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

AI Thread Summary
The discussion centers on calculating the angular momentum of a disk that is both rotating and translating in the xy-plane. The total angular momentum is composed of two parts: the angular momentum from the disk's rotation about its center of mass and the angular momentum due to the translation of the center of mass. The translational speed is provided, but the challenge lies in defining the angular momentum for the translation, as the parallel axis theorem may not apply. The formula for angular momentum is highlighted as L = r x p, where p is the linear momentum and r is the position vector. Understanding these components is crucial for accurately describing the disk's angular momentum in the given coordinate system.
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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.
 
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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)​
 
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
 
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.
 
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