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.
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
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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.
Diagnostic
10-item topic check
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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.
Targeted Practice
Drill a single misconception
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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.