Newton's Three Laws
The three rules that connect forces to motion — and explain almost everything you see move.
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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).
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.
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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.
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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?
- Use \(a = \dfrac{F}{m}\).
- \(a = \dfrac{4000}{1000}\).
✓ 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.