, and gravity and friction are assumed to be zero. It impacts an arm, which it sticks to, and the arm is connected to a frictionless, fixed axle. This cause the arm, with the ball attached, to rotate about the axle with angular momentum ω(Ib+Iarm) and zero linear momentum, due to the fixed axle (I'm guessing that is where it's wonky, if the axle is fixed to something such as a planet [while ignoring gravity], I assume the planet itself would take over the linear momentum?). After a 180o rotation, the arm releases the ball, which now has the linear momentum mb(-Vb) or (-p). This makes perfect sense in my head, but from what I understand it is incorrect. Assuming the axle is fixed to the aforementioned planet, how would you determine the momentum at different points in time? Would the ball still indeed have an equal magnitude momentum before and after it met the arm/axle? Would the planet take on the linear momentum until the ball is released at which point the planet would return to whatever momentum it had prior to contact with the ball? Alternatively, if the axle is not fixed at all, would the center of mass of the ball/arm/axle system gain the linear momentum, but only until the ball was released? EDIT: Also, what if the arm only has a 180o field of movement about the axle, such that the arm stopped rotating at the moment the ball released?