This is how the specific question is framed?
If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame,
one can surely say that:
1: Linear momentum of the system does not change in time.
2: Kinetic energy of the system does not change in time.
3: Angular momentum of the system does not change in time.
4: Potential energy of the system does not change in time.
My attempt
( I will for moment assume that my system of particle might be a rod)
I can surely see that since net external force has a resultant $0$ it easily implies that Linear momentum remain conserved. (A)
The net external forces may be $0$ but the net torque may or may not be $0$ hence the body may start to rotate about some axis and gain rotational kinetic energy, hence answer (B) is incorrect.
Also, Following from above net torque acting on system may not be zero Angular momentum is not conserved. (C) is incorrect.
Now is my problem, I am not able to understand what can i make of potential energy since in the question we are not given anything how is this system with respect to it's environment , I know that if this were in a gravitational field or something the potential energy could change and would change of course due to orientation. Also we are not even told anything about what kind of internal forces acts between the particle of this system. Can conservative and non conservative forces affect this? Can i conclude that this question doesn't give me enough information or I am missing something, please explain in detail, Thank you!
(P.S : This is a kind of problem in which one or more option can be correct.)
Best Answer
You're correct that (B) is incorrect, but for the wrong reason. Kinetic energy doesn't have to be conserved since, in any closed system with only conservative forces, mechanical energy is conserved. There are many physical situations where kinetic energy isn't conserved (inelastic collisions for example), hence we do not know kinetic energy is conserved.
Similarly, (D) is also incorrect. Just imagine a system with two positive charges. As the positive charges repel each other (an internal force), the potential energy decreases. Again, potential energy is not in general conserved, mechanical energy is.
Whether the forces on the system are conservative or nonconservative doesn't affect your answer.