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47.2: Conservation of Angular Momentum

Last updated

Aug 8, 2024
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- 47.1: Introduction to Angular Momentum
- 48: Conservation Laws

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Angular momentum, like linear momentum, is a conserved vector quantity: in a closed system (in which no angular momentum enters or leaves the system), the total angular momentum is constant. Since angular momentum is a vector, this means that the following are all conserved:

The vector angular momentum, $\mathbf{L}$ ;
The magnitude of the angular momentum, $L$ ; and
Each component of the angular momentum, $L_{x}, L_{y}$ , and $L_{z}$ .

In a closed system, angular momentum may be transferred from one body to another, but the total angular momentum - the sum of the angular momenta of all bodies in the system — will remain constant.

As a common example, conservation of angular momentum is illustrated by the spinning of a figure skater. As she's doing a spin, a figure skater will rotate about a vertical axis. As she brings her arms in closer to her body, the figure skater decreases her moment of inertia. By Eq. 47.1.3, if the moment of inertia $I$ decreases, then the angular velocity $\omega$ must increase in order to keep the angular momentum $L$ constant.

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