Mistake Master

Conservation of Angular Momentum

A skater pulls her arms in and spins faster. A blob drops onto a spinning disk and the whole thing reorganizes. A wheel slows when its axle drags. One rule covers all three: pick a system, check whether anything outside applies a torque, and if nothing does, the system's total angular momentum stays the same. The traps are which torques count as external, and what does and does not change when $I$ shifts.

Before arms out slow L (kg·m²/s) K (J) 8 8 L stays no external torque After arms in fast L (kg·m²/s) K (J) 8 32
Fig. 6.4.1 Skater pull-in. $I$ shrinks, $\omega$ rises so the product $L = I\omega$ stays the same. The yellow $K_{rot}$ bar grows because her muscles did work pulling the arms inward. $L$ conservation is not energy conservation.
Conservation Lab · Open the sandbox →

Three traps drive the misses. First, treating $\omega$ as the conserved quantity instead of $L = I\omega$, so a change in $I$ gets ignored. Second, assuming any rotating object has $L$ conserved, when an axle-friction torque is bleeding it away. Third, missing that external depends on where you draw the system boundary.

The work

3 ways in · any order
Lesson
Conservation of Angular Momentum

The rule, what "system" means, and how to apply $L_f = L_i$. Worked examples for the two classic setups: the vertical mass-drop (the falling mass starts with $L = 0$ about the spin axis) and the skater pull-in ($I$ shrinks, $\omega$ rises). A ten-scenario applet drills the criterion, the $I$-versus-$\omega$ rescaling, signed sums for opposite-spin couplings, and the $L$-versus-$K_{rot}$ split. Mix of conceptual, algebraic, and numeric items.

Skill check · 10 scenarios
Diagnostic
10-item topic check

Ten items probing the conservation criterion, the $L = I\omega$ rescaling, signed sums for multi-body systems, the vertical-drop boundary case, and the split between $L$ and $K_{rot}$. Each missed item flags the misconception that fired, so the drill knows where to send you next.

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