How Newton's Laws Explain Motion

Newton's first law says that an object remains at rest or continues moving at constant velocity unless an unbalanced external force acts on it. Constant velocity means constant speed in a straight line. Motion does not need a continuing forward force when resistance is absent.

On Earth, friction and air resistance often slow moving objects, so it can seem as though motion naturally runs out. Those resistive forces are the reason for the change. In space, where resistance may be tiny, an object can continue moving for a very long time.

The tendency to resist changes in motion is called inertia. Greater mass means greater inertia, so a heavy object is harder to start, stop or turn than a lighter object under similar conditions.

An unbalanced force causes acceleration, which means a change in velocity. The acceleration points in the direction of the resultant force. A larger resultant force produces greater acceleration when mass stays the same.

For a fixed force, a larger mass produces less acceleration. This is why the same push changes the motion of an empty shopping trolley more than a loaded one. The relationship is commonly written as force equals mass multiplied by acceleration.

Resultant force means the overall effect after all forces are combined. If equal forces act in opposite directions, the resultant is zero and there is no acceleration. The object may remain still or keep moving steadily.

Newton's third law says that when one object exerts a force on another, the second object exerts an equal and opposite force on the first. The two forces act on different objects, so they do not cancel each other on one force diagram.

When you walk, your foot pushes the ground backward and the ground pushes you forward. A rocket pushes exhaust gases backward and the gases push the rocket forward. The forces appear together as part of one interaction.

Use this order when solving a force problem:

• •Choose the object you are analysing.
• •List every external force acting on it.
• •Find the resultant force and its direction.
• •Use mass to predict the acceleration.
• •Place third-law partner forces on the other object.

Newton's laws are not the last word. At speeds approaching that of light, Einstein's relativity takes over and mass no longer behaves as a fixed quantity; at the scale of atoms, quantum mechanics replaces the idea of a particle following one definite path. Neither of these matters for a car, a rocket or a planet, which is why engineers and astronomers still work almost entirely with the laws of 1687. The Apollo missions were navigated with them, and so is every satellite launched today.

There is also a useful subtlety inside the third law. The pair of forces is always the same kind of force acting between the same two objects, so the weight of a book on a table is not paired with the table's upward push on the book; it is paired with the book's gravitational pull on the Earth. Spotting that distinction is the difference between a correct force diagram and one that quietly cancels the wrong things.

Bathroom scales do not measure your weight directly. They measure how hard they have to push up on you. Suppose your mass is 50 kilograms, so gravity pulls you down with a force of about 490 newtons. When the lift is still, or moving up or down at a steady speed, the resultant force on you must be zero. The scales therefore push up with 490 newtons and display 50 kilograms. Steady motion in a lift feels exactly like standing on the ground, just as the first law suggests.

Now let the lift accelerate upwards at 2 metres per second squared. The second law says you need a resultant upward force of 50 times 2, which is 100 newtons, so the scales must push with about 590 newtons and read roughly 60 kilograms. Accelerating downwards at the same rate, the push drops to about 390 newtons and the reading to roughly 40. If the lift fell freely, the scales would read zero. Astronauts in orbit float for the same reason: they and their spacecraft are falling together, not escaping gravity.

For about two thousand years, the dominant view of motion came from Aristotle, who taught that moving objects naturally come to rest and that continuing motion needs a continuing cause. Everyday experience seems to agree, since a cart stops soon after you stop pushing it. Thrown objects were a puzzle, because nothing visibly pushes a stone after it leaves your hand, so medieval scholars suggested the thrower gave it an internal impetus that gradually wore away. This felt sensible, and researchers who study physics teaching find that many students still hold a similar intuition before they learn Newton's first law.

In the early seventeenth century, Galileo attacked the problem with an argument about ramps. A ball rolling down one smooth slope will climb a facing slope to almost the height it started from. Make the second slope gentler and the ball travels further to reach that height. Make it perfectly flat and there is no height to reach, so the ball would keep rolling indefinitely if nothing slowed it. Galileo concluded that friction and air resistance, not a natural tendency, bring things to rest. Newton later built this insight into the first of his laws.

Newton originally stated his second law in terms of what he called quantity of motion, now known as momentum, which is mass multiplied by velocity. Rearranged, the law says that a force acting over a period of time changes an object's momentum: force multiplied by time equals the change in momentum. So the same change in momentum can come from a large force acting briefly or a smaller force acting for longer. Stopping a moving body always means removing all of its momentum, but how much damage the stop does depends on how quickly that happens.

Imagine a 60 kilogram passenger travelling at 15 metres per second, about 54 kilometres per hour. Their momentum is 60 times 15, or 900 kilogram metres per second. If a hard dashboard stopped them in one hundredth of a second, the average force would be 90,000 newtons. If a seatbelt, an airbag and a crumpling car body spread the stop over a tenth of a second, the force falls to 9,000 newtons, ten times smaller. The first law explains why the belt is needed at all, since an unrestrained passenger keeps moving when the car stops. Bending your knees as you land from a jump uses the same idea.

Newton's laws explain steady motion, acceleration and interactions. Balanced forces preserve velocity, unbalanced forces create acceleration and every force belongs to an equal and opposite interaction pair. Keep track of which object each force acts on, and many motion problems become far less tangled.