Newton's laws of motion

Why does a passenger fall forward when a bus brakes? Why is it harder to push a loaded cart than an empty one? Why does a gun kick back when fired? In 1687 Sir Isaac Newton answered all such questions with three short laws.

First law: the law of inertia

An object stays at rest, or keeps moving in a straight line at the same speed, unless an unbalanced force acts on it.

Things do not start, stop or turn by themselves. This unwillingness to change is called inertia. The more mass an object has, the greater its inertia: a truck is harder to start and harder to stop than a bicycle.

• When a bus starts suddenly, your feet move with it but your upper body tends to stay at rest. You fall backward.
• When it brakes, your body tends to keep moving. You fall forward. This is why we wear seat belts.
• Flick a card from under a coin placed on a glass: the card flies off and the coin drops into the glass.

A ball rolling on the ground does stop, but only because friction acts on it. On a perfectly smooth surface it would roll on for ever.

Second law: force and acceleration

The momentum of a body is its mass multiplied by its velocity (p = mv). A fast cricket ball has more momentum than a slow one, and a moving truck far more than a moving bicycle.

The rate of change of momentum of a body is proportional to the force applied and takes place in the direction of the force. For a body of constant mass, this gives the famous equation:

Force = mass × acceleration, or F = ma

Force is measured in newtons (N). One newton is the force that gives a mass of 1 kg an acceleration of 1 m/s².

Worked example: a force acts on a 5 kg trolley and gives it an acceleration of 2 m/s². F = ma = 5 × 2 = 10 N.

The law explains much that we see. The same push gives a light object a bigger acceleration than a heavy one. A fielder pulls the hands back while catching a fast ball: this increases the time taken to stop the ball, so the force on the hands is smaller. High jumpers land on thick foam for the same reason.

Third law: action and reaction

To every action there is an equal and opposite reaction.

Forces always come in pairs. If A pushes B, then B pushes A just as hard in the opposite direction. The two forces act on different objects, so they do not cancel each other.

• When we walk, our foot pushes the ground backward; the ground pushes us forward.
• A swimmer pushes the water back; the water pushes the swimmer ahead.
• A rocket throws hot gases downward at great speed; the gases push the rocket upward.
• When a bullet is fired forward, the gun recoils backward. The gun moves much more slowly because its mass is much greater.
• Step from a small boat to the bank and the boat moves away behind you.

Conservation of momentum

From the second and third laws together comes an important result: when two bodies interact and no outside force acts, their total momentum stays the same. The momentum lost by one is gained by the other. This explains collisions, recoil and rocket flight.