Three laws, published in 1687, still underpin every dynamics problem you will meet before university. They are short enough to memorize and subtle enough to be misread, so it is worth learning what each one actually claims.
The first law: inertia
This overturns the intuition that things need a push to keep moving. A puck slides across ice and eventually stops, but not because it 'runs out of push' — it stops because friction is a net force acting on it. Remove the friction and it would keep going forever. Inertia is the name for this resistance to a change in velocity, and mass is the measure of inertia: a loaded shopping trolley is harder to start and harder to stop than an empty one.
- A passenger lurches forward when a bus brakes — the passenger keeps moving at the old velocity while the bus slows beneath them.
- A headrest exists because in a rear-end collision the car and torso are pushed forward while the head, obeying the first law, stays put.
- Seatbelts supply the force that decelerates you with the car instead of with the windscreen.
The second law: net force, mass and acceleration
This is the most used equation in the unit, and the word that carries it is net. It is not any one force that produces acceleration — it is the vector sum of all of them. A crate pushed with against of friction has a large applied force and zero acceleration, because the net force is zero.
| If you... | ...then the acceleration | Because |
|---|---|---|
| Double the net force on the same mass | Doubles | at constant mass |
| Double the mass under the same net force | Halves | at constant force |
| Make the net force zero | Becomes zero | Constant velocity — the first law is the second law with |
| Reverse the net force | Reverses | Acceleration always points along the net force |
The third law: action and reaction
The usual objection is: if every force has an equal opposite, how does anything ever accelerate? The answer is that the two forces in a pair never act on the same object, so they never appear on the same free-body diagram and never cancel each other. You push the ground backwards; the ground pushes you forwards. Your force acts on the Earth and the Earth's force acts on you — only the second one moves you.
- Two forces on different objects
- Always the same type of force
- Always equal in size, opposite in direction
- Never cancel, because they act on different things
- Example: ball pushes bat back; bat pushes ball forward
- Two forces on the same object
- Often different types of force
- Equal and opposite only when there is no acceleration
- Do cancel — that is what balanced means
- Example: weight down and normal force up on a resting book
- Walking — your foot pushes back on the ground, the ground pushes forward on you. On ice there is no friction to push against, so you go nowhere.
- Rockets — the engine pushes exhaust gas out, the gas pushes the rocket forward. No air is needed, which is why rockets work in space.
- Swimming — you push water backwards, the water pushes you forwards.
- Recoil — the rifle pushes the bullet forward, the bullet pushes the rifle back. The forces are equal; the accelerations are not, because the masses differ enormously.