Mistake Master

Linear Momentum

Momentum is mass times velocity: $\vec p = m\vec v$. Velocity has direction, so momentum does too. A minus sign on $p$ means direction along your chosen axis, not a smaller number and not a stopped object. To find the momentum of a two-object system, add the momenta as vectors with signs, not as speeds. Most traps in this topic come from forgetting that $\vec p$ is a vector.

Momentum diagram: a moving cart with its velocity and momentum vectors A 2 kilogram cart on a horizontal track moves to the right at 3 meters per second. A blue velocity arrow above the cart points right. A pink momentum arrow below the cart points right and is twice as long, because momentum equals mass times velocity, giving 6 kilogram meters per second. VELOCITY ROW MOMENTUM ROW m v = 3 m/s p = 6 kg·m/s p = mv Same direction as velocity. ONE CART · VELOCITY EAST · MOMENTUM EAST
A 2 kg cart moves east at 3 m/s. The blue arrow shows $\vec v$; the pink arrow shows $\vec p = m\vec v$. Both point the same way because mass is positive. The pink arrow is twice as long because multiplying by $m = 2$ kg doubles the size. Flip the velocity sign and both arrows flip with it. The pink arrow being longer than the blue one means $|\vec p|$ is bigger, not that the cart is moving faster.
Momentum Lab · Open the sandbox →

Most traps cluster around the vector nature of $\vec p$. Some students drop the direction and give momentum as a single number. Others read a negative $p$ as smaller magnitude or as a stopped object, when it just means direction along an axis. Another trap: ranking momenta by mass alone or by speed alone, when you need both. The lesson walks all of these.

The work

3 ways in · any order
Lesson
Linear Momentum

Start with $\vec p = m\vec v$ for a single object, then build to a two-object system. Covers what direction means on a momentum vector, why a heavy slow object can carry the same momentum as a light fast one, and how to add momenta when their directions disagree. Ends with a ten-scenario applet on one- and two-object setups.

Skill check · 10 scenarios
Diagnostic
10-item topic check

Ten questions on the vector character of momentum, how a sign tells direction (not size), why both mass and speed matter for $|\vec p|$, and how system momentum adds as vectors. Each distractor maps to a specific misconception so the targeted-practice round can drill exactly what you missed.

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

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

Take the diagnostic to identify your misconceptions