# Rotating Disk translation

1. Nov 11, 2004

### 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)

2. Nov 11, 2004

### Staff: Mentor

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)​

3. Nov 11, 2004

### 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

4. Nov 11, 2004

### Staff: Mentor

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.