Newton's Second Law and Free-Body Diagrams

Concise answer

For a constant-mass system, choose the system boundary, draw only external forces, and apply the vector equation $\sum \vec{F}_{\mathrm{ext}} = m\vec{a}$ component by component.

Definitions

System: The object or collection of objects whose motion you are analyzing.
Net external force: The vector sum of forces exerted on the chosen system by objects outside it.
Free-body diagram: A diagram that isolates the chosen system and shows the external forces acting on it.

Intuition

Acceleration responds to the combined external push or pull, not to any one force in isolation. Equal opposing forces can be individually large while producing zero acceleration.

The system boundary decides which forces count as external. A force between two parts included in one system is internal to that combined system.

Concept walkthrough

Newton's second law is a relationship between the net external force on a chosen system, the system's mass, and its acceleration. The law is vector-valued: the acceleration points in the same direction as the net force when mass is positive and constant.

For GRE Physics-style mechanics, the most important step is usually not algebra. It is defining the system and drawing a free-body diagram that includes external forces only. After that, choose axes and write the component equations.

After this page, you should be able to

Choose the system whose motion is being analyzed.
Separate external forces from forces internal to the chosen system.
Apply the vector form of Newton's second law component by component.
Check whether vertical forces cancel before assuming one-dimensional motion.

Formulas and assumptions

Newton's second law for constant mass

\sum \vec{F}_{\text{ext}} = m\vec{a}

Variables

sum F_ext: vector sum of external forces
m: mass in kilograms
a: acceleration in meters per second squared

Assumptions

Mass is constant.
Forces are measured in an inertial frame or an explicitly handled non-inertial frame.
Internal forces within the chosen system cancel in pairs.

Worked example

Horizontal net-force check

A $2.0\,\text{kg}$ block on a horizontal surface has a $10\,\text{N}$ pull to the right and $3\,\text{N}$ kinetic friction to the left. What is its horizontal acceleration?

1Choose the block as the system.
2Vertical forces cancel if the block has no vertical acceleration.
3The horizontal net force is $10\,\text{N} - 3\,\text{N} = 7\,\text{N}$ to the right.
4Use $a = \dfrac{\sum F_x}{m} = \dfrac{7\,\text{N}}{2.0\,\text{kg}}$ .

The block accelerates at $3.5\,\text{m/s}^2$ to the right.

Common traps

Adding normal force and weight into the horizontal equation when the axes are not tilted.
Treating the applied force as the net force before subtracting friction or other opposing forces.
Including forces between parts of the chosen system after deciding to analyze those parts together.

GRE Physics overview Net force public explainer Sign in for current practice

Question depth and domain coverage vary by exam. Practice answers are checked after submission.

Sources

GRE Subject Test Content and Structure — ETS. Accessed 2026-07-06. Use as a cited source for exam facts; do not imply affiliation or reproduce protected test material.
University Physics Volume 1, Section 5.3: Newton's Second Law — OpenStax. Accessed 2026-07-06. OpenStax textbook content is CC BY-NC-SA 4.0; attribute and avoid verbatim reuse beyond short cited references.

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Last source check: 2026-07-06
Next scheduled review: 2026-10-06

Recheck ETS content areas and OpenStax mechanics references before each major GRE Physics preparation cycle.

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