Question

If the resultant of all external forces acting on a system of particles is zero, then from an inertial frame one can surely say that:

• A. Linear momentum of the system does not change in time
• B. Kinetic energy of the system does not change in time
• C. Potential energy of the system does not change in time
• D. Angular momentum of the system does not change in time

Hint:

When the resultant external force is zero, linear momentum is conserved in an inertial frame of reference. However, kinetic and potential energy may still change due to internal forces.

Answer 1

The Correct Option is A

When the resultant external force acting on a system of particles is zero, the system is said to be in a state where no external force is acting on it. According to Newton's first law, in an inertial frame of reference, an object remains at rest or continues to move with constant velocity unless acted upon by an external force.
In this case, if the resultant external force is zero, the system's linear momentum will remain constant over time. The law of conservation of linear momentum states that: \[ \frac{d\vec{p}}{dt} = \vec{F}_{\text{ext}} \] where \( \vec{p} \) is the linear momentum and \( \vec{F}_{\text{ext}} \) is the external force. Since \( \vec{F}_{\text{ext}} = 0 \), we have: \[ \frac{d\vec{p}}{dt} = 0 \] Thus, the linear momentum of the system does not change in time.
The kinetic energy and potential energy of the system may still change due to internal interactions, but the linear momentum remains conserved in the absence of external forces. Similarly, the angular momentum can change depending on internal torques even if the net external force is zero.
Thus, the correct statement is that the linear momentum of the system does not change in time.