# Newton's Laws of Motion

> Three simple rules that explain why things move the way they do, from shopping trolleys to rockets.

From HSC Physics on WhizzNotes, free study notes for NSW students: https://whizznotes.com/physics/newtons-laws/. Updated 2 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: The bus that braked
Ella is standing on a crowded bus, scrolling on her phone, not holding on. The driver suddenly slams on the brakes. Ella lurches forward and grabs a pole just in time.

Nobody pushed her forward. So why did she move?

Her body was moving at the same speed as the bus. When the bus stopped, nothing stopped **her**. She simply kept going. Over 300 years ago, Isaac Newton wrote this idea down as his First Law. He wrote two more. Together they explain almost every motion you see.

**In short:** Newton's three laws explain how forces change motion. An object keeps its motion unless a net force acts (first law), the net force equals mass times acceleration, $F = ma$ (second law), and forces come in equal and opposite pairs acting on different objects (third law).

## Newton's First Law: the law of inertia

> An object stays at rest, or keeps moving at a constant velocity, **unless a net force acts on it**.

Objects "like" to keep doing what they are already doing. This resistance to change is called **inertia**. The more **mass** an object has, the more inertia it has. That is why a loaded truck is harder to stop than a bicycle.

**Everyday examples**
- Ella lurching forward when the bus brakes.
- A tablecloth pulled away fast, leaving the plates behind.
- Seatbelts: they provide the force to stop **you** when the car stops suddenly.

## Newton's Second Law: F = ma

> The acceleration of an object depends on the **net force** on it and its **mass**.

$$F_{\text{net}} = m \times a$$

- $F$ = net force (N)
- $m$ = mass (kg)
- $a$ = acceleration (m/s²)

So 1 newton is the force that makes a 1 kg mass accelerate at 1 m/s².

What this means:
- **More force** gives **more acceleration** (same mass).
- **More mass** gives **less acceleration** (same force).

### Worked example: Pushing a trolley
An empty shopping trolley has a mass of 15 kg. You push it with a net force of 30 N.

$$a = \frac{F}{m} = \frac{30}{15} = 2 \text{ m/s}^2$$

Fill it with 45 kg of groceries (total 60 kg) and push just as hard:

$$a = \frac{30}{60} = 0.5 \text{ m/s}^2$$

Four times the mass, a quarter of the acceleration.

### Watch out: Use the NET force
If you push a box with 50 N and friction is 20 N, the force in $F = ma$ is $50 - 20 = 30$ N, not 50 N.

## Newton's Third Law: action and reaction

> When object A pushes on object B, object B pushes back on object A with a force that is **equal in size** and **opposite in direction**.

Forces always come in **pairs**.

- You push down on the floor. The floor pushes up on you.
- A swimmer pushes water backwards. The water pushes the swimmer forwards.
- A rocket pushes hot gas down. The gas pushes the rocket up.
- Earth pulls you down. You pull Earth up with exactly the same force.

### Key idea: Why don't the pair cancel?
The two forces in a Third Law pair act on **different objects**. Forces only cancel when they act on the **same** object. Your push acts on the floor. The floor's push acts on you.

### Worked example: The skateboard push
Liam (60 kg) and Noah (40 kg) stand on skateboards facing each other. Liam pushes Noah with 120 N.

By the Third Law, Noah pushes back on Liam with 120 N. Both move apart.

- Noah: $a = 120 \div 40 = 3 \text{ m/s}^2$
- Liam: $a = 120 \div 60 = 2 \text{ m/s}^2$

Same force, but the lighter person accelerates more.

**Mind map**

```text
Newton's laws
  First law
    Inertia
    No net force = no change
    More mass, more inertia
    Seatbelts
  Second law
    F = ma
    More force, more a
    More mass, less a
    Use net force
  Third law
    Equal and opposite pairs
    Act on different objects
    Rockets, swimming, walking
```

### Year 11: Momentum and impulse
**Momentum** is mass in motion: $p = mv$ (unit kg m/s). It is a vector.

Newton actually wrote the Second Law as: force equals the rate of change of momentum.

$$F = \frac{\Delta p}{\Delta t} \qquad \text{so} \qquad F\Delta t = \Delta p$$

$F\Delta t$ is called **impulse**. For the same change in momentum, a **longer** stopping time means a **smaller** force. This is how airbags, crumple zones, bike helmets and bending your knees when you land all protect you.

In any collision where no outside force acts, **total momentum is conserved**:

$$m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$$

### Year 12: Newton's laws in circular motion and orbits
Newton's Second Law still works in circles. The net force needed is the centripetal force:

$$F_{\text{net}} = \frac{mv^2}{r}$$

For a satellite, gravity supplies this force. Setting $\dfrac{GMm}{r^2} = \dfrac{mv^2}{r}$ gives the orbital speed $v = \sqrt{\dfrac{GM}{r}}$. The satellite's own mass cancels out, so a tiny screw and the space station orbit at the same speed at the same height.

## Quick summary

- **First Law**: no net force means no change in motion. This is inertia. More mass, more inertia.
- **Second Law**: $F_{\text{net}} = ma$. Bigger force, bigger acceleration. Bigger mass, smaller acceleration.
- **Third Law**: forces come in equal and opposite pairs acting on **different** objects.
- Always use the **net** force in $F = ma$.
- 1 N accelerates 1 kg at 1 m/s².

## Quiz

Try these questions from the chapter quiz.

1. When a car stops suddenly, passengers lurch forward. Which law explains this?
   - A. Newton's First Law
   - B. Newton's Second Law
   - C. Newton's Third Law
   - D. The law of gravity
   - Answer: A. Newton's First Law. Passengers keep moving because of inertia until a force (the seatbelt) stops them.

2. A net force of 20 N acts on a 4 kg mass. Its acceleration is:
   - A. 80 m/s²
   - B. 5 m/s²
   - C. 0.2 m/s²
   - D. 24 m/s²
   - Answer: B. 5 m/s². a = F ÷ m = 20 ÷ 4 = 5 m/s².

3. What net force is needed to give a 1200 kg car an acceleration of 2 m/s²?
   - A. 600 N
   - B. 1202 N
   - C. 2400 N
   - D. 24 000 N
   - Answer: C. 2400 N. F = ma = 1200 × 2 = 2400 N.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/physics/newtons-laws/#quiz