Newton’s laws

What you'll learn

How forces are interactions between objects, and how to show them with arrows.
How resultant force links to motion using Newton’s first and second laws.
How momentum, work done and power are calculated.
How Newton’s third law and circular motion fit into the same force ideas.

Forces start with interactions

A force is a push or pull. Forces only happen because objects interact with other objects.

Some forces need touching:

Normal contact force: a surface pushes back on an object touching it.
Friction: a contact force that opposes motion, or attempted motion.
Air resistance: friction from moving through air.

Some forces act without touching:

Gravity: attraction between masses.
Magnetism: forces between magnets or magnetic materials.
Electrostatics: forces between charged objects.

Definition

Force

A force is a push or pull caused by an interaction between objects. Force is measured in newtons (N).

Whenever two objects interact, each object feels a force. For example, Earth pulls a falling ball down, and the ball pulls Earth up. The forces are on different objects.

Forces are vectors

A scalar has size only, such as mass or temperature. A vector has size and direction. Force is a vector, so you must include direction.

A force arrow shows:

direction: which way the force acts
length: the size of the force, if drawn to scale
label: what type of force it is

A free-body diagram shows just the object you are analysing, with the forces acting on that object only.

Definition

Resultant force

The resultant force is the single overall force that has the same effect as all the forces acting together.

If forces balance, the resultant force is zero. This is called equilibrium.

Free-body diagrams showing balanced forces, unbalanced forces and terminal velocity

Example

Finding a resultant force

A trolley has a 12 N pulling force to the right and 5 N friction to the left. Its weight and normal contact force are balanced.

Work horizontally because the vertical forces cancel, so they do not affect the horizontal resultant.
Opposite horizontal forces subtract: $N12\ \text{N} - 5\ \text{N} = 7\ \text{N}$ .
The larger force is to the right, so the resultant force is 7 N to the right.

Common Mistake

Putting forces on the wrong object

In a free-body diagram, only draw forces acting on the chosen object. Do not draw the force that the object exerts on something else.

Resolving forces

Resolving a force means splitting one force into components, usually horizontal and vertical parts. In this spec, scale drawings are limited to parallel and perpendicular vectors.

For parallel forces, add forces in the same direction and subtract forces in opposite directions. For perpendicular forces, draw the arrows to scale and use the diagonal to show the resultant.

Newton’s first law

Newton’s first law is about what happens when the resultant force is zero.

Key Idea

Newton’s first law

If the resultant force on an object is zero, a stationary object stays stationary, and a moving object continues with uniform velocity.

Uniform velocity means constant speed in a straight line. If speed changes or direction changes, velocity has changed, so there must be a non-zero resultant force.

This is a big idea: an object does not need a resultant force to keep moving steadily. It only needs a resultant force to change its motion.

Common Mistake

Thinking moving objects need a forward resultant force

A car moving at constant velocity has balanced forces. The driving force forwards equals the resistive forces backwards, so the resultant force is zero.

Terminal velocity

An object falling through air has weight downwards and air resistance upwards. At first, weight is bigger, so it accelerates downwards. As speed increases, air resistance increases. Eventually air resistance equals weight, so the resultant force becomes zero. The object then falls at constant velocity: this is terminal velocity.

The same idea can apply to vehicles: when driving force equals resistive forces, the vehicle moves at constant velocity.

Newton’s second law

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

Definition

Acceleration

Acceleration is the rate of change of velocity. It is measured in metres per second squared, written as m/s².

The equation is:

F = ma

where $F$ is resultant force in newtons, $m$ is mass in kilograms, and $a$ is acceleration in m/s².

OCR lists this equation as recall and apply, so learn it rather than relying on it being given.

Example

Calculating acceleration

A 1200 kg car has a resultant force of 2400 N forwards. Calculate its acceleration.

Choose Newton’s second law and rearrange for acceleration: $\frac{F}{m}$ .
Substitute the values: $\frac{2400\ \text{N}}{1200\ \text{kg}} = 2\ \text{m/s}^2$ .
The acceleration is 2 m/s² forwards, in the direction of the resultant force.

Definition

Inertia and inertial mass

Inertia is how difficult it is to change an object’s velocity. Inertial mass is defined by $\frac{F}{a}$ , using the resultant force and the acceleration it produces.

A larger mass has more inertia. For the same resultant force, a larger mass has a smaller acceleration.

This linking of force, mass, velocity and acceleration is included in separate Physics J249. It is not part of OCR Gateway Combined Science J250.

Momentum and collisions

Momentum describes how much motion an object has. A more massive object, or a faster object, has more momentum.

Definition

Momentum

Momentum is given by $p = m v$ , where $p$ is momentum, $m$ is mass, and $v$ is velocity. Momentum is measured in kg m/s.

The calculation $p = m v$ is Higher Tier only and is listed as recall and apply. Momentum is a vector because velocity is a vector.

In a collision, if there is no external resultant force on the system, total momentum is conserved. This means total momentum before the collision equals total momentum after the collision.

Example

Using conservation of momentum

A 2 kg trolley moving at 3 m/s collides with a stationary 1 kg trolley. They stick together. Calculate their shared velocity after the collision.

Find total momentum before: $(2\ \text{kg})(3\ \text{m/s}) + (1\ \text{kg})(0\ \text{m/s}) = 6\ \text{kg m/s}$ .
Momentum is conserved, so after the collision the combined 3 kg mass still has total momentum 6 kg m/s: $kg)v6\ \text{kg m/s} = (3\ \text{kg})v$ .
Solve for velocity: $\frac{6}{3} = 2\ \text{m/s}$ , in the original direction of motion.

Work done and energy transfer

Work done means energy transferred by a force moving an object through a distance. The distance must be along the line of action of the force, meaning in the direction the force acts.

The equation is:

done=Fd\text{work done} = Fd

Work done is measured in joules (J). A newton-metre is the same as a joule: 1 N m = 1 J.

OCR lists this as recall and apply.

Common Mistake

Distance must match the force direction

If a force acts horizontally but the object moves vertically, that force does not do work in the vertical direction. Use the distance moved along the line of action of the force.

Power

Power is the rate at which energy is transferred, or the rate at which work is done.

\frac{\text{work done}}{t}

Power is measured in watts (W). One watt means one joule per second. This equation is also recall and apply.

Example

Calculating work done and power

A student lifts a box with weight 100 N through a vertical height of 1.5 m in 3 s.

The force and movement are both vertical, so use $done=Fd\text{work done} = Fd$ .
Substitute: $J\text{work done} = 100\ \text{N} \times 1.5\ \text{m} = 150\ \text{J}$ .
Calculate power: $\frac{150\ \text{J}}{3\ \text{s}} = 50\ \text{W}$ .

Newton’s third law

Newton’s third law describes force pairs.

Key Idea

Newton’s third law

When two objects interact, they exert equal and opposite forces on each other. These forces act on different objects.

This applies whether the objects are in equilibrium or accelerating. The pair of forces does not cancel because the forces are not acting on the same object.

Newton’s third law shown by a person pushing a wall and a rocket pushing gases downwards

Example

Identifying a third-law force pair

A swimmer pushes water backwards and moves forwards.

Identify one force: the swimmer pushes the water backwards.
The paired force is the water pushing the swimmer forwards.
The forces are equal and opposite, but they act on different objects, so the swimmer can still accelerate forwards.

Constant speed in a circle

Velocity is a vector, so direction matters. An object moving in a circle may have constant speed, but its direction keeps changing. Therefore its velocity is changing.

By Newton’s first law, a changing velocity needs a non-zero resultant force. For circular motion, this resultant force acts towards the centre of the circle.

Circular motion showing tangent velocity arrows and inward force arrows

Tip

Speed vs velocity

Constant speed does not always mean constant velocity. If direction changes, velocity changes.

Exam technique

In the exam

Draw a free-body diagram before calculating: include only forces acting on the object named in the question.
For $F = ma$ , use the resultant force, not just any force mentioned.
State both size and direction for vector answers, especially resultant force, velocity and momentum.

Self review

Check yourself

A cyclist moves at constant velocity. What must be true about the resultant force?
Why do Newton’s third-law force pairs not cancel each other?
A force of 80 N moves an object 2.5 m in the same direction. What work is done?

Newton’s laws

What you'll learn

How forces are interactions between objects, and how to show them with arrows.
How resultant force links to motion using Newton’s first and second laws.
How momentum, work done and power are calculated.
How Newton’s third law and circular motion fit into the same force ideas.

Forces start with interactions

A force is a push or pull. Forces only happen because objects interact with other objects.

Some forces need touching:

Normal contact force: a surface pushes back on an object touching it.
Friction: a contact force that opposes motion, or attempted motion.
Air resistance: friction from moving through air.

Some forces act without touching:

Gravity: attraction between masses.
Magnetism: forces between magnets or magnetic materials.
Electrostatics: forces between charged objects.

Definition

Force

A force is a push or pull caused by an interaction between objects. Force is measured in newtons (N).

Whenever two objects interact, each object feels a force. For example, Earth pulls a falling ball down, and the ball pulls Earth up. The forces are on different objects.

Forces are vectors

A scalar has size only, such as mass or temperature. A vector has size and direction. Force is a vector, so you must include direction.

A force arrow shows:

direction: which way the force acts
length: the size of the force, if drawn to scale
label: what type of force it is

A free-body diagram shows just the object you are analysing, with the forces acting on that object only.

Definition

Resultant force

The resultant force is the single overall force that has the same effect as all the forces acting together.

If forces balance, the resultant force is zero. This is called equilibrium.

Free-body diagrams showing balanced forces, unbalanced forces and terminal velocity

Example

Finding a resultant force

A trolley has a 12 N pulling force to the right and 5 N friction to the left. Its weight and normal contact force are balanced.

Work horizontally because the vertical forces cancel, so they do not affect the horizontal resultant.
Opposite horizontal forces subtract: $N12\ \text{N} - 5\ \text{N} = 7\ \text{N}$ .
The larger force is to the right, so the resultant force is 7 N to the right.

Common Mistake

Putting forces on the wrong object

In a free-body diagram, only draw forces acting on the chosen object. Do not draw the force that the object exerts on something else.

Resolving forces

Resolving a force means splitting one force into components, usually horizontal and vertical parts. In this spec, scale drawings are limited to parallel and perpendicular vectors.

For parallel forces, add forces in the same direction and subtract forces in opposite directions. For perpendicular forces, draw the arrows to scale and use the diagonal to show the resultant.

Newton’s first law

Newton’s first law is about what happens when the resultant force is zero.

Key Idea

Newton’s first law

If the resultant force on an object is zero, a stationary object stays stationary, and a moving object continues with uniform velocity.

Uniform velocity means constant speed in a straight line. If speed changes or direction changes, velocity has changed, so there must be a non-zero resultant force.

This is a big idea: an object does not need a resultant force to keep moving steadily. It only needs a resultant force to change its motion.

Common Mistake

Thinking moving objects need a forward resultant force

A car moving at constant velocity has balanced forces. The driving force forwards equals the resistive forces backwards, so the resultant force is zero.

Terminal velocity

The same idea can apply to vehicles: when driving force equals resistive forces, the vehicle moves at constant velocity.

Newton’s second law

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

Definition

Acceleration

Acceleration is the rate of change of velocity. It is measured in metres per second squared, written as m/s².

The equation is:

F = ma

where $F$ is resultant force in newtons, $m$ is mass in kilograms, and $a$ is acceleration in m/s².

OCR lists this equation as recall and apply, so learn it rather than relying on it being given.

Example

Calculating acceleration

A 1200 kg car has a resultant force of 2400 N forwards. Calculate its acceleration.

Choose Newton’s second law and rearrange for acceleration: $\frac{F}{m}$ .
Substitute the values: $\frac{2400\ \text{N}}{1200\ \text{kg}} = 2\ \text{m/s}^2$ .
The acceleration is 2 m/s² forwards, in the direction of the resultant force.

Definition

Inertia and inertial mass

Inertia is how difficult it is to change an object’s velocity. Inertial mass is defined by $\frac{F}{a}$ , using the resultant force and the acceleration it produces.

A larger mass has more inertia. For the same resultant force, a larger mass has a smaller acceleration.

This linking of force, mass, velocity and acceleration is included in separate Physics J249. It is not part of OCR Gateway Combined Science J250.

Momentum and collisions

Momentum describes how much motion an object has. A more massive object, or a faster object, has more momentum.

Definition

Momentum

Momentum is given by $p = m v$ , where $p$ is momentum, $m$ is mass, and $v$ is velocity. Momentum is measured in kg m/s.

The calculation $p = m v$ is Higher Tier only and is listed as recall and apply. Momentum is a vector because velocity is a vector.

In a collision, if there is no external resultant force on the system, total momentum is conserved. This means total momentum before the collision equals total momentum after the collision.

Example

Using conservation of momentum

A 2 kg trolley moving at 3 m/s collides with a stationary 1 kg trolley. They stick together. Calculate their shared velocity after the collision.

Find total momentum before: $(2\ \text{kg})(3\ \text{m/s}) + (1\ \text{kg})(0\ \text{m/s}) = 6\ \text{kg m/s}$ .
Momentum is conserved, so after the collision the combined 3 kg mass still has total momentum 6 kg m/s: $kg)v6\ \text{kg m/s} = (3\ \text{kg})v$ .
Solve for velocity: $\frac{6}{3} = 2\ \text{m/s}$ , in the original direction of motion.

Work done and energy transfer

Work done means energy transferred by a force moving an object through a distance. The distance must be along the line of action of the force, meaning in the direction the force acts.

The equation is:

done=Fd\text{work done} = Fd

Work done is measured in joules (J). A newton-metre is the same as a joule: 1 N m = 1 J.

OCR lists this as recall and apply.

Common Mistake

Distance must match the force direction

If a force acts horizontally but the object moves vertically, that force does not do work in the vertical direction. Use the distance moved along the line of action of the force.

Power

Power is the rate at which energy is transferred, or the rate at which work is done.

\frac{\text{work done}}{t}

Power is measured in watts (W). One watt means one joule per second. This equation is also recall and apply.

Example

Calculating work done and power

A student lifts a box with weight 100 N through a vertical height of 1.5 m in 3 s.

The force and movement are both vertical, so use $done=Fd\text{work done} = Fd$ .
Substitute: $J\text{work done} = 100\ \text{N} \times 1.5\ \text{m} = 150\ \text{J}$ .
Calculate power: $\frac{150\ \text{J}}{3\ \text{s}} = 50\ \text{W}$ .

Newton’s third law

Newton’s third law describes force pairs.

Key Idea

Newton’s third law

When two objects interact, they exert equal and opposite forces on each other. These forces act on different objects.

This applies whether the objects are in equilibrium or accelerating. The pair of forces does not cancel because the forces are not acting on the same object.

Newton’s third law shown by a person pushing a wall and a rocket pushing gases downwards

Example

Identifying a third-law force pair

A swimmer pushes water backwards and moves forwards.

Identify one force: the swimmer pushes the water backwards.
The paired force is the water pushing the swimmer forwards.
The forces are equal and opposite, but they act on different objects, so the swimmer can still accelerate forwards.

Constant speed in a circle

Velocity is a vector, so direction matters. An object moving in a circle may have constant speed, but its direction keeps changing. Therefore its velocity is changing.

By Newton’s first law, a changing velocity needs a non-zero resultant force. For circular motion, this resultant force acts towards the centre of the circle.

Circular motion showing tangent velocity arrows and inward force arrows

Tip

Speed vs velocity

Constant speed does not always mean constant velocity. If direction changes, velocity changes.

Exam technique

In the exam

Draw a free-body diagram before calculating: include only forces acting on the object named in the question.
For $F = ma$ , use the resultant force, not just any force mentioned.
State both size and direction for vector answers, especially resultant force, velocity and momentum.

Self review

Check yourself

A cyclist moves at constant velocity. What must be true about the resultant force?
Why do Newton’s third-law force pairs not cancel each other?
A force of 80 N moves an object 2.5 m in the same direction. What work is done?

Newton’s laws

What you'll learn

Forces start with interactions

Forces are vectors

Resolving forces

Newton’s first law

Terminal velocity

Newton’s second law

Momentum and collisions

Work done and energy transfer

Power

Newton’s third law

Constant speed in a circle

Recap questions

You've reached the end

Newton’s laws

What you'll learn

Forces start with interactions

Forces are vectors

Resolving forces

Newton’s first law

Terminal velocity

Newton’s second law

Momentum and collisions

Work done and energy transfer

Power

Newton’s third law

Constant speed in a circle

Recap questions

You've reached the end

Newton’s laws

What you'll learn

Forces start with interactions

Forces are vectors

Resolving forces

Newton’s first law

Terminal velocity

Newton’s second law

Momentum and collisions

Work done and energy transfer

Power

Newton’s third law

Constant speed in a circle

Recap questions

You've reached the end

Newton’s laws Revision Guide

Newton’s laws

What you'll learn

Forces start with interactions

Forces are vectors

Resolving forces

Newton’s first law

Terminal velocity

Newton’s second law

Momentum and collisions

Work done and energy transfer

Power

Newton’s third law

Constant speed in a circle

Recap questions

You've reached the end

Newton’s laws Revision Guide