>[!summary] Angular momentum is used to describe how much force an object has when rotating. This type of momentum is not always conserved, nor is it an intrinsic property > An object can be moving linearly but still have angular momentum > > **Key equations:** > Angular momentum: $\vec{L} = \vec{r} \times \vec{p}$ > Special case where a body is rotating symmetrically: $\vec{L} = I\omega$ >[!info]+ Read Time **⏱ 2 mins** # Definition Angular momentum is used to describe how much "hard" it is to give an object rotation. It's similar to [[Linear Momentum|linear momentum]] in that it **can be** a conversed quantity, but is **not an intrinsic property, nor is it always conserved.** It depends on your reference frame. >[!warning] Angular momentum does not **ALWAYS** mean spinning in a circle Most situations of angular momentum involve an object spinning in a circle. You can also have angular momentum if an object has [[Linear Momentum|linear momentum]] and has a sideways component (not moving straight) Mathematically, angular momentum is the cross product between [[Linear Momentum|linear momentum]] and the r displacement [[Scalar & Vectors|vector]]. The r [[Displacement|displacement]] vector is the reference point, which can be arbitrarily chosen. Meaning certain reference frames will not have angular momentum. $\vec{L} = \vec{r} \times \vec{p}$ > [!note] Angular Momentum Diagram ![[ang_4.png]] [^2] Example of angular momentum of a point like mass # Special Case For Rotating Rigid Bodies >[!warning] Assumption For this special case, assume the following: > - The object is rotating symmetrically. > - The origin at in the middle of the rotating object > - The rotation can be described from [[Rotational Kinematics|rotational kinematics]] $v = \omega \times r$ > > Use the diagram below as a visual aid of a rotating body rotating symmetrically. ![[am_1.png]] $\begin{array}{c} L = r \times p \\ L = r \times (mv) \\ L = mr \times (\omega \times r) \\ L = mr^2 \omega \\ L = I\omega \\ \end{array}$