Momentum: mass in motion
Which is harder to stop: a bicycle at 10 km/h or a truck at 10 km/h? The truck, obviously. A tennis ball thrown gently or a tennis ball from a serve at 200 km/h? The serve. How hard something is to stop depends on both its mass and its velocity. Physicists combine them into one quantity: momentum.
Say it out loud: “momentum equals mass times velocity.”
Momentum· measured in kg·m/s
'Quantity of motion'. A vector — it points the way the object moves.
Mass· measured in kg
More mass, more momentum.
Velocity· measured in m/s
Faster, more momentum. Negative velocity → negative momentum.
Remember the skaters in the previous lesson? The 80 kg skater moved at half the speed of the 40 kg one. Multiply mass by velocity: . The total momentum was zero before the push (both still) and zero after. That's not a coincidence. It's a law.
The law: momentum is conserved
If no outside force acts on a group of objects, their total momentum never changes — no matter how they push, pull, crash or stick together.
Two carts on a track roll toward each other and collide. Set each cart's mass and starting velocity and choose an elastic, partly elastic or sticky collision, then press Play. The readings show that total momentum stays the same, while kinetic energy is only kept in elastic collisions.
Collision lab
InteractiveType of collision
The math, with your numbers
Momentum before = momentum after, for every type of collision. Kinetic energy is only kept in a bouncy one.
Try this
- →Equal masses, elastic, cart 2 at rest. What happens? (This is the 'Newton's cradle' effect.)
- →Make cart 1 light and cart 2 heavy and at rest. Cart 1 bounces back — but total momentum is still the same!
- →Choose 'Sticky'. Momentum is kept. What about kinetic energy?
Bouncy vs sticky collisions
Momentum is always conserved in a collision. Kinetic energy is a different story:
- Elastic (bouncy): kinetic energy is also kept. Think pool balls, or a Newton's cradle. Very close to this in real life, but never perfect.
- Inelastic (sticky): some kinetic energy turns into heat, sound and bent metal. If the objects stick together, the most possible energy is lost — but momentum is still conserved.
Worked example: a 1,000 kg car at 20 m/s hits a stopped 1,500 kg car; they lock together
Step 1 of 4- 1Total momentum before (the stopped car has zero):
Recoil and rockets
Make a prediction first
Why does a tiny bullet make a heavy rifle kick back?
Think about it, then click to reveal the answer.
Make a prediction first
Why does a tiny bullet make a heavy rifle kick back?
Think about it, then click to reveal the answer.
Before firing, everything is at rest: total momentum zero. After firing, the bullet has momentum forward, so the rifle must have equal momentum backward to keep the total at zero. A 0.01 kg bullet at 400 m/s has 4 kg·m/s. A 4 kg rifle must then move back at 1 m/s. Tiny mass × huge speed = big mass × small speed.
Wrap-up
Key ideas to remember
- Momentum is a vector measured in kg·m/s.
- With no outside forces, total momentum is conserved — in every collision and explosion.
- It follows from Newton's third law: equal and opposite forces for equal times.
- Elastic collisions also keep kinetic energy; sticky ones turn some into heat and sound.
Check your understanding
Sources & further reading
Everything in this lesson agrees with these references. They're all free to read.