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

Step 1: Analyze the linear momentum of the system.

According to Newton's second law for a system of particles, the rate of change of total linear momentum $\vec{P}$ is equal to the net external force.

$$\frac{d\vec{P}}{dt} = \sum \vec{F}_{\text{ext}}$$

Since the resultant of all external forces is zero:

$$\sum \vec{F}_{\text{ext}} = \vec{0}$$ $$\frac{d\vec{P}}{dt} = \vec{0}$$ $$\vec{P} = \text{constant}$$

Thus, the linear momentum of the system must remain constant.

Step 2: Analyze the kinetic energy of the system.

Internal forces can perform net work on the particles, such as during an inelastic collision where kinetic energy is lost as heat.

$$W_{\text{internal}} \neq 0$$ $$\Delta K \neq 0$$

Therefore, the kinetic energy does not necessarily remain constant.

Step 3: Analyze the potential energy of the system.

The potential energy of the system depends on its internal configuration, which can change due to internal forces (such as springs compressing or stretching).

$$U = U(\text{internal configuration})$$

Therefore, the potential energy does not necessarily remain constant.

Step 4: Analyze the angular momentum of the system.

The rate of change of angular momentum $\vec{L}$ depends on the net external torque.

$$\frac{d\vec{L}}{dt} = \vec{\tau}_{\text{ext}}$$

A system can experience a non-zero net torque even when the net external force is zero, such as when a force couple acts on the system.

$$\vec{\tau}_{\text{ext}} \neq \vec{0}$$

Therefore, the angular momentum does not necessarily remain constant.

Answer: The linear momentum of the system does not change with time.