Newton's first law of motion

Newton's first law says that an object stays at rest, or keeps moving at the same speed in the same direction, unless a resultant force acts on it. If the forces on an object are balanced, its velocity does not change: a parked car stays parked, and a car cruising at a steady 30 m/s keeps cruising. This tendency to keep doing what it is already doing is called inertia, which is why Newton's first law is also known as the law of inertia.

Newton's first law of motion

AQA's GCSE Physics specification states it like this. If the resultant force acting on an object is zero and:

• the object is stationary, the object remains stationary;
• the object is moving, the object continues to move at the same speed and in the same direction.

So the object continues to move at the same velocity. Turn it round and you get the most useful form: the velocity of an object, its speed or its direction, only changes if a resultant force acts on it.

NASA's version puts it in plain words: an object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line, unless acted on by an unbalanced force. Newton set out this law, with the other two, in his book the Principia.

What is a resultant force?

The resultant force is the single force that has the same effect as all the forces on an object added together, taking their directions into account. If 500 N pushes right and 500 N pushes left, the resultant is zero: the forces are balanced. Newton's first law is about what happens when the resultant force is zero. It does not say there are no forces, only that they cancel out.

Newton's first law formula

There is no separate equation to learn. Newton's first law is the special case of Newton's second law, F = ma, when the resultant force is zero:

Σ (sigma) means "the sum of", so ΣF is the resultant force. Zero acceleration means the velocity is constant, and a constant velocity of zero means staying still. At A-level the same idea is written as the condition for equilibrium: the forces in every direction add to zero. AQA's A-level specification makes the point that an object in equilibrium can be at rest or moving with constant velocity.

Two situations, one law

Objects at rest

A book on a table has two forces on it: its weight pulling down and the normal contact force from the table pushing up. They are equal and opposite, the resultant is zero, and the book stays where it is. To start it moving, something must supply a resultant force, such as a push.

Objects already moving

This is the part that surprises people. A moving object does not need a force to keep it moving. It needs a force to change its motion. On Earth, things seem to slow down by themselves, but that is because friction and air resistance are acting on them. Take those away and an object would carry on forever. A puck sliding on smooth ice goes a long way, because there is very little friction to stop it. A space probe far from any planet coasts with its engines off.

A car at a steady speed on a straight, level road has its engine running all the time. That is not because motion needs a force. The engine's driving force is needed to balance the resistive forces, friction and air resistance. In AQA's words, when a vehicle travels at a steady speed the resistive forces balance the driving force.

Inertia

Inertia is the tendency of an object to stay at rest or keep moving at the same velocity. Every object has it. The more mass an object has, the more inertia it has, and the harder it is to start, stop or turn. A loaded lorry needs a far bigger force than a bicycle to reach the same speed in the same time, and to stop again. The GCSE Higher term for this is inertial mass, which our guide to Newton's second law covers.

Newton's first law examples in real life

• Seat belts: when a car brakes hard, your body keeps moving forwards at the old speed. The seat belt supplies the force that slows you down with the car.
• Headrests: when a car is hit from behind, the car and your body are pushed forwards, but your head tends to stay where it was. The headrest pushes it forwards too.
• The tablecloth trick: pull a smooth cloth out quickly and the plates stay put. The friction acts for such a short time that it barely changes their velocity.
• A coin on a card: flick a card from under a coin balanced on a glass, and the coin drops straight into the glass instead of flying off with the card.
• Standing on a bus: when the bus pulls away, you seem to lurch backwards. In fact your body is staying where it was while the bus moves forwards under you.
• A turning car: on a sharp bend, loose objects slide across the seat. They are trying to keep moving in a straight line while the car turns.

Terminal velocity: Newton's first law in action

A skydiver shows both sides of the law. Just after jumping, weight is the only force, so they speed up. As they get faster, air resistance grows. Eventually air resistance equals their weight, the resultant force is zero, and they fall at a steady speed called terminal velocity.

Here x is the time after jumping in seconds and y is the velocity in m/s, for a model skydiver with a terminal velocity of 50 m/s. Where the curve is steep, the forces are unbalanced and the skydiver accelerates. Where it is flat, the forces are balanced, the acceleration is zero and the velocity stays the same, just as Newton's first law says.

Try it yourself. For each moment of the jump, decide whether air resistance is less than, equal to or more than the weight, then press Mark to check it in the course.

Newton's first law worked examples

Example 1: a steady speed

A car travels along a straight, level road at a steady 25 m/s. Its engine provides a driving force of 1850 N. What is the total resistive force?

Neither the speed nor the direction changes, so the velocity is constant. Newton's first law then tells you the forces must cancel, which means the resistive forces add up to the same as the driving force: 1850 N.

Example 2: terminal velocity

A skydiver of mass 75 kg falls at terminal velocity. Find the air resistance on them. Use g = 9.8 N/kg.

At terminal velocity the forces are balanced, so air resistance equals the weight.

The air resistance is 735 N, upwards.

Example 3: a crane at constant speed

A crane lifts a 450 kg load upwards at a constant speed. What is the tension in the cable? Use g = 9.8 N/kg.

Constant speed in a straight line means zero resultant force, so the tension balances the weight: 450 × 9.8 = 4410 N. It makes no difference how fast the load moves, as long as the speed is steady.

Example 4: when the forces stop balancing

A 30 kg box is pushed across a floor at a constant velocity with a force of 120 N. The push is then increased to 180 N. What happens?

At constant velocity, friction must be 120 N. When the push rises to 180 N, the resultant force is 180 − 120 = 60 N, so Newton's first law no longer applies. Newton's second law gives the acceleration:

The box speeds up at 2 m/s² for as long as the forces stay unbalanced.

Example 5: forces at an angle (A-level)

A suitcase of mass 18 kg is pulled across a level floor at a constant velocity by its handle, which makes an angle of 40° with the horizontal. The pull in the handle is 50 N. Find the friction force and the normal contact force. Use g = 9.81 N/kg.

Resolve the pull into a horizontal and a vertical part. The velocity is constant, so the forces balance in each direction.

Horizontally, friction balances the horizontal part of the pull:

Vertically, the normal force and the vertical part of the pull together balance the weight:

Friction is 38.3 N and the normal contact force is 144 N to 3 significant figures. Pulling upwards at an angle takes some weight off the floor, which is why the normal force is less than the weight.

Example 6: sliding down a slope (A-level)

A 5.0 kg box slides down a ramp at 20° to the horizontal at a constant velocity. Find the friction force on it.

Along the slope, the part of the weight pulling the box down the slope is mg sin 20°. Constant velocity means friction balances it exactly:

Is the Moon obeying Newton's first law?

No. The Moon moves at a roughly constant speed, but its direction changes all the time as it goes round the Earth. A change of direction is a change of velocity, so there must be a resultant force: the Earth's gravitational pull, towards the centre of the orbit. Constant speed is not enough for Newton's first law. You need constant speed and constant direction.

Common mistakes

• Thinking a moving object needs a force to keep moving. It only needs a force to speed up, slow down or turn. At a steady velocity the forces are balanced.
• Thinking zero resultant force means the object is at rest. It can be at rest or moving at a constant velocity.
• Saying "there are no forces". Usually there are several forces; they just add to zero. Say "the forces are balanced" or "the resultant force is zero".
• Forgetting direction. An object moving in a circle at constant speed is accelerating, because its direction keeps changing.
• Mixing up the first and third laws. Balanced forces in the first law act on the same object. Third law pairs act on two different objects.

Newton's three laws together

• First law: zero resultant force means no change in velocity.
• Second law: a resultant force causes an acceleration, F = ma.
• Third law: two interacting objects push or pull on each other equally hard, in opposite directions. See our guide to Newton's third law.

The first two laws are about the forces on one object; the third is about the forces between two objects. The Laws of Motion course covers all three, with a section where you watch a cart slide on surfaces with less and less friction. The Force Calculator works out the resultant force, mass or acceleration when the forces do not balance.

Practise forces in a short timed paper

GCSE Physics Higher and A-level Physics: Year 1 each give you a short timed paper every day, with 8 questions worth 25 to 35 marks across the course.

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