CLS-01

Newton's second law

F = m a for a particle of constant mass.

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Laws of motionNewton 1687

Governing equation

F = ma = \dfrac{\mathrm{d}p}{\mathrm{d}t}

$a \in \left[-20, 20\right]$

where

m: Mass (kg)
a: Acceleration (m/s²)
F: Force (N)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

F = ma = \dfrac{\mathrm{d}p}{\mathrm{d}t}

$a \in \left[-20, 20\right]$

$a = -20$ $F = -100$

Along the curve

②

Domain of the variable — blue

a_{\min} = -20,\quad a_{\max} = 20

$a \in \left[-20, 20\right]$

$a = -20$ $a = -20$

Along the curve

③

Response curve — green

F = ma = \dfrac{\mathrm{d}p}{\mathrm{d}t}

$a \in \left[-20, 20\right]$

$a = -20$ $F = -100$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}F}{\mathrm{d}a}

$a \in \left[-20, 20\right]$

$a = -19.75$ $F^{\prime} = 5$

Along the curve

Lecture brief

Historical brief

Newtonian mechanics (1687) plus energy, angular momentum, Kepler and the ballistic parabola remain the first language of motion. Every sheet here is a closed-form orbit, throw, spin or oscillator. This sheet (CLS-01 — Newton's second law) is the form associated with Newton 1687. Working symbols: $m$ , $a$ $\rightarrow$ $F$ . Newton stated that the change of motion is proportional to the motive force and takes place along the line of that force, now written F = dp/dt = m a.

Purpose

Purpose: compute

F

from

m

a

in Classical mechanics via

F = ma = \dfrac{\mathrm{d}p}{\mathrm{d}t}

F = m a for a particle of constant mass. Use it when a real classical mechanics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

m = 5.000\,\mathrm{kg}

a = 2.000\,\mathrm{m/s^{2}}

, the governing relation

F = ma = \dfrac{\mathrm{d}p}{\mathrm{d}t}

yields

F = 10.000\,\mathrm{N}

. Inertial frame, constant mass, one-dimensional. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mass m5 kgAcceleration a2 m/s²

Outputs

Force F10.000 N

Reading speed

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Narration of this film

Inertial frame, constant mass, one-dimensional.

Newton stated that the change of motion is proportional to the motive force and takes place along the line of that force, now written F = dp/dt = m a.

Reading speed

Watch on YouTube