Law

Newton's second law

(M2.1.1) M2.1 · The Three Laws of Motion →

F_{net} = m a

Statement

The net force on an object equals its mass times its acceleration; force causes a change in motion, in proportion to inertia.

Symbols and units

$F_{net}$	sum of external forces	N
$m$	mass	kg
$a$	acceleration	m/s²

When it applies

Any object in an inertial reference frame; m must be constant (not, for example, a rocket losing fuel mass).

Derivation

An empirical law, not derived from anything more basic: doubling the net force on a given mass doubles its acceleration, and doubling the mass for a given force halves the acceleration.

F_{net} = m a

Worked examples

Acceleration of a pushed crate

A 50 kg crate is pushed with 150 N against 30 N of friction:

a = \frac{F _{net}}{m} = \frac{150 - 30}{50} = 2.4 m/s^{2}

Watch out for

F_net is the vector sum of every external force. Omitting one force, or including an internal one, is the single most common source of error in mechanics problems.

Connects to

Newton's third law