Mistake Master

Linear Momentum

▶︎  Watch it animatedinteractive step-through · ~3 min · optional

Momentum is mass times velocity, p = m v, measured in kg·m/s, and it points where the velocity points. The product is what counts, not either factor alone: a slow truck can out-momentum a fast baseball. The momentum of a system is the vector sum: pick a positive direction, keep the signs, and add, so equal-and-opposite momenta cancel to zero.

MOMENTUM IS MASS TIMES VELOCITY: p = m·v 8 kg at 2 m/s 2 kg at 5 m/s p = 16 kg·m/s p = 10 kg·m/s the faster cart carries LESS momentum p = m·v · DIRECTION COUNTS: THE SIGNED SUM · SAME p IS NOT SAME K
An 8 kg cart rolling at 2 m/s carries p = (8)(2) = 16 kg·m/s; a 2 kg cart at 5 m/s carries only (2)(5) = 10. Momentum is the product of mass and velocity, so the faster cart can lose: neither the speed nor the mass ranks it alone.
Momentum Explorer · Open the sandbox →

Most of the lost points here come from forgetting that momentum is both a product and a vector. Rank it by speed or mass alone and the slow, heavy object surprises you — p = m v is a product, and v = p/m means equal momenta force the lighter object to move faster. Pile up magnitudes and two carts at +12 and −12 kg·m/s look like 24 instead of the zero they sum to. And momentum and kinetic energy keep different books: K = p²/2m, so at equal momenta the lighter, faster object carries more energy, and doubling the speed doubles p but quadruples K.

The work

3 ways in · any order
Lesson
Linear Momentum

How momentum is the product p = m v in kg·m/s, so neither the mass nor the speed ranks it alone and a slow truck can out-momentum a fast ball; why momentum is a vector pointing along the velocity, so the momentum of a system is the signed sum and equal-and-opposite momenta cancel to zero; and how momentum and kinetic energy keep different books on the same motion, with K = p²/2m giving the lighter object more energy at equal momenta. Worked examples handle product comparisons, signed system sums, and same-p-different-K contrasts. Closes with a ten-scenario skill check on all three traps.

Skill check · 10 scenarios
Diagnostic
10-item topic check

Ten items on the main mistakes for Topic 4.1: ranking momentum by speed or mass alone instead of the product p = m v, adding momentum magnitudes when the directions oppose, and reading equal momenta as equal kinetic energies. Take it cold to find what is shaky, or after the lesson to confirm it is not.

Not started · 10 items · ~15 min
Targeted Practice
Drill a single misconception

Pick one of the mistakes you've missed and drill it on its own. The round is adaptive: two correct in a row clears it and you move on.

Take the diagnostic to identify your misconceptions