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Newton's second law (F = ma) and the idea of a system

Summary

Newton's second law says a system's acceleration is proportional to the net external force on it and inversely proportional to its mass: a = F_net / m, usually written F_net = ma. Acceleration points the same way as the net force. To apply the law, first choose the system's boundary. Only forces from outside that boundary count.

Draft. License: CC BY 4.0 (this summary). Sources: [S1] OpenStax (Rice University), "College Physics, 4.3 Newton's Second Law of Motion: Concept of a System" (CC BY 4.0).

Facts

• id: F1 claim: A change in motion means a change in velocity, which is an acceleration; a net external force causes acceleration. confidence: medium date: 2026-11-02 sources: [S1] license: CC BY 4.0 checked_on: 2026-11-02
• id: F2 claim: An external force acts from outside the system of interest; internal forces act between parts of the system and cancel, so they do not change the system's motion. confidence: medium date: 2026-11-02 sources: [S1] license: CC BY 4.0 checked_on: 2026-11-02
• id: F3 claim: You must define the system's boundaries before deciding which forces are external. confidence: medium date: 2026-11-02 sources: [S1] license: CC BY 4.0 checked_on: 2026-11-02
• id: F4 claim: Acceleration is directly proportional to, and in the same direction as, the net external force. confidence: medium date: 2026-11-02 sources: [S1] license: CC BY 4.0 checked_on: 2026-11-02
• id: F5 claim: Acceleration is inversely proportional to the system's mass: the same force accelerates a car far less than a basketball. confidence: medium date: 2026-11-02 sources: [S1] license: CC BY 4.0 checked_on: 2026-11-02
• id: F6 claim: Combined: a = F_net / m, or F_net = m a; in SI units a newton is the force that accelerates 1 kg at 1 m/s^2 (1 N = 1 kg·m/s^2). confidence: high date: 2026-11-02 sources: [S1] license: CC BY 4.0 checked_on: 2026-11-02
• id: F7 claim: The net external force is the vector sum of all external forces, found graphically (head-to-tail) or with components. confidence: medium date: 2026-11-02 sources: [S1] license: CC BY 4.0 checked_on: 2026-11-02

Caveats

• Valid for speeds well below light speed and for objects much larger than atoms (classical mechanics).

Pointers

• id: P1 answers: Full details and updates where: https://openstax.org/books/college-physics/pages/4-3-newtons-second-law-of-motion-concept-of-a-system access: free, public web page

@misc{iil_note_6f8j9419,
  author = {{iinventedlight Library}},
  title = {{Newton's second law (F = ma) and the idea of a system}},
  howpublished = {iinventedlight Library},
  year = {2026},
  date = {2026-11-02},
  url = {https://iinventedlight.com/library/reference/us-gov/newtons-second-law/},
  note = {Permanent ID iil:note:6f8j9419. License: CC-BY-4.0. Summary of https://openstax.org/books/college-physics/pages/4-3-newtons-second-law-of-motion-concept-of-a-system.},
}

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