Forces and motion: three laws that took two thousand years
The hard part was not the maths. It was noticing that motion does not need a cause.
Newton published three laws of motion in 1687, and they are brief enough to fit on a postcard. They took roughly two thousand years to arrive because each one contradicts something that feels obviously true.
First law: things keep going
An object continues at rest, or moving at constant velocity in a straight line, unless a net force acts on it.
This is the one Aristotle got wrong for two millennia, and understandably. Everything we push stops when we stop pushing, so motion appears to require a continuous cause.
It does not. The stopping is caused by friction and air resistance, which are so constant on Earth that they are invisible - a force we never notice because we have never been without it. Remove them, as in space, and a thrown object simply keeps going forever.
So the question 'what keeps it moving?' is the wrong question. Nothing has to. The right question is always 'what is slowing it down?'
Second law: force changes motion
F = ma. Force equals mass times acceleration.
The crucial word is acceleration, not speed. A force does not maintain velocity, it changes it. Push something twice as hard and you double how quickly its velocity changes; make it twice as heavy and the same push changes it half as fast.
Acceleration in physics also means any change in velocity, including direction. A car going round a corner at constant speed is accelerating, because its direction is changing - which is why you feel pushed sideways.
Galileo is said to have demonstrated this from Pisa; whether or not he did, the cancellation is the reason. In air a feather loses to a hammer because of air resistance, not weight - and on the Moon, where Apollo 15 actually ran this test, they landed together.
Third law: forces come in pairs
For every action there is an equal and opposite reaction.
The most misquoted sentence in physics. It does not mean forces cancel out and nothing moves. The two forces act on different objects, which is the entire point.
- You push the ground backwards; the ground pushes you forwards. You walk.
- A rocket pushes gas out; the gas pushes the rocket up. No air required, which is why rockets work in space.
- The Earth pulls you down with your weight; you pull the Earth up with exactly the same force. The Earth accelerates too - by an amount too small to measure, because F = ma and its mass is enormous.
The common error: 'if the forces are equal and opposite, how does anything move?' Because a pair acts on two different bodies. To work out whether you accelerate, add up only the forces acting on you. The one you exert on something else never appears in your own sum.
Momentum, and why it is conserved
Momentum is mass times velocity. In any collision, the total momentum of everything involved before equals the total after - always, with no exceptions ever observed.
It follows directly from the third law. During a collision each object feels an equal and opposite force for exactly the same duration, so each gains momentum the other loses. Nothing is created; it is transferred.
This is why a car crumple zone helps. It cannot change the momentum that has to be lost, but it spreads the change over a longer time. Force is the rate of change of momentum, so the same change over a longer time means a smaller force - and the force is what injures people.