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# Angular momentum conservation

Just like we have a linear momentum conservation law telling us how the sum of all momentum never changes (the same before and after any impact), $\sum \vec p_\text{before}= \sum \vec p_\text{after}$, we also happen to have the equivalent angular momentum conservation law:[1]

$$\sum \vec L_\text{before}= \sum \vec L_\text{after}$$

This law explains how the ballerina spins faster by pulling her arms in, and how the gymnast can spin fast enough to make a backflip by pulling arms and legs in.

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