Mistake Master

Conservation of Angular Momentum

▶︎  Watch it animatedinteractive step-through · ~3 min · optional

When 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.

CONSERVATION OF ANGULAR MOMENTUM I₁ω₁ = I₂ω₂ No external torque keeps the product I ω fixed. ω₁ L I₁ large · ω₁ small pull in I ↓ ω ↑ ω₂ L I₂ small · ω₂ large K = ½ I ω² rises kinetic energy not conserved L = I ω holds angular momentum conserved conserved : L = I ω not conserved : K = ½ I ω²
With no external torque, L = I ω is conserved. Pulling the masses inward lowers the moment of inertia, so the angular speed rises to keep the product fixed. The angular momentum vector (out of the page) is unchanged; the kinetic energy, by contrast, is not conserved: it rises because work is done pulling in.
Angular momentum stays; the spin rate does not · Open the sandbox →

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

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.

Skill check · 10 scenarios
Diagnostic
10-item topic check

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.

Not started · 10 items · ~15 min
Targeted Practice
Drill a single misconception

Pick one mistake you keep making and drill it on its own. Two correct in a row clears it and you move on.

Take the diagnostic to identify your misconceptions