What is the angular velocity vector of a rotating rod?

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The rod rotates around its endpoints with a constant angular velocity of 12 rad/s. To determine the angular velocity vector, one must first calculate the components in the x, y, and z directions, followed by the corresponding unit vectors. The direction of the angular velocity vector is perpendicular to both the velocity vector and the position vector. The relevant equations for this calculation include v = ω × r and ω = dθ/dt. Understanding these concepts is crucial for accurately determining the angular velocity vector in radians per second.
Louie3
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The problem has a picture of a rod on a 3 dimensional coordinate system and gives the measurements.

The rod rotates around the line joining each of the two endpoints with a constant angular velocity of 12 rad/s.

The problem has you do things in steps, first finding the components in x, y, and z and then the unit vectors in x, y, and z - both simple to do. Next, it asks for the angular velocity vector of the rod? It wants the answer in radians/seconds.

The closest equations I can find to helping are v= w X r or w= derivative of theta / dt

Thanks for any insight.
 
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Hi Louie, and welcome to PF.

You know the magnitude of the angular velocity. To find the direction, remember that it's perpendicular to both the direction of v and r.
 

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