Section 5.20 Angular Momentum
There is one last translational quantity for which you can write an angular analogue: momentum. This angular analogue is known as angular momentum.
Definition 5.20.1. Angular Momentum for a Rigid Object.
The angular momentum of a rigid object about a given axis is the product of the object’s moment of inertia and angular velocity about that axis:
\begin{equation*}
\vec{L} = I\vec{\omega}
\end{equation*}
Interestingly, it is not only rotating rigid objects that have angular momentum. Any object with translational momentum also has angular momentum, as long as it is moving perpendicular to some axis!
Definition 5.20.2. Angular Momentum for a Point Particle.
The angular momentum of a point particle about a given axis is the cross product between the object’s position and its translational momentum:
\begin{equation*}
\vec{L} = \vec{r} \times \vec{p}
\end{equation*}
One especially critical feature of angular momentum (along with many other angular quantities) for a point particle is that it depends on your choice of axis. Interestingly, the angular momentum of a rotating rigid object does not depend on your choice of axis (because it is actually rotating around a fixed axis!).
Exercises Activities
1. Summarize What You Learned - Angular Momentum.
Write a 1-2 sentence description of what the definitions of angular momentum say in words. How can you tell which definition to use?
2. Sensemaking: Units.
What are the units of angular momentum? How do they compare to the units of translational momentum?
3. Explanation: Adding Momentum?
Suppose a friend of yours wrote down the following equation for something they call the "total momentum": \(\vec{p} + \vec{L}\text{.}\) How could you convince your friend that this equation is incorrect, and that there cannot be such a thing as total momentum.
Hint.Look at the units you found for the angular momentum.
