Center of mass rigid body, the gravity forces will not cause the body to rotate, which means the weight of the body can be considered to be concentrated at the center of mass. The linear and angular momentum of a collection of particles can be simplified by measuring the position and velocity of the particles relative to the center of mass. Let the system of particles "P", "i"=1...,"n" of masses "m" be located at the coordinates r with velocities v. Select a reference point R and compute the relative position and velocity vectors, The total linear and angular momentum vectors relative to the
Sum and Product Puzzle "X" + "Y" and P knows the product "X" × "Y". Both S and P know all the information in this paragraph. The following conversation occurs: What are "X" and "Y"? The solution has "X" and "Y" as 4 and 13, with P initially knowing the product is 52 and S knowing the sum is 17. Initially P does not know the solution, since and S knows that P does not know the solution since all the possible sums to 17 within the constraints produce similarly ambiguous products. However, each can work out the solution by eliminating other possibilities following