## Angular Momentum and Its Conservation – IP

Read this to understand angular momentum, how torque plays a role, and how angular momentum is conserved without torque.

### Angular Momentum and Its Conservation

Why does Earth keep on spinning? What started it spinning to begin with? And how does an ice skater manage to spin faster and faster simply by pulling her arms in? Why does she not have to exert a torque to spin faster? Questions like these have answers based in angular momentum, the rotational analog to linear momentum.

By now the pattern is clear – every rotational phenomenon has a direct translational analog. It seems quite reasonable, then, to define angular momentum $L$ as

$L=I \omega$

This equation is an analog to the definition of linear momentum as $p=mv$. Units for linear momentum are $\mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$ while units for angular momentum are $\mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s}$. As we would expect, an object that has a large moment of inertia $I$, such as Earth, has a very large angular momentum. An object that has a large angular velocity $\omega$, such as a centrifuge, also has a rather large angular momentum.

#### Making Connections

Angular momentum is completely analogous to linear momentum, first presented in Uniform Circular Motion and Gravitation. It has the same implications in terms of carrying rotation forward, and it is conserved when the net external torque is zero. Angular momentum, like linear momentum, is also a property of the atoms and subatomic particles.

Source: Rice University, https://openstax.org/books/college-physics/pages/10-5-angular-momentum-and-its-conservation This work is licensed under a Creative Commons Attribution 4.0 License.