Newton's Second Law⚠ unverified
Physics / Mechanics · Compute acceleration a = F / m
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| force | F | N | 10.0 | Net force |
| mass | m | kg | 1.0 | Mass |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| acceleration | a | m/s^2 | Acceleration |
The science & history
Understanding the Parameters
-
$F$ — net force (sum of all forces). A single applied force is not enough if friction or other loads remain.
-
$m$ — resistance to acceleration; larger $m$ → smaller $a$ for the same $F$.
- $a$ — rate of change of velocity. Constant $F$ and $m$ give constant $a$ (uniform acceleration).
Derivation (Approaching a Proof)
Newton’s second law in modern form is $\mathbf{F}_{\mathrm{net}} = d\mathbf{p}/dt$ with $\mathbf{p} = m\mathbf{v}$. For constant mass, $d\mathbf{p}/dt = m\,d\mathbf{v}/dt = m\mathbf{a}$, so $\mathbf{F} = m\mathbf{a}$ and $a = F/m$ along a chosen axis. The law is a postulate of classical mechanics, tested by experiment, not derived from something more elementary within Newtonian theory.
Dimensional check: $1\,\text{N} = 1\,\text{kg}\cdot\text{m/s}^{2}$ by definition of the newton.
History
Isaac Newton’s Principia (1687) stated the laws of motion; the modern $F=ma$ textbook form is a later algebraic packaging of his momentum-rate idea, refined through Euler and 18th-century mechanics.
Related Concepts: Momentum, Impulse, Kinetic Energy, Torque, Centripetal Force
Notes: Registry calculator newtons-second-law (unverified). Constant-mass particle form; variable
mass systems (rockets) need $F = \dot p$ carefully.