Newton's laws and momentum

What you'll learn

How resultant force controls whether an object keeps moving steadily or accelerates.
How to use $\times a$ and $\times g$ in calculations.
How the trolley core practical investigates force, mass and acceleration.
How Newton’s third law and, on Higher Tier, momentum explain collisions.

The starting point: forces and motion

A force is a push or pull. Forces are measured in newtons, N. A force can change an object’s speed, direction or shape.

A body just means an object. In this topic, “body” and “object” are usually interchangeable.

Definition

Resultant force

The resultant force is the single overall force you get after combining all the forces acting on an object. If forces are balanced, the resultant force is 0 N.

A free-body diagram shows the forces acting on one object using arrows. The arrow direction shows the force direction, and a longer arrow usually means a larger force.

Free-body diagrams showing balanced and unbalanced forces on a box

Newton’s first law

Newton’s first law says that an object will remain at rest, or keep moving at constant velocity, unless acted on by a non-zero resultant force.

Definition

Constant velocity

Velocity means speed in a stated direction. Constant velocity means both the speed and the direction stay the same.

So if the resultant force is zero:

an object at rest stays at rest
a moving object continues at the same speed in the same direction

If the resultant force is not zero, the object accelerates: its speed and/or direction changes.

Key Idea

Balanced forces do not mean no motion

Balanced forces mean no change in motion. An object can be moving at constant velocity while the resultant force is 0 N.

Example

Using Newton’s first law

A cyclist moves forwards at a steady speed. The driving force is 80 N forwards and air resistance plus friction is 80 N backwards.

Compare the forces in the direction of motion: 80 N forwards and 80 N backwards are equal and opposite.
Work out the resultant force: $\text{ N}$ .
Apply Newton’s first law: because the resultant force is zero, the cyclist continues at constant velocity.

Common Mistake

Thinking a moving object needs a resultant force

A moving object does not need a resultant force to keep moving. It needs a resultant force only to change its velocity. On Earth, a steady push is often needed because friction and air resistance must be balanced.

Newton’s second law

Newton’s second law links resultant force, mass and acceleration:

\times a

where:

$F$ is resultant force in newtons, N
$m$ is mass in kilograms, kg
$a$ is acceleration in metres per second squared, m/s^2

For Edexcel 1PH0, this is a recall and use equation, so you should practise remembering it.

Definition

Acceleration

Acceleration is the rate of change of velocity. It can mean speeding up, slowing down, or changing direction.

Key Idea

What F = ma means

For the same mass, a bigger resultant force gives a bigger acceleration. For the same resultant force, a bigger mass gives a smaller acceleration.

Example

Calculating acceleration from force and mass

A 6 kg trolley has a resultant force of 18 N acting on it. Calculate its acceleration.

Choose Newton’s second law because the question links force, mass and acceleration: $\times a$ .
Rearrange for acceleration: $\frac{F}{m}$ .
Substitute the values with units: $\frac{18 \text{ N}}{6 \text{ kg}} = 3 \text{ m/s}^2$ .

For Higher Tier, inertial mass is the measure of how difficult it is to change the velocity of an object, including from rest. It is defined as:

minertial=Fam_\text{inertial} = \frac{F}{a}

A larger inertial mass needs a larger force for the same acceleration.

Weight, mass and gravitational field strength

Mass and weight are not the same.

Definition

Weight

Weight is the force on an object due to gravity. It is measured in newtons, N.

Mass is the amount of matter in an object and is measured in kilograms, kg. Your mass stays the same on different planets, but your weight changes because the gravitational field strength changes.

The equation for weight is:

\times g

where:

$W$ is weight in newtons, N
$m$ is mass in kilograms, kg
$g$ is gravitational field strength in newtons per kilogram, N/kg

This is also a recall and use equation. Use the value of $g$ given in the question; if none is given, GCSE questions often use $\approx 10 \text{ N/kg}$ on Earth.

Definition

Gravitational field strength

Gravitational field strength, $g$ , is the force of gravity on each kilogram of mass.

Weight is measured using a newton meter or calibrated spring balance. The object is hung from the spring, and the stretch of the spring gives the weight in newtons.

Example

Calculating weight

A 55 kg student is on Earth, where $\text{ N/kg}$ . Calculate the student’s weight.

Use the weight equation: $\times g$ .
Substitute the mass and gravitational field strength: $\text{ kg} \times 10 \text{ N/kg}$ .
Calculate the weight: $\text{ N}$ .

Tip

Weight is proportional to g

For the same object, if $g$ doubles, weight doubles. If $g$ is smaller, such as on the Moon, the same mass has a smaller weight.

Core practical: force, mass and acceleration

In the core practical, you investigate how force, mass and acceleration are related using a trolley, masses, a pulley and a light gate or motion sensor.

Trolley experiment setup for investigating force, mass and acceleration

To investigate force:

Use a low-friction track.
Keep the total mass as constant as possible.
Change the pulling force, usually by changing the hanging mass.
Measure the acceleration using a light gate, data logger or motion sensor.
Repeat and calculate mean values.

To investigate mass:

Keep the pulling force the same.
Add masses to the trolley.
Measure the new acceleration.
Repeat for several masses.

The expected relationships are:

if mass is constant, acceleration is directly proportional to resultant force
if resultant force is constant, acceleration decreases as mass increases

Tip

Core practical graph idea

A graph of acceleration against force should be a straight line through the origin if mass is constant. This supports $\times a$ .

Circular motion: Higher Tier idea

At constant speed in a circle, an object is still accelerating because its direction is constantly changing. Since velocity includes direction, its velocity is changing even when the speed stays the same.

For circular motion, there must be a resultant force towards the centre of the circle. This is called the centripetal force. It is not a new type of force; it could be tension, gravity, friction or another force acting towards the centre.

Circular motion and momentum conservation in collisions

Definition

Centripetal force

A centripetal force is a resultant force that acts towards the centre of a circle and keeps an object moving in circular motion.

Newton’s third law

Newton’s third law says that when two objects interact, they exert equal and opposite forces on each other.

For example, if a trolley pushes another trolley forwards during a collision, the second trolley pushes back with an equal force in the opposite direction.

Key Idea

Third-law pairs act on different objects

Newton’s third-law forces are equal and opposite, but they act on different objects, so they do not cancel each other out on one object.

Example

Choosing a third-law force pair

A book rests on a table. Identify a Newton’s third-law pair involving the table.

Focus on one interaction: the book and the table are pushing on each other.
State the force from the book on the table: the book pushes down on the table.
State the matching force from the table on the book: the table pushes up on the book with an equal and opposite force.

Common Mistake

Mixing up balanced forces and third-law pairs

The book’s weight and the table’s upward contact force can balance because they act on the same object. But they are not a third-law pair, because they come from different interactions.

Momentum: Higher Tier idea

Definition

Momentum

Momentum, $p$ , is a measure of how much motion an object has. It depends on mass and velocity.

The equation is:

\times v

where:

$p$ is momentum in kilogram metres per second, kg m/s
$m$ is mass in kilograms, kg
$v$ is velocity in metres per second, m/s

This Higher Tier equation is listed as recall and use.

Momentum has direction because velocity has direction. A fast small object can have a large momentum, and a slow heavy object can also have a large momentum.

In a collision, if no external resultant force acts, total momentum before the collision equals total momentum after the collision. This is called conservation of momentum.

Newton’s third law helps explain this: during a collision, the objects exert equal and opposite forces on each other for the same time, so their momentum changes are equal and opposite.

Force and change in momentum: Higher Tier

Newton’s second law can also be written as:

\frac{mv - mu}{t}

where:

$m$ is mass in kg
$u$ is initial velocity in m/s
$v$ is final velocity in m/s
$t$ is time in s
$m v - m u$ is the change in momentum

This means force is the rate of change of momentum. For the same change in momentum, increasing the collision time reduces the force. This is why seatbelts, airbags, helmets and crumple zones are useful.

Example

Calculating impact force

A 60 kg passenger travelling at 12 m/s is brought to rest by a seatbelt in 0.40 s. Calculate the average force on the passenger.

Identify the velocities: the passenger starts at $\text{ m/s}$ and ends at $\text{ m/s}$ .
Calculate the change in momentum: $\times 0) - (60 \times 12) = -720 \text{ kg m/s}$ .
Divide by the time: $\frac{-720}{0.40} = -1800 \text{ N}$ .
Interpret the sign: the force is 1800 N opposite to the passenger’s original direction of motion.

Exam technique

In the exam

Start force questions by drawing or imagining the forces, then find the resultant force.
Use SI units: kg for mass, N for force, m/s for velocity, and s for time.
For Newton’s third law, name the two interacting objects and check the forces act on different objects.
For momentum questions, choose one direction as positive and keep signs consistent.

Self review

Check yourself

What happens to an object’s motion when the resultant force on it is 0 N?
How are mass, weight and gravitational field strength related?
Why does increasing collision time reduce the force during a crash?

Newton's laws and momentum

What you'll learn

How resultant force controls whether an object keeps moving steadily or accelerates.
How to use $\times a$ and $\times g$ in calculations.
How the trolley core practical investigates force, mass and acceleration.
How Newton’s third law and, on Higher Tier, momentum explain collisions.

The starting point: forces and motion

A force is a push or pull. Forces are measured in newtons, N. A force can change an object’s speed, direction or shape.

A body just means an object. In this topic, “body” and “object” are usually interchangeable.

Definition

Resultant force

The resultant force is the single overall force you get after combining all the forces acting on an object. If forces are balanced, the resultant force is 0 N.

A free-body diagram shows the forces acting on one object using arrows. The arrow direction shows the force direction, and a longer arrow usually means a larger force.

Free-body diagrams showing balanced and unbalanced forces on a box

Newton’s first law

Newton’s first law says that an object will remain at rest, or keep moving at constant velocity, unless acted on by a non-zero resultant force.

Definition

Constant velocity

Velocity means speed in a stated direction. Constant velocity means both the speed and the direction stay the same.

So if the resultant force is zero:

an object at rest stays at rest
a moving object continues at the same speed in the same direction

If the resultant force is not zero, the object accelerates: its speed and/or direction changes.

Key Idea

Balanced forces do not mean no motion

Balanced forces mean no change in motion. An object can be moving at constant velocity while the resultant force is 0 N.

Example

Using Newton’s first law

A cyclist moves forwards at a steady speed. The driving force is 80 N forwards and air resistance plus friction is 80 N backwards.

Compare the forces in the direction of motion: 80 N forwards and 80 N backwards are equal and opposite.
Work out the resultant force: $\text{ N}$ .
Apply Newton’s first law: because the resultant force is zero, the cyclist continues at constant velocity.

Common Mistake

Thinking a moving object needs a resultant force

Newton’s second law

Newton’s second law links resultant force, mass and acceleration:

\times a

where:

$F$ is resultant force in newtons, N
$m$ is mass in kilograms, kg
$a$ is acceleration in metres per second squared, m/s^2

For Edexcel 1PH0, this is a recall and use equation, so you should practise remembering it.

Definition

Acceleration

Acceleration is the rate of change of velocity. It can mean speeding up, slowing down, or changing direction.

Key Idea

What F = ma means

For the same mass, a bigger resultant force gives a bigger acceleration. For the same resultant force, a bigger mass gives a smaller acceleration.

Example

Calculating acceleration from force and mass

A 6 kg trolley has a resultant force of 18 N acting on it. Calculate its acceleration.

Choose Newton’s second law because the question links force, mass and acceleration: $\times a$ .
Rearrange for acceleration: $\frac{F}{m}$ .
Substitute the values with units: $\frac{18 \text{ N}}{6 \text{ kg}} = 3 \text{ m/s}^2$ .

For Higher Tier, inertial mass is the measure of how difficult it is to change the velocity of an object, including from rest. It is defined as:

minertial=Fam_\text{inertial} = \frac{F}{a}

A larger inertial mass needs a larger force for the same acceleration.

Weight, mass and gravitational field strength

Mass and weight are not the same.

Definition

Weight

Weight is the force on an object due to gravity. It is measured in newtons, N.

Mass is the amount of matter in an object and is measured in kilograms, kg. Your mass stays the same on different planets, but your weight changes because the gravitational field strength changes.

The equation for weight is:

\times g

where:

$W$ is weight in newtons, N
$m$ is mass in kilograms, kg
$g$ is gravitational field strength in newtons per kilogram, N/kg

This is also a recall and use equation. Use the value of $g$ given in the question; if none is given, GCSE questions often use $\approx 10 \text{ N/kg}$ on Earth.

Definition

Gravitational field strength

Gravitational field strength, $g$ , is the force of gravity on each kilogram of mass.

Weight is measured using a newton meter or calibrated spring balance. The object is hung from the spring, and the stretch of the spring gives the weight in newtons.

Example

Calculating weight

A 55 kg student is on Earth, where $\text{ N/kg}$ . Calculate the student’s weight.

Use the weight equation: $\times g$ .
Substitute the mass and gravitational field strength: $\text{ kg} \times 10 \text{ N/kg}$ .
Calculate the weight: $\text{ N}$ .

Tip

Weight is proportional to g

For the same object, if $g$ doubles, weight doubles. If $g$ is smaller, such as on the Moon, the same mass has a smaller weight.

Core practical: force, mass and acceleration

In the core practical, you investigate how force, mass and acceleration are related using a trolley, masses, a pulley and a light gate or motion sensor.

Trolley experiment setup for investigating force, mass and acceleration

To investigate force:

Use a low-friction track.
Keep the total mass as constant as possible.
Change the pulling force, usually by changing the hanging mass.
Measure the acceleration using a light gate, data logger or motion sensor.
Repeat and calculate mean values.

To investigate mass:

Keep the pulling force the same.
Add masses to the trolley.
Measure the new acceleration.
Repeat for several masses.

The expected relationships are:

if mass is constant, acceleration is directly proportional to resultant force
if resultant force is constant, acceleration decreases as mass increases

Tip

Core practical graph idea

A graph of acceleration against force should be a straight line through the origin if mass is constant. This supports $\times a$ .

Circular motion: Higher Tier idea

Circular motion and momentum conservation in collisions

Definition

Centripetal force

A centripetal force is a resultant force that acts towards the centre of a circle and keeps an object moving in circular motion.

Newton’s third law

Newton’s third law says that when two objects interact, they exert equal and opposite forces on each other.

For example, if a trolley pushes another trolley forwards during a collision, the second trolley pushes back with an equal force in the opposite direction.

Key Idea

Third-law pairs act on different objects

Newton’s third-law forces are equal and opposite, but they act on different objects, so they do not cancel each other out on one object.

Example

Choosing a third-law force pair

A book rests on a table. Identify a Newton’s third-law pair involving the table.

Focus on one interaction: the book and the table are pushing on each other.
State the force from the book on the table: the book pushes down on the table.
State the matching force from the table on the book: the table pushes up on the book with an equal and opposite force.

Common Mistake

Mixing up balanced forces and third-law pairs

The book’s weight and the table’s upward contact force can balance because they act on the same object. But they are not a third-law pair, because they come from different interactions.

Momentum: Higher Tier idea

Definition

Momentum

Momentum, $p$ , is a measure of how much motion an object has. It depends on mass and velocity.

The equation is:

\times v

where:

$p$ is momentum in kilogram metres per second, kg m/s
$m$ is mass in kilograms, kg
$v$ is velocity in metres per second, m/s

This Higher Tier equation is listed as recall and use.

Momentum has direction because velocity has direction. A fast small object can have a large momentum, and a slow heavy object can also have a large momentum.

In a collision, if no external resultant force acts, total momentum before the collision equals total momentum after the collision. This is called conservation of momentum.

Newton’s third law helps explain this: during a collision, the objects exert equal and opposite forces on each other for the same time, so their momentum changes are equal and opposite.

Force and change in momentum: Higher Tier

Newton’s second law can also be written as:

\frac{mv - mu}{t}

where:

$m$ is mass in kg
$u$ is initial velocity in m/s
$v$ is final velocity in m/s
$t$ is time in s
$m v - m u$ is the change in momentum

Example

Calculating impact force

A 60 kg passenger travelling at 12 m/s is brought to rest by a seatbelt in 0.40 s. Calculate the average force on the passenger.

Identify the velocities: the passenger starts at $\text{ m/s}$ and ends at $\text{ m/s}$ .
Calculate the change in momentum: $\times 0) - (60 \times 12) = -720 \text{ kg m/s}$ .
Divide by the time: $\frac{-720}{0.40} = -1800 \text{ N}$ .
Interpret the sign: the force is 1800 N opposite to the passenger’s original direction of motion.

Exam technique

In the exam

Start force questions by drawing or imagining the forces, then find the resultant force.
Use SI units: kg for mass, N for force, m/s for velocity, and s for time.
For Newton’s third law, name the two interacting objects and check the forces act on different objects.
For momentum questions, choose one direction as positive and keep signs consistent.

Self review

Check yourself

What happens to an object’s motion when the resultant force on it is 0 N?
How are mass, weight and gravitational field strength related?
Why does increasing collision time reduce the force during a crash?

Newton's laws and momentum

What you'll learn

The starting point: forces and motion

Newton’s first law

Newton’s second law

Weight, mass and gravitational field strength

Core practical: force, mass and acceleration

Circular motion: Higher Tier idea

Newton’s third law

Momentum: Higher Tier idea

Force and change in momentum: Higher Tier

Recap questions

Newton's laws and momentum

What you'll learn

The starting point: forces and motion

Newton’s first law

Newton’s second law

Weight, mass and gravitational field strength

Core practical: force, mass and acceleration

Circular motion: Higher Tier idea

Newton’s third law

Momentum: Higher Tier idea

Force and change in momentum: Higher Tier

Recap questions

Newton's laws and momentum

What you'll learn

The starting point: forces and motion

Newton’s first law

Newton’s second law

Weight, mass and gravitational field strength

Core practical: force, mass and acceleration

Circular motion: Higher Tier idea

Newton’s third law

Momentum: Higher Tier idea

Force and change in momentum: Higher Tier

Recap questions

Newton's laws and momentum Revision Guide

Newton's laws and momentum

What you'll learn

The starting point: forces and motion

Newton’s first law

Newton’s second law

Weight, mass and gravitational field strength

Core practical: force, mass and acceleration

Circular motion: Higher Tier idea

Newton’s third law

Momentum: Higher Tier idea

Force and change in momentum: Higher Tier

Recap questions

Newton's laws and momentum Revision Guide