Newton's second law

High School

Definition

The principle that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, written as F = ma. It explains how the size of a force determines how quickly an object speeds up.

Worked examples

\(F = ma \)→\( 20\,\)N\( = (5\,\)kg\()(4\,\)m/s\(^2)\)

A 20-newton net force accelerates a 5-kilogram object at 4 meters per second squared.

\(a = \frac{F}{m} \)→\( a = \frac{10\,\)N\(}{2\,\)kg\(} = 5\,\)m/s\(^2\)

Rearranging the equation shows that doubling the mass halves the acceleration for the same force.

Common mistakes

\(F = ma\) means force equals mass times velocity → \(F = ma\) means force equals mass times acceleration Acceleration is the rate of change of velocity, not velocity itself.
A heavier object always experiences more force → A heavier object needs more force to achieve the same acceleration Mass and force are independent; the equation relates force, mass, and the resulting acceleration.
\(F = ma\) applies to any force acting on an object → \(F\) is the net force (sum of all forces) acting on the object You must add all forces as vectors to find the net force before applying the equation.

Where you'll use it next

You'll apply Newton's second law to solve dynamics problems in physics, analyze motion with friction and tension, design experiments measuring force and acceleration, and later connect it to momentum, energy, and rotational motion in advanced mechanics.

Found in 1 StudyPug lesson

Newton's Second Law of Motion: Understanding F=ma

AS-Level Maths

Dive into the fundamental principle of F=ma. Learn how force, mass, and acceleration interact, and apply this knowledge to real-world scenarios. Master problem-solving skills in classical mechanics.

11th Grade11th