🎳Momentum

Flying at you at 10 m/s, a ping-pong ball can be caught with a bare hand; a bowling ball calls for a quick exit. Same speed, utterly different punch — the difference is mass. Physicists gave this punch a name: momentum. It is the star of this lesson and the key step from Speed into the world of collisions.

Momentum equals mass times velocity

$p = mv$

The unit is kg·m/s. A 60 kg runner moving at 8 m/s carries 480 kg·m/s of momentum; a 2.7 g ping-pong ball at 10 m/s carries about 0.03 kg·m/s; a 6 kg bowling ball needs only 2 m/s to carry 12 kg·m/s — roughly 400 times the ping-pong ball. And it carries something Speed does not: direction. Momentum is a vector — 5 kg·m/s to the right is +5, to the left is −5. The signs are not decoration; they are part of the ledger.

🏃 Runner A speed6🐢 Runner B speed4

▶ Start

s = v·t → A: 6×0.0 = 0.0 m · B: 4×0.0 = 0.0 m

Move the two sliders and watch A and B race toward the 100 m finish at different speeds. Now imagine masses: make A a loaded truck and B a bicycle. At equal speeds, whose momentum is larger? How much would the light one need to speed up to catch up? Read the velocities, multiply by your imagined masses, and before any collision happens you can see who carries more cargo of motion.

The total never changes in a collision

When two objects collide, momentum passes from one to the other, but the total stays put. The reason lives in the Force lesson: in every collision, the action and reaction forces are equal in size and opposite in direction, so the momentum A loses is exactly the momentum B gains — one entry out, one entry in, the ledger unchanged. The law treats billiards, car crashes and rockets alike: a rocket blasts gas backward, hands it momentum, and carries an equal share of opposite momentum forward.

Stretch the time, shrink the force

Airbags, crumple zones, pulling your hands back to catch a ball, bending your knees on landing — all do the same one thing: extend the time over which momentum drops to zero. Your change in momentum is fixed (from full speed down to 0), and change in momentum = average force × time. Stretch the time a few times over and the average force shrinks by the same factor. A hard hit completes the "braking" in 0.01 seconds — a frightening force; an airbag stretches 0.01 s into 0.1 s, leaving a tenth of the force. What saves you is not the softness of the cushion but the lengthening of the ledger.

Momentum versus kinetic energy, in one breath

Momentum $mv$ is a vector, cares about direction, and is conserved in collisions; kinetic energy $\frac{1}{2}mv^2$ is a scalar, knows only size, and is tied to the capacity to do work (see Energy). The stuck carts above are a ready counterexample: before, kinetic energy was $\frac{1}{2} \times 2 \times 5^2 = 25$ J; after, $\frac{1}{2} \times 5 \times 2^2 = 10$ J. The missing 15 J became heat and sound — kinetic energy is not conserved. One ledger tracks where motion flows; the other prices what motion is worth.

Check yourself

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Quick quiz

↺ Try again

1. 1. The unit of momentum is?

   kg·m/skg·m/s²N

2. 2. A 2 kg cart at 5 m/s hits a stationary 3 kg cart and they stick. Common speed?

   2 m/s3 m/s5 m/s

3. 3. Airbags protect you because they?

   extend the time of momentum change, reducing the forcereduce your change in momentumstore your kinetic energy as potential energy