- #1

Dustgil

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## Homework Statement

A thin uniform rod of length l and mass m is constrained to rotate with constant angular velocity omega about an axis passing through the center O of the rod and making an angle alpha with the rod.

a) Show the the angular momentum L about O is perpendicular to the rod and is of magnitude

[tex] \frac {ml^{2} \omega} {12} sin(\alpha)[/tex]

b) Show that the torque vector N is perpendicular to the rod and to L and is of magnitude

[tex]\frac {ml^{2} \omega^{2}} {12} sin(\alpha) cos(\alpha)[/tex]

## Homework Equations

I think these two:

[tex]L = I_{x} \omega_{x} i + I_{y} \omega {y} j + I_{z} \omega {z} k[/tex]

[tex]\frac {dL} {dt} = N[/tex]

## The Attempt at a Solution

This chapter has me really confused at the moment. Where do I define the axes? I tried assigning the k axis to be along the length of the rod. then L should be perpendicular to the rod because the moment of inertia is zero in the k direction (because every point on the rod is at zero distance from that axis). The moment of inertia about the i and j axes is

[tex] I = \frac {ml^{2}} {12}[/tex]

This is where i get lost. I'm not sure what the component of omega is in the x and y directions. Soooo not sure if I'm doing this right.