Newton's Second Law and Free-Body Diagrams
A free GRE Physics mechanics note on applying net force, mass, acceleration, and free-body diagrams without hiding assumptions.
Open standalone topic pageWhat you will be able to do
- 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.
Concept overview
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.
Key formulas
Newton's second law for constant mass
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 block on a horizontal surface has a pull to the right and 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 to the right.
- 4Use .
The block accelerates at 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.
Study advice
- If a mechanics problem feels ambiguous, write the system boundary in words before drawing forces.
- Check signs after choosing axes; a negative acceleration is often just a direction result, not a new physical effect.
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Go to practiceSources for this topic
- 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.