Newton's Three Laws of Motion Explained
Published in 1687, Newton's three laws underpin almost everything in classical mechanics. Understanding them — not just memorizing them — makes the rest of physics vastly more intuitive.
Background: What Forces Do
Before the laws: a force is a push or pull — any interaction that, if unopposed, changes the velocity of an object. Forces are vectors: they have both magnitude (how strong) and direction (which way). The SI unit is the newton (N), where 1 N = 1 kg·m/s².
First Law — The Law of Inertia
"An object at rest remains at rest, and an object in motion remains in motion at constant velocity, unless acted upon by a net external force."
This seems obvious for a stationary book on a desk. It is less obvious for a moving object, because in everyday life friction and air resistance constantly act as net forces — meaning objects do slow down without an obvious push. In outer space, with negligible forces, a moving object really does continue forever in a straight line.
Inertia is not a force — it is a property. It is an object's resistance to changes in its state of motion. More mass = more inertia. A bowling ball and a tennis ball dropped from the same height reach the ground at the same time (ignoring air resistance), but the bowling ball is far harder to get moving in the first place.
Real-world example: When a car brakes suddenly, your body continues forward. This is not a "force throwing you forward" — it is your inertia carrying you in the direction you were already going, while the car decelerates around you. The seatbelt provides the net force needed to slow you along with the car.
Second Law — Force, Mass, and Acceleration
"The net force acting on an object equals its mass multiplied by its acceleration."
Or rearranged: a = F/m. Acceleration is directly proportional to net force and inversely proportional to mass. Double the force on the same object and it accelerates twice as fast. Apply the same force to an object twice as heavy and it accelerates half as fast.
Example calculation: A 1,200 kg car accelerates from rest to 20 m/s in 8 seconds. What net force is required?
F = ma = 1200 × 2.5 = 3,000 N
The Net Force Is What Matters
When multiple forces act on an object simultaneously, what matters is their vector sum — the net force. A 10 N force to the right and a 10 N force to the left produce zero net force, and by the first law, the object's velocity does not change. A 10 N force right and a 6 N force left produce a 4 N net force to the right, and the object accelerates right.
Third Law — Action and Reaction
"For every action, there is an equal and opposite reaction."
More precisely: when object A exerts a force on object B, object B simultaneously exerts a force of equal magnitude and opposite direction on object A. These forces are called an action-reaction pair.
Example 1 — Walking: You push backward on the ground (action). The ground pushes forward on you (reaction). The reaction force from the ground is what propels you forward. Without friction — on ice — your foot slides and the reaction force is reduced.
Example 2 — Rocket propulsion: A rocket expels gas downward at high speed (action). The gas exerts an equal force upward on the rocket (reaction). No air or ground is needed; rockets work in vacuum for exactly this reason.
Action-reaction forces act on different objects, so they never cancel each other out. A horse pulls a cart forward; the cart pulls the horse backward with equal force. Yet the horse-cart system moves forward because the ground pushes the horse's hooves forward — a separate interaction entirely. Confusion arises when students try to apply all forces from different pairs to the same free-body diagram.
The Laws Working Together: A Skateboarding Example
You stand on a skateboard and push backward against a wall:
- Third law: You push the wall; the wall pushes you forward with equal force.
- Second law: The net forward force on you (plus skateboard) causes you to accelerate in proportion to your combined mass.
- First law: Once you stop pushing and coast away, you continue at constant velocity — no net force, no further acceleration (ignoring friction).
Units and Conversions to Know
- 1 newton (N) = 1 kg·m/s²
- Weight = mg (mass × gravitational acceleration). On Earth, g ≈ 9.8 m/s².
- A 70 kg person weighs 70 × 9.8 ≈ 686 N — this is the gravitational force on them, not their mass.
Summary
Newton's first law: objects resist changes in motion (inertia). The second law: net force equals mass times acceleration (F = ma) — the central equation of classical mechanics. The third law: forces always come in equal and opposite pairs acting on different objects. These three laws are not independent — they form an interlocking system. Master their interaction and almost every classical mechanics problem becomes a matter of identifying forces, drawing a free-body diagram, and applying F = ma.