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PhysicsClassical Physics

State the Second Law of Motion: Meaning, Formula, and Conditions

Newton’s second law relates net external force to momentum change and reduces to net force equals mass times acceleration when the system mass is constant.

Question

State Newton's second law of motion.

Answer

Newton's second law states that the net external force on a system equals the instantaneous rate of change of that system's momentum:

∑F⃗ext=dp⃗dt.\sum \vec F_{\mathrm{ext}}=\frac{d\vec p}{dt}.

The net force and the rate of change of momentum are vectors that point in the same direction. For a system of constant mass, p⃗=mv⃗\vec p=m\vec v, so

∑F⃗ext=mdv⃗dt=ma⃗.\sum \vec F_{\mathrm{ext}}=m\frac{d\vec v}{dt}=m\vec a.

Thus acceleration points in the direction of the net external force, grows in proportion to that force for fixed mass, and decreases as mass increases for a fixed force. The word net matters: individual external forces must be added as vectors. Internal forces are not included in the net external force on the chosen system.

Evidence boundary

This answer uses classical mechanics in an inertial reference frame and requires a defined system boundary. The familiar sum of external forces equals mass times acceleration form assumes constant mass. The momentum-rate form applies directly to a closed material system. Variable-mass or open-system problems require careful treatment of momentum carried across the system boundary.

Sources

These references support the concepts and methods used in the explanation above.