2.5 Newton's Second Law

Newton's Second Law

Newton's Second Law states that the net force on an object equals its mass times acceleration: ΣF = ma. Acceleration is directly proportional to the net force and inversely proportional to mass. Force and acceleration are vectors — they point in the same direction. This law lets us predict motion whenever we know the forces acting on a system.

Free-Body Diagrams and Net Force

To apply ΣF = ma, draw a free-body diagram showing all forces acting on the object (gravity, normal, tension, friction, applied force). Sum forces component-wise (often x and y separately) to find the net force, then divide by mass to get acceleration. Forces that cancel produce zero net force and zero acceleration (constant velocity or rest).

Systems of Multiple Objects

When objects are connected (like blocks linked by a string) or interacting, treat them as a system with a shared acceleration, or analyze each object separately using Newton's Third Law pairs for interaction forces. The same net force equation applies to each object individually, and internal forces between objects must be consistent with each object's own free-body diagram.

Key terms

Newton's Second Law

ΣF = ma; the net force on an object equals its mass times its acceleration.

Net force

The vector sum of all forces acting on an object.

Free-body diagram

A diagram showing all forces acting on a single object, used to find net force.

Relationship between force and acceleration

Acceleration is directly proportional to net force and inversely proportional to mass.

Zero net force result

Zero net force means zero acceleration — the object is at rest or moving at constant velocity.

Try an AP-style question

A 20 N net force acts on a 4 kg box. What is its acceleration?

1. 80 m/s²
2. 0.2 m/s²
3. 5 m/s²
4. 24 m/s²