Mistake Master

Systems and Center of Mass

A system is a collection of objects you choose to analyze together; everything else is the environment. Once the boundary is drawn, forces split into internal (between pieces inside the system) and external (from the environment), and the system's overall motion can be tracked through one point, the center of mass, weighted by where the mass actually sits.

midpoint −3 0 +3 x [m] 4 kg 2 kg COM x = −1 m
The geometric midpoint sits at x = 0, but the center of mass lands at x = −1 m, pulled toward the heavier 4 kg mass. Equal spacing about the origin does not mean equal weighting.
Balance the Beam · Open the sandbox →

The trap most students fall into is averaging the positions and skipping the mass weighting, which lands the COM at the geometric midpoint no matter how lopsided the masses are. The second trap is treating internal pushes between pieces of the system as if they could move the system as a whole; only external forces do that.

The work

3 ways in · any order
Lesson
Systems and Center of Mass

Pick the system, sort internal from external forces, and compute the mass-weighted center of mass. Locks in with a ten-scenario applet that asks you to predict where the COM lands before the math runs.

Skill check · 10 scenarios
Diagnostic
10-item topic check

Ten items covering system choice, the internal vs external distinction, and where the center of mass actually sits when masses or spacings are unequal.

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