Hopefully the image is self-explanatory, if not: A cylinder is rotating around its central axis with angular momentum L1; an angular impulse, ΔL is then added to the cylinder, perpendicularly with respect to L1. The hypothetical result is: the cylinder has one angular mometum at the end, L-result. L-result is equivalent in magnitude to L1, and its direction is shifted counter-clockwise by a certain ammount so that a line parallel to L1 draw from the tip of L-result will meet the tip of ΔL, mathemetically, the angle has increased in the counter-clockwise direction by (90-arccos(ΔL / L1)) degrees. (<-- that stuff is got from basic trignometry) Is this true? If it is false, what is the right way to do it? Additional question: will the cylinder "follow" the angular momentum arrow and also point in the new direction, or will it remain in place and then rotate around the new arrow in a weird fashion?