Physics › 🚀 Mechanics

Newton's Three Laws

The three rules that connect forces to motion — and explain almost everything you see move.

High schoolAP Physics 1 levelUni Year 1
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The big idea: A force is a push or a pull. Newton's three laws tell you exactly what forces do: things keep doing what they're doing unless a force acts (1st), a net force produces acceleration in proportion to mass (2nd, F = ma), and every force comes in an equal-and-opposite pair (3rd).
🎯 By the end, you'll be able to
  • State Newton's three laws in plain language
  • Use F = ma to relate force, mass and acceleration
  • Explain motion using the idea of a net (unbalanced) force
  • Identify the two members of an action–reaction pair
📎 You should already know
  • Velocity & Acceleration
  • Vectors (direction of a force)

First law — the law of inertia

An object at rest stays at rest, and an object in motion keeps moving in a straight line at constant speed — unless a net force acts on it. This stubbornness is called inertia. A hockey puck on smooth ice glides forever; the only reason everyday objects stop is hidden forces like friction and air resistance.

🔑 Second law — F = ma
A net force makes an object accelerate. The bigger the force, the bigger the acceleration; the bigger the mass, the smaller the acceleration for the same push. This is the single most useful equation in mechanics.
\[ F = m\,a \qquad\Longleftrightarrow\qquad a = \frac{F}{m} \]
Force equals mass times acceleration. Rearranged: acceleration is force divided by mass.
🎮 Interactive: F = ma LIVE
Change the force and the mass and watch the acceleration respond. Double the force → double the acceleration. Double the mass → half the acceleration. The green arrow shows the resulting acceleration.

Third law — action and reaction

For every action there is an equal and opposite reaction. When you push on a wall, the wall pushes back on you just as hard. A rocket throws gas downward, and the gas throws the rocket upward. The two forces are always equal in size, opposite in direction — and crucially, they act on different objects.

⚠️ The pair acts on different objects
Action–reaction forces never cancel out, because they push on two different bodies. Your feet push back on the ground; the ground pushes forward on you — and that forward push is what lets you walk. If both forces acted on the same object, nothing could ever accelerate.
📝 Worked example: A 1,000 kg car experiences a net forward force of 4,000 N. What is its acceleration?
  1. Use \(a = \dfrac{F}{m}\).
  2. \(a = \dfrac{4000}{1000}\).
✓ a = 4 m/s². (Every second, the car gains 4 m/s of speed.)

Check your understanding

1. You apply the same force to a shopping trolley, first empty, then full. When full (more mass), its acceleration is…
a = F/m. For the same force, more mass means less acceleration.
2. A 2 kg object accelerates at 5 m/s². What net force acts on it?
F = m·a = 2 × 5 = 10 N.
3. A book rests on a table. The table pushes up on the book. By Newton's third law, the equal-and-opposite reaction is…
The reaction to 'table pushes up on book' is 'book pushes down on table' — same pair, opposite directions, on the two different objects. (Gravity is a separate force, not the reaction partner.)
✅ Key takeaways
  • 1st law (inertia): objects keep their state of motion unless a net force acts.
  • 2nd law: a net force causes acceleration, F = ma (so a = F/m).
  • 3rd law: forces come in equal, opposite pairs acting on different objects.
  • Bigger force → more acceleration; bigger mass → less acceleration.
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