Newton's Second Law
Net force equals mass times acceleration (rate of change of momentum).
Formula
Variables
Example
Doubling the force on a fixed mass doubles its acceleration.
How it works
Newton's Second Law says that an object's motion changes only when a net force acts on it, and the size of that change depends on both the force and the mass. For a fixed mass, a larger net force produces a larger acceleration; for the same force, a larger mass accelerates less because it is harder to change its motion. The momentum form, F = dp/dt, is the more general version and means force is the rate at which momentum changes with time.
When to use it
Use this formula whenever you need to connect force, mass, and acceleration in mechanics problems, such as pushing carts, braking vehicles, or analysing falling objects. It is also useful in momentum problems where mass may change or where you want to think about how quickly motion is changing.
Worked example, step by step
A 4.0 kg box is pushed with a net force of 12 N. Use Newton's Second Law: F = ma Rearrange to find acceleration: a = F / m Substitute the values: a = 12 / 4.0 Calculate: a = 3.0 m/s^2 Final answer: the box accelerates at 3.0 m/s^2
Common mistakes to avoid
- using the total applied force instead of the net force after all forces are combined
- forgetting to convert units so mass is in kilograms and acceleration is in m/s^2
- assuming acceleration must be in the direction of the applied force rather than the net force
Did You Know?
Newton originally stated his second law in terms of momentum, not the familiar F = ma.
Share this formula
More in Physics Laws & Theorems
View allNewton's First Law (Inertia)
BasicAn object stays at rest or in uniform motion unless acted on by a net force.
Newton's Third Law
BasicFor every action there is an equal and opposite reaction.
Conservation of Momentum
IntermediateTotal momentum of an isolated system stays constant.
Conservation of Energy
BasicEnergy cannot be created or destroyed, only transformed.
Archimedes' Principle
IntermediateBuoyant force equals the weight of fluid displaced.
Pascal's Law
IntermediatePressure applied to a confined fluid transmits equally in all directions.