Can Zero Torque Occur if Angular Momentum and Velocity Vectors Aren't Parallel?

[KBriggs]

Hey all,

I have a physics problem here and I have come across an odd scenario, I wonder if you could tell me if this means that I have the wrong answer.

I have an ideal bar rotating about an arbitrary axis. The angular velocity vector \omega is NOT colinear with the angular momentum vector. However, \omega is constant, so when I try to find the torque on the bar by using hte time dervitive of the angular momentum vector, I get 0.

My question is this: is it possible for there to be 0 torque on the bar if the angular momentum and angular velocity vectors are not parallel? Because I was under the impression that the only time when they were not parallel was when there was some applied torque, but I have done this problem using three different methods now, all with the same result.

 

[bcrowell]

Hi, KBriggs,

In general, the relationship between L and w for a rigidly rotating body is not L=Iw, where I is a scalar; I has to be a 3x3 matrix. Even for an isolated body with no torques acting on it, it is not necessary for L and w to be collinear. Here is a discussion of this kind of thing that might help: http://www.lightandmatter.com/html_books/0sn/ch04/ch04.html#Section4.3

Ben

 

[KBriggs]

Thanks

So getting 0 torque doesn't mean I went wrong somewhere.

I know about the matrix notation, but I am new to this stuff so I am getting a little lost in the definitions.