Angular Momentum
Learning Objectives
1. Understand what angular momentum is and how it is related to linear momentum.
2. Be able to calculate the angular momentum for a rotating object.
3. Be able to calculate the angular momentum for an object with linear motion.
4. Be able to use the conservation of angular momentum to calculate and predict changes to angular velocity and rotational inertia.
Key Terms
| Definition | SI Units | Symbol and Equation | |
| Angular Momentum | Angular Momentum can be thought of as a measure of how hard it would be to stop a rotating object. | \(kg\frac{m^2}{s}\) | \(L=I\omega \\ L=mvr\) |
| Conservation of Angular Momentum | Angular Momentum is conserved for isolated systems independently from linear momentum. | \(\Sigma L_i=\Sigma L_f\) |
Angular Momentum For Rotating Objects
Angular momentum has two major equations that we need to know. The fist is rotational inertia times angular velocity or \(L=I\omega \) . This is used for objects that are rotating. It is analogous to translational velocity’s \(p=mv\) equation.
\(L=I\omega\)
L = angular momentum
I = rotational inertia
\(\omega \) = angular momentum
Angular Momentum For Nonrotating Objects
An object moving linearly can also have an angular momentum depending on what is measured in reference to.
\(L=mvr\)
L = angular momentum
m = mass
r = the distance from where linear moving object strikes an object, and that objects point of rotation
Conservation on Angular Momentum
If there is no external torque on a system then the angular momentum of that system will be conserved.
\(\Sigma L_i = \Sigma L_f\)
\(\)\Sigma L_i /latex] = sum of the initial angular momentum
latex]\Sigma L_f/latex] = sum of the final angular momentum