Conservation of Angular Momentum
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalWhen the net external torque on a system is zero, its angular momentum is conserved: L = I ω stays fixed. If the mass redistributes so the moment of inertia changes, the angular speed changes the opposite way to keep the product constant: I₁ ω₁ = I₂ ω₂.
Here the algebra is easy; the conditions are what bite. Conserving L is not conserving ω or the kinetic energy: when a skater pulls in, ω and K both climb while L holds. Conservation needs zero net external torque, so a brake or a dragging foot breaks it. And L is a vector, so counter-rotating bodies carry opposite signs that can cancel.
Conservation of angular momentum
3 ways in · any order
Lesson
Conservation of Angular Momentum
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Conservation of angular momentum: with no external torque, I1 omega1 = I2 omega2. Covers why a smaller moment of inertia means a faster spin, why kinetic energy is not conserved when a skater pulls in, when an external torque breaks conservation, and how the signs work for counter-rotating bodies. Closes with a ten-scenario skill check.
Diagnostic
10-item topic check
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Ten items across the four Topic 6.4 mistakes: holding the angular speed fixed when the moment of inertia changes, assuming kinetic energy is conserved along with angular momentum, applying conservation when a net external torque acts, and dropping the sign or direction of the angular momentum vector. Take it cold to see what still trips you up, or after the lesson to confirm it doesn't.
Targeted Practice
Drill a single misconception
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Pick one mistake you keep making and drill it on its own. Two correct in a row clears it and you move on.