# Newton's laws of motion

> CIE A-Level Physics · 9702
> Source: https://www.owlsprep.com/study/cie-9702-u3-newton-s-laws-of-motion/

This module breaks down Newton's three laws of motion, covers their correct definitions, exam expectations, and common misconceptions. You will learn to apply these laws to solve force and acceleration problems correctly.

**Prerequisites:** [Scalars and vectors](https://www.owlsprep.com/study/cie-9702-u2-scalars-and-vectors/); [Kinematics equations](https://www.owlsprep.com/study/cie-9702-u2-kinematics-equations/)

## Learning objectives

- State each of Newton's three laws of motion correctly for exam responses
- Apply Newton's second law to calculate acceleration from resultant force
- Distinguish between action-reaction force pairs and balanced forces
- Solve basic force problems for static and moving objects

## Newton's First Law of Motion

**Newton's First Law** — A body will remain at rest, or continue to move at a constant velocity, unless acted upon by a resultant external force.

*Notation:* F_{net} = 0

*Example:* An ice puck sliding on a frictionless surface maintains constant speed.

> **info**
>
> Inertia is the property of a body that resists change in motion. Mass is a measure of a body's inertia.

**Worked example:** A truck travels at constant speed of 22 m/s along a straight horizontal road. The engine provides a driving force of 8500 N. What is the total resistive force acting on the truck?

1. 1. Constant speed in a straight line means constant velocity, so per Newton's First Law, the resultant net force on the truck is zero.
2. 2. Sum of forces: driving force minus total resistive force equals zero:
3. $$F_{driving} - F_{resistive} = 0$$
4. 3. Solve for resistive force:
5. $$F_{resistive} = F_{driving} = 8500 \text{ N}$$
6. The resistive force acts opposite to the direction of motion.

> **Exam tip:** Always confirm both speed AND direction are constant before concluding net force is zero

## Newton's Second Law of Motion

**Newton's Second Law** — The rate of change of momentum of a body is equal to the resultant force acting on it, and acts in the same direction as the resultant force.

*Notation:* F_{net} = \frac{dp}{dt} = ma

*Example:* For a 3 kg mass accelerating at 4 m/s², net force is 3 × 4 = 12 N.

**Worked example:** A 4 kg block is pulled along a rough horizontal surface by a force of 25 N parallel to the surface. Friction opposes motion with magnitude 9 N. Calculate the acceleration of the block.

1. 1. Calculate the resultant force acting parallel to the surface:
2. $$F_{net} = 25 - 9 = 16 \text{ N}$$
3. 2. Use Newton's Second Law for constant mass, $F_{net} = ma$, rearrange for acceleration:
4. $$a = \frac{F_{net}}{m}$$
5. 3. Substitute values:
6. $$a = \frac{16}{4} = 4 \text{ m s}^{-2}$$

**Check your understanding**

1. What is the net force on a 12 kg object accelerating at 2.5 m/s²?

   - 14.5 N
   - 30 N
   - 4.8 N
   - 120 N

   *Why:* Correct: $F_{net} = ma = 12 \times 2.5 = 30$ N

## Newton's Third Law of Motion

**Newton's Third Law** — If body A exerts a force on body B, then body B exerts a force of the same type that is equal in magnitude and opposite in direction on body A.

*Notation:* F_{AB} = -F_{BA}

*Example:* A bat exerts a force on a ball, the ball exerts an equal opposite force on the bat.

> **warning**
>
> Action-reaction pairs always act on two *different* bodies. Balanced forces act on the same body, so they are not an action-reaction pair.

**Worked example:** A person stands stationary on the ground. State one valid action-reaction pair in this system, and explain why the person's weight and the normal force from the ground are not a third law pair.

1. 1. One valid action-reaction pair is: (1) The Earth exerts a downward gravitational force (weight) on the person, (2) The person exerts an upward gravitational force of equal magnitude on the Earth.
2. 2. The weight of the person (gravity from Earth) and the normal force from the ground are not an action-reaction pair because: they act on the same body (the person) and are different types of force.
3. Additionally, they do not have to be equal if the person is accelerating vertically (e.g. in an accelerating elevator).

> **Exam tip:** Always mention that action-reaction forces are the same type and act on different bodies in your exam answers.

## Common pitfalls

- **Wrong:** Claiming balanced forces are an action-reaction pair per Newton's third law
  - Why it fails: Action-reaction pairs act on two different bodies, while balanced forces both act on the same body
  - Correct: Always check which body each force acts on, and confirm the two forces are the same type
- **Wrong:** Using $F=ma$ for systems with changing mass without adjusting for momentum change
  - Why it fails: $F=ma$ only holds for constant mass; the general form of Newton's second law uses rate of change of momentum
  - Correct: Use $F_{net} = \frac{\Delta p}{\Delta t}$ for all problems, especially those with changing mass like rocket propulsion
- **Wrong:** Calculating acceleration using only the applied force, forgetting to find the resultant net force
  - Why it fails: Newton's second law requires the sum of all forces, not just the single applied force you are given
  - Correct: Always sum all forces in the direction of motion to find $F_{net}$ before calculating acceleration
- **Wrong:** Omitting the full statement of Newton's first law, calling it just a special case of the second law
  - Why it fails: Examiners require you to state all three laws separately when asked, and the first law defines inertial reference frames
  - Correct: Learn and write the full, complete statement of Newton's first law for exam responses

## Cheatsheet

| Law | Key Statement | Key Rule |
| --- | --- | --- |
| First Law | Constant velocity if no resultant force | $F_{net} = 0 \implies a = 0$ |
| Second Law (constant mass) | Resultant force equals mass times acceleration | $F_{net} = ma$ |
| Second Law (general) | Resultant force equals rate of change of momentum | $F_{net} = \frac{\Delta (mv)}{\Delta t}$ |
| Third Law | Equal opposite forces on different bodies | Same force type, acts on two different objects |

## What's next

Newton's laws of motion form the entire foundation of classical dynamics for CIE A-Level Physics, and underpin almost every topic that comes after this unit. Mastering the correct definition of each law and how to identify resultant forces is critical for solving all future force problems, from connected systems to circular motion and harmonic motion. This sub-topic also introduces momentum, which becomes a key tool for solving collisions and explosions problems. Below are the next key concepts you should study to build on this knowledge.

- [Linear momentum](https://www.owlsprep.com/study/cie-9702-u3-linear-momentum/)
- [Conservation of momentum](https://www.owlsprep.com/study/cie-9702-u3-conservation-of-momentum/)
- [Collisions](https://www.owlsprep.com/study/cie-9702-u3-collisions/)

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