Forces and Newton's Laws

The three rules that explain why anything in the universe moves the way it does.

What is a force?

A force is a push or a pull. That’s it. That’s the whole definition.

• Pushing a shopping cart → force.
• Earth pulling you down → force (we call it gravity).
• A magnet grabbing a paperclip → force.
• The floor holding you up → force (yes, the floor is actively pushing you up).

Forces are measured in newtons (N). One newton is roughly the weight of a small apple sitting in your hand. Remember that — it makes every number you see less abstract.

Newton’s three laws, in plain English

Newton wrote three sentences that explain basically all of mechanical motion. Here they are, translated.

1st Law — The Lazy Law

An object keeps doing what it’s doing unless a force changes it.

If it’s still, it stays still. If it’s moving, it keeps moving in a straight line at the same speed. Forever.

“But wait, things stop on their own all the time.”

No, they don’t. A ball rolling on grass stops because of friction (a force from the grass) and air resistance (a force from the air). Take those away — imagine the ball on a frictionless surface in a vacuum — and it would roll forever.

This law is also called inertia. Inertia is just the universe’s laziness: stuff doesn’t change its motion unless something forces it to.

2nd Law — The Math Law

Force = mass × acceleration. $F = ma$

This one tiny equation is doing a lot of work. Let’s read what it actually says.

• More force → more acceleration. Push a cart harder, it speeds up faster. Obvious.
• More mass → less acceleration for the same force. Push a car as hard as you push a shopping cart — the car barely budges. Also obvious, once you see it.

So mass is just how stubbornly something resists being accelerated. A bowling ball is “heavy” because it resists. A ping-pong ball doesn’t.

Try it in your head

You push a 1 kg book with 2 N of force. How fast does it speed up?

$a = \frac{F}{m} = \frac{2 \text{ N}}{1 \text{ kg}} = 2 \text{ m/s}^2$

Every second, it’s 2 m/s faster. Neat.

Now push a 10 kg backpack with the same 2 N.

$a = \frac{2}{10} = 0.2 \text{ m/s}^2$

Ten times the mass → one tenth the acceleration. The equation matches your gut.

3rd Law — The Pushback Law

For every action, there’s an equal and opposite reaction.

Whenever you push something, it pushes back on you with the exact same force.

This sounds weirder than it is. Examples:

• You push the ground down with your foot → the ground pushes you up. That’s how you walk.
• A rocket pushes hot gas downward → the gas pushes the rocket upward. That’s how rockets fly.
• You lean against a wall → the wall pushes you back with the same force. If it didn’t, you’d fall through it.

Common confusion: if the forces are equal and opposite, why does anything ever move? Because the two forces act on different objects. When you push a cart, you feel a backward push and the cart feels a forward push. The cart accelerates forward, you stay put (because friction with the floor balances the cart’s pushback on you).

The forces you’ll meet over and over

Gravity

Earth pulling everything toward its center. On Earth’s surface, it accelerates anything at about 9.8 m/s² (we call this $g$). A 1 kg object feels a downward force of about 9.8 N. That’s its weight.

Normal force

The push a surface gives back when something rests on it. Sit on a chair → chair pushes up on you with exactly enough force to hold you. It’s Newton’s 3rd Law in action.

Friction

The force that resists sliding between two surfaces. Without it, you couldn’t walk, drive, or hold a pencil. With too much of it, nothing would move. Engineers spend half their lives managing friction.

Tension

The pull along a rope, cable, or string. If you hang a weight from a rope, the rope is in tension. The whole rope pulls equally along its length — that’s why one weak link breaks the whole chain.

Applied force

Whatever you (or a motor, or a spring) directly push or pull with. The “input” force in most problems.

How to solve any force problem (the engineer’s method)

1. Draw the object

   Just a box. Doesn’t need to be art.

2. Draw every force acting on it as an arrow

   Arrow length = how big the force is. Arrow direction = which way it pushes. This is called a free-body diagram, and it’s the single most useful tool in mechanics.

3. Add up the forces in each direction

   Forces going opposite ways cancel. What’s left is the net force.

4. Apply F = ma

   Net force divided by mass = acceleration. Done.

If net force = 0, acceleration = 0. The object either sits still or coasts at constant velocity. This is called equilibrium, and it’s how every bridge, building, and chair stays where it is.

Next: Energy and Work

The other way to think about forces — often easier, always elegant.