- #1
subzero0137
- 91
- 4
Problem: Consider a system for which Newton's second law is $$ \frac {d \vec v}{dt} = - [ \frac {h(r)h'(r)}{r} + \frac {k}{r^3} ] \vec r- \frac {h'(r)}{r} \vec L $$ where k is a constant, h(r) is some function of r, h'(r) is its derivative and L = r x v is the angular momentum. Show that $$ \frac {d \vec L}{dt} = - \frac {h'(r)}{r} \vec r × \vec L$$ and use this equation to prove that L is not generally conserved, but its magnitude L is conserved.
Attempt: I've done the first part of the question, but I don't know how I should go about showing that L is not conserved but its magnitude is conserved. Any hints would be appreciated.
Attempt: I've done the first part of the question, but I don't know how I should go about showing that L is not conserved but its magnitude is conserved. Any hints would be appreciated.