Newton’s Equations of motion

Newton's First Law

Or the principle of inertia.

A body remains at rest, or in constant motion in a strait line, unless it is acted upon by a force

Newton's Second Law

The force on a body at a given time is equal to its mass times it's acceleration or the rate at which it's momentum changes.

Momentum is given as

$p=mv$

Where:

• $p$ is the momentum of the object (kg ms${}^{-1}$)
• $m$ is it's mass in kg
• $v$ is it's velocity in metres per second ms${}^{-1}$

$F={\displaystyle \frac{p}{dt}}=m{\displaystyle \frac{dv}{dt}}$

Leading to

$F=ma$

Where:

• $F$ is force in newtons (N)
• $m$ is the mass in kilograms (kg)
• $a$ is acceleration in metres per second squared (ms${}^{-2}$)

1 N = 1 kg ms${}^{-2}$

Newton's Third Law

If two bodies exert a force upon each other, these forces are equal in magnitude but opposite in direction.

If two bodies hav momentums $p_1$ and $p_2$, then the total moimentum of the pair is

$p=p_1+p_2$

and the rate of change of $p$ is

${\displaystyle \frac{dp}{dt}}={\displaystyle \frac{d{p}_1}{dt}}+{\displaystyle \frac{d{p}_2}{dt}}$

Planted: Wednesday 23 October 2024
Last tended: Sunday 13 July 2025