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Forces and Motion

Nothing starts, stops, or turns without a push or a pull.

Why does your body lurch forward when a car brakes hard? Why is an empty shopping cart easier to shove than a full one? How does a rocket fly in space, where there is no air to push against? One set of ideas answers all three. On this page you'll learn what forces are, how to describe motion, and the three laws Isaac Newton published in 1687.

Try the F = ma slider Take the quiz
A skateboarder rolling to the right on a sidewalk, pushing off the ground with one foot, with a big arrow labeled push behind them and a small arrow labeled friction pointing backward along the wheels pushfriction

What is a force?

A force is a push or a pull on an object. Opening a door, kicking a ball, and a magnet tugging a paper clip are all forces.

Every force has a size (how strong) and a direction (which way). That's why diagrams draw forces as arrows: a longer arrow means a stronger force.

Scientists measure force in newtons (symbol N), named after Isaac Newton. One newton is about the weight of a small apple (roughly 100 g).

Balanced and unbalanced forces

Most objects have several forces acting on them at once. What matters is the net force: what's left over when you add them all up.

Balanced forces cancel out, so the net force is zero. In a tug-of-war where both teams pull equally hard, the rope doesn't move. A book resting on a table is balanced too: gravity pulls it down and the table pushes it up just as hard.

Unbalanced forces don't cancel. When one tug-of-war team pulls harder, the rope speeds up toward them. Unbalanced forces are the only thing that can change an object's motion.

Quick math: If you push a box right with 30 N and friction pushes left with 10 N, the net force is 30 − 10 = 20 N to the right. The box speeds up to the right.

Friction

Friction is a force that resists two surfaces sliding past each other. It always acts against the motion, or against the motion that is trying to happen.

Rough surfaces usually make more friction than smooth ones, and pressing surfaces together harder increases it. That's why sneakers grip a gym floor but slide on ice.

Friction is often helpful. It lets you walk without slipping, lets car brakes stop the wheels, and keeps a knot tied. Sometimes we want less of it, so we use wheels, ball bearings, oil, or wax.

Air resistance (also called drag) is a kind of friction caused by air. It's why a flat sheet of paper floats down slowly but the same sheet crumpled into a ball falls fast.

Gravity

Gravity is a pull between any two objects that have mass. The more mass, the stronger the pull. Earth is so massive that its gravity holds you, the oceans, and the air on the planet, and it keeps the Moon in orbit.

Mass is how much matter is in an object, measured in kilograms (kg). Weight is the force of gravity on that mass, measured in newtons. Your mass is the same everywhere, but your weight changes: on the Moon, gravity is only about one-sixth as strong as on Earth, so you'd weigh about one-sixth as much.

Near Earth's surface, if you ignore air resistance, everything falls with the same acceleration, about 9.8 m/s². In 1971, Apollo 15 astronaut David Scott dropped a hammer and a falcon feather on the airless Moon, and they hit the ground at the same time.

Speed, velocity, and acceleration

Speed is how far something goes in a certain time.

speed = distance ÷ time

If you bike 300 meters in 60 seconds, your speed is 300 ÷ 60 = 5 m/s (meters per second).

Velocity is speed plus direction, like "5 m/s north." Two cars going 50 km/h in opposite directions have the same speed but different velocities.

Acceleration is how fast velocity changes. Speeding up, slowing down, and turning a corner are all acceleration, because each one changes speed or direction.

acceleration = change in velocity ÷ time

A skateboarder going from 0 to 6 m/s in 3 seconds accelerates at 6 ÷ 3 = 2 m/s². That means the velocity grows by 2 m/s every second.

Newton's three laws of motion

Who was Isaac Newton? Newton was an English scientist and mathematician. In 1687 he published a book in Latin called Philosophiæ Naturalis Principia Mathematica ("Mathematical Principles of Natural Philosophy"), usually just called the Principia. In it he set out three laws of motion and his law of universal gravitation. He built on earlier work, including Galileo Galilei's experiments with rolling balls.

First law · Inertia

An object keeps doing what it's doing unless a net force acts on it

An object at rest stays at rest, and a moving object keeps moving at the same speed in a straight line, unless an unbalanced force changes that. This "keep doing what you're doing" tendency is called inertia.

Everyday examples: When a car brakes suddenly, your body keeps moving forward. A seatbelt supplies the force that stops you. A soccer ball sits still until someone kicks it. A hockey puck glides a long way on smooth ice because there's very little friction to slow it.

Second law · F = ma

Force equals mass times acceleration

F = m × a

The bigger the net force, the bigger the acceleration. The bigger the mass, the smaller the acceleration for the same force. Force is in newtons (N), mass in kilograms (kg), and acceleration in meters per second squared (m/s²). In fact, 1 N = 1 kg·m/s².

Worked example 1: You push a 10 kg wagon so it accelerates at 2 m/s². F = 10 kg × 2 m/s² = 20 N.

Worked example 2: A 50 kg skateboarder gets a net push of 100 N. Rearrange to a = F ÷ m = 100 N ÷ 50 kg = 2 m/s².

Worked example 3 (weight): Weight is F = m × g. A 40 kg student on Earth weighs about 40 kg × 9.8 m/s² = 392 N.

Everyday example: An empty shopping cart speeds up easily; a full one needs a much bigger push for the same acceleration.

Third law · Action and reaction

For every action, there is an equal and opposite reaction

Forces always come in pairs. If object A pushes on object B, then B pushes back on A just as hard, in the opposite direction. The two forces act on different objects, so they don't cancel each other out.

Everyday examples: A rocket pushes hot gas out of its engines downward, and the gas pushes the rocket upward. That's why rockets work in space with no air around them. When you step off a skateboard, the board shoots backward. A swimmer pushes water back, and the water pushes the swimmer forward.

Try it: the F = ma slider

Change the net force and the mass. The tool works out the acceleration with a = F ÷ m.

a = 20 N ÷ 10 kg = 2.00 m/s²

Double the force and the acceleration doubles. Double the mass and it halves.

Experiments to try at home

Ask an adult before you start. Work on the floor, away from breakable things and people's faces.

Quick quiz

1. What is the net force if you push right with 50 N and friction pushes left with 20 N?

2. Why does a seatbelt matter when a car stops suddenly?

3. A 5 kg box accelerates at 4 m/s². What net force acts on it?

4. Which of these is NOT an acceleration?

5. How does a rocket move forward in space, where there's no air?

6. On the Moon, what happens to your mass?

Talk about it

  • Which would be harder to stop: a slow truck or a fast bicycle (think mass and speed)? What does it depend on?
  • Name a way friction helps you before lunch, and one time you wish there were less of it.

Sources

Credits: All illustrations on this page are original, hand-coded SVG by Galileo. The share image was drawn in code.