The big idea: Push an empty shopping trolley and it leaps forward. Load it with bricks and the same push barely moves it.
That's the heart of Newton's laws: the net force on an object (all the forces added up) and its mass decide how it speeds up — and with no net force, it just keeps going.
1st law — no net force, no change
With zero net force, an object stays still or keeps moving at constant velocity. Motion doesn't need a force — only a change in motion does.
2nd law — net force makes it accelerate
A net force gives an acceleration in the same direction: F = ma. Bigger force → bigger acceleration; bigger mass → smaller acceleration.
3rd law — forces come in pairs
If A pushes B, then B pushes A back equally hard, the opposite way. The two forces act on different objects, so they never cancel on one body.
Spot which law you need: Constant velocity or at rest? → 1st law: net force = 0.
Speeding up, slowing down or turning? → 2nd law: net force = ma.
Two objects pushing on each other? → 3rd law: an equal, opposite pair.
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Newton's second law links the net force on an object to its acceleration. The same law can be written using momentum (momentum = mass × velocity): the net force equals how fast the momentum changes.
- net (resultant) force (N)
- mass (kg)
- acceleration (m s⁻²)
- change in momentum (kg m s⁻¹)
- time interval (s)
It's the NET force: The F in F = ma is the net force — every force on the object added together (direction matters).
Always find the net force first, then divide by the mass to get the acceleration.
Free-body diagram: the horizontal NET force is the pull minus friction; weight and normal cancel vertically.
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A 4.0 kg trolley is pulled forward by a 30 N force while a 6.0 N friction force acts backward. Find its acceleration.
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How this is tested — most forces questions are: draw a free-body diagram, then apply F = ma. It comes up two ways:
Paper 1A
- Quick net-force calculations.
- A block driven by an angled force; the acceleration of a single body.
Paper 2
- Connected systems — two masses on a string, an elevator cable, stacked blocks.
- Apply F = ma to one body to find a tension or contact force.
The classic trap: Plugging in one force instead of the net force — or forgetting that connected objects share the same acceleration.
Connected bodies share an acceleration: When two objects are joined (by a string, or stacked so they move together), they have the same acceleration.
To find a connecting force (a string tension, or the friction between stacked blocks), cover everything except one object and apply F = ma to it.
The trick is asking what is still touching it: a force applied to the other block never acts on this one, so usually only the string (or the friction) is left — and that force must be what accelerates it.
| Set-up | Whole system | One body alone |
|---|---|---|
| Two masses on a string | a = (driving force) ÷ (total mass) | tension = (that body's mass) × a |
| Elevator going up/down | net force = T − mg | a = (T − mg) ÷ m |
| Stacked blocks | a = F ÷ (total mass) | friction on top = (top mass) × a |
Tap each set-up to see the same two moves play out with real numbers.
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Two blocks are joined by a light string on a smooth floor: a 3.0 kg block in front, a 5.0 kg block behind. A 24 N force pulls the front block. (a) Find the acceleration of the pair. (b) Find the tension in the string.
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The question above, drawn — and the two views that solve it.
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