1. The problem statement, all variables and given/known data A particle of mass m moves under the influence of a central force F(r)=-mk[(3/r^2)-2a/r^3]rhat Show that if the particle is moving in a circular orbit of radius a, then its angular momentum is L=mh=m√(ka) 2. Relevant equations L=mvr for circular orbit 3. The attempt at a solution From the equation, we extract the second derivative of the position vector r''=-k[(3/r^2)-2a/r^3]rhat. We integrate this in order to find the velocity to use in L=mvr. (At this point, can I dot product both sides by rhat to get rid of the vector?) r''=-k[(3/r^2)-2a/r^3] Integrating: r'=-k[-3/r+a/r^2]=-k[(-3r+a)/r^2] Using the angular momentum equation L=mvr=m*r'*r: L=m*-k[(-3r+a)/r^2]*r. We have r=a, so L=m*(-k[(-3a+a)/a^2]*a)=m2k. So obviously, the integration is wrong because I haven't included the integrating constant and also the answer we get is wrong. And intuitively by substituting in r=a, we are saying that r doesn't change. How could I correctly approach this problem? Thank you!