How Can Angular Momentum Be Described for a Rotating and Translating Disk?

[Zenshin]

Hello. Could anyone give me a hint in this problem? There´s a disk (mass m ad radius a) rotating with angular velocity w0 (only rotation). If this disk is translating in xy plane, parallel with the y-axis with its center aligned at x0, how ca I describe the angular momentum L (t), and it´s components, Lx Ly and Lz (with respect with the xyz coordinate system). Any ideas? (I think it´ll have variational Lx and Ly and a fixed Lz)

Thanks in advance.

 

[Doc Al]

I assume you are given the translational speed?

In any case, the total angular momentum is the sum of:

(1) angular momentum of the disk due to its rotation about the center of mass
(2) angular momentum of the disk due to the translation of its center of mass (consider the mass concentrated at the center of mass)​

 

[Zenshin]

Oh yes, I forgot, the translation velocity is also given (v). But, since the disc translates in a linear way (it only rotates about itself), how can I define a angular momentum of it's translation? I think the parallel axis theorem (Steiner) doesn't apply here.

Thanks

 

[Doc Al]

The angular momentum (with respect to the origin) of a moving particle is defined as $\vec{L} = \vec{r}\times\vec{p}$, where $\vec{p}$ is the linear momentum and $\vec{r}$ is the position vector.