## anonymous one year ago can anyone help me understand the angular momentum questions

1. rvc

The formula for angular momentum (L) is $$\Large\rm \color{red}L=\color{darkblue}{I~\omega }$$ Where I : Moment of Inertia $$\omega$$ : Angular velocity The SI unit of A.M (L) = $$\Large\sf\frac{ Kg~ m^2}{s}$$

2. anonymous

excuse but particularly i can give some example like their is a bat a ball ht the base of bat now the angular momentum of the bat

3. anonymous

@rvc

4. rvc

?

5. rvc

@Michele_Laino :)

6. Michele_Laino

an example og the angular momentum can be this: please think about a metallic rod which is oscillating around to its one end, like in the drawing below: |dw:1435074583207:dw|

7. Michele_Laino

of course our rod is oscillating as effect of gravity on it. Now The Moment of Inertia of our rod, with respect to it center of oscillation, is: $\Large I = \frac{1}{3}M{L^2}$ where M is the mass of our rod Now the moment of the external force which is acting on our rod, namely its weight, is: $\Large {\mathbf{M}}_{\mathbf{O}}^{\mathbf{E}} = - \frac{{MgL}}{2}\sin \theta {\mathbf{\hat z}}$ |dw:1435075148006:dw|

8. Michele_Laino

|dw:1435075254161:dw|

9. Michele_Laino

so, applying the second cardinal equation of Mechanics, we can write: $\Large \begin{gathered} \frac{d}{{dt}}\left( {I\omega } \right) = - \frac{{MgL}}{2}\sin \theta \hfill \\ \hfill \\ I\dot \omega = - \frac{{MgL}}{2}\sin \theta \hfill \\ \hfill \\ I\ddot \theta = - \frac{{MgL}}{2}\sin \theta \hfill \\ \hfill \\ \ddot \theta + \frac{{MgL}}{{2I}}\sin \theta = 0 \hfill \\ \end{gathered}$

10. Michele_Laino

substituting I=(1/3) M*L^2, we get: $\Large \ddot \theta + \frac{{3g}}{{2L}}\sin \theta = 0$ finally, considering the "little oscillation" case, namely: $\Large \sin \theta \cong \theta$ we get: $\Large \ddot \theta + \frac{{3g}}{{2L}}\theta = 0$ That above, is a simple application of angular momentum of a rigid body Can you compute the period of little oscillation, starting from the last equation?