Chapter 3 of 8

All 8 chapters
  1. 1Scalars and vectors, readunderstood
  2. 2Velocity and acceleration, readunderstood
  3. 3Newton's first law, readunderstood
  4. 4Newton's second law, readunderstood
  5. 5Weight and falling, readunderstood
  6. 6Newton's third law, readunderstood
  7. 7Momentum, readunderstood
  8. 8Stopping distances, readunderstood

S4.8.3 Chapter 3

Newton's first law

When I stop pedalling, my bicycle slows down. Does a moving thing need a force to keep moving?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Explain why an object keeps moving unless a resultant force acts
  • Explain how seat belts protect passengers using inertia

For about two thousand years, many thinkers said that a moving thing needs a push to keep moving. It fits daily life. A cart stops when the ox stops pulling.

In the early 1600s, Galileo rolled balls down one slope and up another. The smoother the slopes, the nearer the ball rolled to its first height. He reasoned that on a perfectly smooth, flat track it would never stop.

Isaac Newton wrote this idea as the first of his three laws of motion. Here it is in modern words.

Newton’s first law: an object stays at rest, or keeps moving at a constant velocity, unless a resultant force acts on it. Constant velocity means the same speed and the same direction.

Two pictures of a trolley on a very smooth, level track, one labelled earlier and one labelled later. The trolley is labelled 2 kg in both. In both it has an arrow to the right of the same length, labelled 3 m/s. A key says positive direction.earlier2 kg3 m/slater2 kg3 m/spositive direction
No force acts along the track. The trolley has moved on, and its velocity has not changed.
The forces on the gliding trolley, drawn as a block. An arrow down is labelled weight 20 N. An arrow up of the same length is labelled support 20 N. There is no arrow to the left or right. A bar marked bar = 10 N shows the scale.weight 20 Nsupport 20 Nbar = 10 N
The two vertical forces are equal and opposite. Nothing pushes or pulls along the track.

Read the law with care. It does not say that no force acts. It says that no resultant force acts. Many forces can act, as long as they cancel. The weight and the support above cancel.

See it three ways

As a picture

A block with an arrow to the right labelled push, 30 N and an arrow to the left of the same length labelled friction, 30 N. A bar marked bar = 10 N shows the scale.push30 Nfriction30 Nbar = 10 N

In words

When the forces on an object are balanced, the resultant force is zero. The object then keeps its velocity.

In symbols

resultant = 30 N − 30 N = 0 N

A car cruises at a steady 20 m/s on a level road. The engine drives it forward. Air and the road drag it back. If the car holds a constant velocity, the first law says the resultant force is 0 N. So drive and drag are equal.

A car with two arrows. An arrow to the right is labelled drive, 800 N. An arrow to the left of the same length is labelled drag, 800 N. A bar marked bar = 400 N shows the scale.drive800 Ndrag800 Nbar = 400 N
Only the forces along the road are drawn. The weight and the road’s upward push are equal and also cancel.

This is why a bicycle slows when you stop pedalling. The drive is gone, but drag and friction remain. The resultant now points backwards, so the velocity falls. Friction does the slowing. Nothing is needed to keep the bicycle moving.

In space a probe far from any planet keeps going with its engines off. Almost no force acts on it, so its velocity hardly changes. That is the first law at work.

The first law also says that an object at rest stays at rest. A stone on a table does not move by itself. It needs a resultant force to start moving.

Inertia is the tendency of an object to keep its velocity. The more mass an object has, the more inertia it has, and the harder it is to start, stop or turn. A loaded truck is harder to stop than an empty one.

Inertia explains seat belts. A car moves at 15 m/s with a passenger in it. The passenger has the same velocity as the car. Now the car hits a wall and stops in a very short time.

Draw it first

A car stops and the passenger does not

  1. Three pictures of a car with a passenger, each with a key saying positive direction. First, labelled moving together: the car has an arrow of 15 m/s below it and the passenger has an arrow of 15 m/s above. Second, labelled the car stops: the car shows 0 m/s and the passenger, who has moved forward, still has an arrow of 15 m/s. Third, labelled the belt holds: the car shows 0 m/s, the passenger shows 0 m/s, and a short arrow pointing back on the passenger is labelled belt.moving together15 m/s15 m/spositive direction

    1 The car and the passenger both move at 15 m/s. No resultant force acts on the passenger, so the passenger keeps this velocity.

  2. Three pictures of a car with a passenger, each with a key saying positive direction. First, labelled moving together: the car has an arrow of 15 m/s below it and the passenger has an arrow of 15 m/s above. Second, labelled the car stops: the car shows 0 m/s and the passenger, who has moved forward, still has an arrow of 15 m/s. Third, labelled the belt holds: the car shows 0 m/s, the passenger shows 0 m/s, and a short arrow pointing back on the passenger is labelled belt.the car stops15 m/s0 m/spositive direction

    2 The car stops. The passenger has no force to slow them yet, so they keep moving forward at 15 m/s.

  3. Three pictures of a car with a passenger, each with a key saying positive direction. First, labelled moving together: the car has an arrow of 15 m/s below it and the passenger has an arrow of 15 m/s above. Second, labelled the car stops: the car shows 0 m/s and the passenger, who has moved forward, still has an arrow of 15 m/s. Third, labelled the belt holds: the car shows 0 m/s, the passenger shows 0 m/s, and a short arrow pointing back on the passenger is labelled belt.the belt holds0 m/sbelt0 m/spositive direction

    3 A seat belt pulls back on the passenger. This force slows the passenger to a stop along with the car.

Without a belt the passenger keeps moving until something stops them, such as the dashboard or the windscreen. That stop is sudden and the force is very large.

A seat belt acts on the passenger at once and slows them with the car. It is made to stretch a little, so it slows the passenger over a longer time. It also spreads the force over the strong bones of the chest and hips.

A headrest works the same way. When a car is hit from behind, the seat pushes the body forward. The head would stay behind because of its inertia. The headrest pushes it forward with the body.

Try it

Drop a stone into a cup

You need: a plastic or metal cup, a stiff piece of card, such as from a box, a small stone.

Be safe: Flick the card away from people and away from your face.

  1. Stand the cup on a table. Lay the card on top of the cup.
  2. Put the stone on the card, over the middle of the cup.
  3. Flick the edge of the card sideways with one finger. Do it hard and fast.
  4. Watch the stone.

What you will see: The card shoots out sideways. The stone drops straight down into the cup. The card was too quick to pull the stone along. Friction pulled on the stone for only a moment, so it hardly moved sideways. Then gravity pulled it down.

If you cannot try it, this is what happens.
A table with the columns Part and What happens. Card: moves away. Stone: drops down.PartWhat happenscardmoves awaystonedrops down

A wrong idea many people have

A force is needed to keep an object moving.

Why it feels right: In daily life, things stop when we stop pushing. A cart, a ball and a bicycle all slow down.

The test that breaks it: Slide a stone on a rough floor, then on a smooth tiled floor. It stops sooner on the rough one. Friction is the force that stops it. The less friction there is, the further it goes.

What is true: No force is needed to keep a constant velocity. A resultant force is needed to change the velocity. Moving things slow down because friction and air resistance act on them.

A wrong idea many people have

If an object is at rest, no forces act on it.

Why it feels right: We notice forces when things move, and a still thing looks as if nothing is happening.

The test that breaks it: A book lies still on a table. Its weight pulls it down, and the table pushes it up. Take the table away and the book falls at once.

What is true: Forces can act on a thing at rest. They are balanced, so the resultant force is zero. The first law is about the resultant, not about each force.

A wrong idea many people have

When a car stops suddenly, a force throws the passengers forward.

Why it feels right: Passengers feel pushed into the belt, and they do move forward.

The test that breaks it: Put a stone on a smooth tray and carry the tray forward. Stop the tray suddenly. The stone slides on. No force pushed it forward. The tray stopped and the stone kept its velocity.

What is true: No forward force acts on the passengers. They keep the velocity they had, while the car slows under them. The belt gives the backward force that slows them.

Key words

first law
an object stays at rest, or keeps a constant velocity, unless a resultant force acts on it.
constant velocity
the same speed in the same direction.
balanced forces
forces whose resultant is zero.
inertia
the tendency of an object to keep its velocity. More mass means more inertia.

Back to your guess

The answer is C: No. The bicycle slows because friction and the air push against it.

A moving thing needs no force to keep its velocity. The bicycle slows because friction and air resistance act on it. A force is needed to change the velocity, not to keep it.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. A trolley glides along a very smooth, level track. Ignore air. What happens to its velocity?

    Tap your answer.

    1. Yes, that is right. With no resultant force the velocity stays constant. The trolley keeps moving at the same speed in a straight line.

    2. Not this one. A push is not a store like fuel. With no resultant force, the velocity does not change. Try another.

    3. Not this one. Speeding up needs a resultant force. With none, the velocity stays the same. Try another.

    See the answer

    It stays the same.

    With no resultant force the velocity stays constant. The trolley keeps moving at the same speed in a straight line.

    • If you chose B: A push is not a store like fuel. With no resultant force, the velocity does not change.
    • If you chose C: Speeding up needs a resultant force. With none, the velocity stays the same.

  2. A box is already sliding to the right. Ravi pushes it to the right with 50 N. Friction pulls it back with 50 N. What happens to the box?

    A box with an arrow to the right labelled push, 50 N and an arrow to the left of the same length labelled friction, 50 N. A bar marked bar = 20 N shows the scale.push50 Nfriction50 Nbar = 20 N
    Tap your answer.

    1. Not this one. To speed up, the push must be bigger than the friction. Here the two are equal. Try another.

    2. Not this one. To slow down, the friction must be bigger than the push. Here the two are equal. Try another.

    3. Not this one. The resultant force is zero. That means no change in velocity, not a stop. Try another.

    4. Yes, that is right. The resultant force is 50 N − 50 N = 0 N. By the first law the box keeps its velocity, so it moves on at a steady speed.

    See the answer

    It keeps the same velocity.

    The resultant force is 50 N − 50 N = 0 N. By the first law the box keeps its velocity, so it moves on at a steady speed.

    • If you chose A: To speed up, the push must be bigger than the friction. Here the two are equal.
    • If you chose B: To slow down, the friction must be bigger than the push. Here the two are equal.
    • If you chose C: The resultant force is zero. That means no change in velocity, not a stop.

  3. A passenger without a seat belt moves forward when the car stops suddenly. Why?

    Tap your answer.

    1. Not this one. No forward force acts. The passenger moves forward only because nothing has slowed them yet. Try another.

    2. Yes, that is right. The car slows under the passenger. With no resultant force on them, the passenger keeps the old velocity. This is inertia.

    3. Not this one. The seat does not pull. It cannot give a forward force on someone who is moving away from it. Try another.

    4. Not this one. Gravity pulls down, not forward. The car stops, and the passenger keeps going by inertia. Try another.

    See the answer

    The passenger keeps the velocity they had, because no force slows them.

    The car slows under the passenger. With no resultant force on them, the passenger keeps the old velocity. This is inertia.

    • If you chose A: No forward force acts. The passenger moves forward only because nothing has slowed them yet.
    • If you chose C: The seat does not pull. It cannot give a forward force on someone who is moving away from it.
    • If you chose D: Gravity pulls down, not forward. The car stops, and the passenger keeps going by inertia.

  4. What does a seat belt do in a crash?

    Tap your answer.

    1. Yes, that is right. The belt gives the passenger the backward force that the first law says is needed to change their velocity. It also stretches a little and spreads the force over the chest and hips.

    2. Not this one. The belt acts on the passenger, not on the car. It does not change how the car stops. Try another.

    3. Not this one. Inertia depends on the passenger’s mass. A belt does not change mass. Try another.

    See the answer

    It gives a force that slows the passenger together with the car.

    The belt gives the passenger the backward force that the first law says is needed to change their velocity. It also stretches a little and spreads the force over the chest and hips.

    • If you chose B: The belt acts on the passenger, not on the car. It does not change how the car stops.
    • If you chose C: Inertia depends on the passenger’s mass. A belt does not change mass.

  5. A loaded trolley and an empty trolley stand side by side. Which is harder to start moving and harder to stop?

    Tap your answer.

    1. Not this one. It is the other way round. The empty trolley has less mass, so less inertia. Try another.

    2. Not this one. Shape does not decide this. The loaded trolley has more mass, so more inertia. Try another.

    3. Yes, that is right. Mass measures inertia. A trolley with more mass resists a change in velocity more, so it is harder to start and harder to stop.

    See the answer

    The loaded trolley, because more mass means more inertia.

    Mass measures inertia. A trolley with more mass resists a change in velocity more, so it is harder to start and harder to stop.

    • If you chose A: It is the other way round. The empty trolley has less mass, so less inertia.
    • If you chose B: Shape does not decide this. The loaded trolley has more mass, so more inertia.

  6. Which sentence is the first law?

    Tap your answer.

    1. Not this one. That is Newton’s second law, in the next chapter. Try another.

    2. Not this one. That is Newton’s third law, a few chapters on. Try another.

    3. Not this one. That is the old idea this chapter showed to be wrong. A force changes the velocity, and keeping it needs none. Try another.

    4. Yes, that is right. With no resultant force the velocity stays the same. A thing at rest stays at rest. A moving thing keeps moving at a constant velocity.

    See the answer

    An object keeps its velocity unless a resultant force acts on it.

    With no resultant force the velocity stays the same. A thing at rest stays at rest. A moving thing keeps moving at a constant velocity.

    • If you chose A: That is Newton’s second law, in the next chapter.
    • If you chose B: That is Newton’s third law, a few chapters on.
    • If you chose C: That is the old idea this chapter showed to be wrong. A force changes the velocity, and keeping it needs none.

  7. From an earlier chapter

    A car’s velocity goes from 4 m/s to 10 m/s in 3 s. What is its acceleration?

    Tap your answer.

    1. Not this one. You divided the time by the change in velocity. It is the change in velocity divided by the time. Go to S4.8.2. Try another.

    2. Yes, that is right. a = (v − u) ÷ t = (10 − 4) ÷ 3 = 6 ÷ 3 = 2 m/s².

    3. Not this one. That is the change in velocity. Divide it by the time. Go to S4.8.2. Try another.

    See the answer

    2 m/s²

    a = (v − u) ÷ t = (10 − 4) ÷ 3 = 6 ÷ 3 = 2 m/s².

    • If you chose A: You divided the time by the change in velocity. It is the change in velocity divided by the time. Go to S4.8.2.
    • If you chose C: That is the change in velocity. Divide it by the time. Go to S4.8.2.

  8. A cyclist pedals with 60 N at a steady velocity. Air pushes back with 25 N. How big is the friction on the tyres?

    See the answer

    35 N

    A steady velocity means the resultant force is 0 N. So the backward forces add up to 60 N. The friction is 60 N − 25 N = 35 N.

  9. A bag weighs 40 N and hangs at rest from a rope. How big is the pull of the rope?

    See the answer

    40 N

    The bag is at rest, so the resultant force is 0 N. The rope pulls up with the same force as the weight pulls down: 40 N.

Keep it

Copy this into your exercise book.

First law: with no resultant force, an object at rest stays at rest and a moving one keeps a constant velocity. Inertia grows with mass. A seat belt gives the force that slows you with the car.

Draw: A car and passenger moving together, then the car stopped and the passenger still moving, with a belt arrow.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (825 KB). It opens on any phone.