Angular Momentum Projection of a Rigid Body: Formula & Proof

[nebbione]

Hi everyone! Which is the formula and the proof of the projection of the angular momentum of a rigid body along the rotation axis?

I searched on the web and on my mechanics book but cannot find anything... does somebody know this curiosity ?

 

[Nessdude14]

If I'm not mistaken, you're looking for a general formula for the angular momentum of a rigid body?

Angular momentum (L) is given by:
$\displaystyle L=Iω$
ω is angular velocity
and the moment of inertia (I) of a rigid body is given by:
$\displaystyle I = \int^{m}_{0}r^{2}\delta m$
m is the mass of the rigid body, and r is the radius from the axis of rotation

So the angular momentum of a rigid body is:
$\displaystyle L = ω \int^{m}_{0}r^{2}\delta m$

 

[nebbione]

Thank you very much!