Newton's third law and conservation of momentum

Newton's third law

tap a force ↓

Each arrow is coloured like the object it acts on: blue on skater A, red on skater B, green on the book.

Tap each force to find out which object it acts on, and why that matters.

Momentum

p = m × v

Momentum (p, in kg m/s) = mass (m, in kg) × velocity (v, in m/s). It's how much motion an object carries, and which way.

Velocity has a direction, so momentum does too: it's a vector. Choose one direction to be positive, and anything moving the other way gets a minus sign. A 2 kg ball rolling right at 3 m/s has +6 kg m/s; the same ball rolling left at 3 m/s has −6 kg m/s.

Momentum is conserved

Trolley A (3 kg) moves right at 2 m/s: 3 × 2 = +6 kg m/s. Trolley B (1 kg) moves left at 2 m/s: 1 × (−2) = −2 kg m/s. Total: +4 kg m/s.

Step through the collision. Each arrow is one trolley's momentum; the black arrow is the total.

Predict, then check

Back to the skaters on the ice, this time with masses.

Skater A (60 kg) and skater B (40 kg) stand still on the ice, then push off each other. What happens next?

What you need to know

• Newton's third law: when two objects interact, each exerts a force on the other, equal in size and opposite in direction.
• A third-law pair is the same type of force acting on two different objects, so the forces never cancel. Balanced forces act on one object.
• Momentum p = m × v, measured in kg m/s. It's a vector, so momenta in opposite directions have opposite signs.
• In a closed system, total momentum before a collision or explosion = total momentum after.

The big picture

Whenever two objects interact, they push or pull on each other with forces that are equal in size and opposite in direction. Those two forces act on different objects, so they never cancel each other out. Momentum is mass × velocity, and it has a direction. Because the two objects push on each other equally and oppositely for the same time, the total momentum before a collision or explosion equals the total after, as long as no outside force acts.

⚠ Watch out

Thinking the two forces of a third-law pair cancel because they're equal and opposite. They act on different objects, so they can't cancel. And in calculations, forgetting the minus sign on a velocity in the opposite direction.

Memory hook

Push and push back: equal, opposite, same type, different objects. And what the push takes from one, it gives to the other, so the total never changes.

Check yourself

At the bumper cars, a big adult's car crashes into a small child's car. Which car feels the bigger force during the crash, and which car's velocity changes more? Explain both answers.