Mistake Master

Conservation of Linear Momentum

Pick any two objects, draw a boundary around them, and call the inside "the system." If no net external force acts on that system, its total linear momentum is the same before and after. The pieces can stick, bounce, or fly apart inside, and $\vec p_\text{system}$ does not change. The only catch is the boundary: move it, and a force that was internal can become external. Then conservation fails.

Fig. 4.3.1 The system (dashed purple boundary) holds two carts. Before the collision only cart 1 moves; after, the carts move together at a smaller speed. The system's total-momentum bar matches in both rows. The contact force is internal, so it cannot change $\vec p_\text{system}$.
System Momentum Lab · Open the sandbox →

Three traps. Students write $\vec p_i = \vec p_f$ across a ball's full flight under gravity, forgetting that gravity is external to the ball alone. They treat a cart-cart contact force as if it were external to the two-cart system, and conclude momentum cannot be conserved. They go from "equal-and-opposite impulses" (true, by Newton's third law) to "equal velocity changes," which is only true when the masses match. The lesson and the diagnostic drill all three.

The work

3 ways in · any order
Lesson
Conservation of Linear Momentum

Build the conservation principle from the boundary out. The lesson asks where the boundary goes, sorts internal versus external forces, and walks through the three flavors of conservation problem: collisions, explosions, and recoils. Closes with a ten-scenario applet that drills the headline traps, including the ball-thrown-up trap and the bullet-and-rifle trap.

Skill check · 10 scenarios
Diagnostic
10-item topic check

Ten problems, mixed flavors. Includes a 2D sticky collision, a head-on collision with signed velocities, an explosion from rest, a ball thrown up and caught, a cannon recoil, and the truck-and-car collision where contact dominates friction. Each wrong answer maps to a named misconception; the targeted-practice card opens after you finish.

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