Answer to Question #205574 in Classical Mechanics for Richard

Question

3.7. Show that: If a particle is subject to a central force only, then its angular momentum is conserved i.e. If V(r) = V(r), then dL/dt = 0.

Answer 1

Answer

When central force is acting then torque of the central about the center will be zero.

So

$\tau=\frac{dL}{dt}$

$\tau=0$

So

$\frac{dL}{dt}=0$

So change is angular momentum is zero so it is conserved.