Newton's Laws of Motion
Newton's three laws of motion with formulas, explanations, and real-world examples.
Foundation of classical mechanics.
Newton's First Law (Law of Inertia)
If ΣF = 0, then v = constant
In simple terms: things keep doing what they are doing unless a force changes that. A ball rolling on a frictionless surface would roll forever.
Newton's Second Law
ΣF = m × a
The net force on an object equals its mass times its acceleration. This is the most used equation in classical mechanics.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| F | Force | Newtons (N) |
| m | Mass | Kilograms (kg) |
| a | Acceleration | m/s² |
| ΣF | Net (total) force | Newtons (N) |
| v | Velocity | m/s |
Newton's Third Law
F₁₂ = −F₂₁
When object A exerts a force on object B, object B exerts an equal force back on object A in the opposite direction. When you push a wall, the wall pushes back on you with the same force.
Example 1 — Second Law
A 5 kg box is pushed with a force of 20 N. What is the acceleration?
F = m × a → a = F / m
a = 20 N / 5 kg
a = 4 m/s²
Example 2 — Weight Force
What is the weight (force of gravity) on a 70 kg person?
Weight = m × g (where g = 9.81 m/s²)
W = 70 × 9.81
W = 686.7 N (about 154.3 lbs of force)
Example 3 — Third Law
A swimmer pushes water backward with 50 N of force. What happens?
By Newton's third law, the water pushes the swimmer forward with 50 N.
The swimmer accelerates forward (F = 50 N in the forward direction).
When to Use Them
- First law: Understanding why objects resist changes in motion (inertia, seatbelts, etc.)
- Second law: Calculating force, mass, or acceleration when two of the three are known
- Third law: Analyzing interactions between objects (rockets, swimming, walking)