1. The problem statement, all variables and given/known data For each of the following potential energy functions in three dimensions, what quantities are conserved (energy, momentum, angular momentum)? 2. Relevant equations U = k/2(x^2 + y^2) U = α/r U = β(z(hat) dotted with r)^2 U = α/r + β(z(hat) dotted with r)^2 Where z(hat) is the unit vector in the z direction. 3. The attempt at a solution So I understand that in order for the angular momentum to be conserved the cross product of r and F, being the force obtained from the negative gradient of U, must be equal to zero. However I am not sure what to use for the position vector r.