What is the angular velocity vector of a rotating rod?

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SUMMARY

The angular velocity vector of a rotating rod, which rotates around the line joining its endpoints with a constant angular velocity of 12 rad/s, can be determined using vector cross product principles. The components of the angular velocity vector can be derived from the position vector and the linear velocity vector. The equations v = ω × r and ω = dθ/dt are essential for calculating the angular velocity vector in radians/seconds. The direction of the angular velocity vector is perpendicular to both the linear velocity and the position vector.

PREREQUISITES
  • Understanding of angular velocity and its representation in physics.
  • Familiarity with vector cross product operations.
  • Knowledge of 3D coordinate systems and unit vectors.
  • Basic calculus concepts, particularly derivatives.
NEXT STEPS
  • Study vector cross product applications in rotational dynamics.
  • Learn how to calculate angular momentum using angular velocity vectors.
  • Explore the relationship between linear and angular motion in physics.
  • Investigate the use of unit vectors in three-dimensional space for rotational problems.
USEFUL FOR

Physics students, mechanical engineers, and anyone involved in rotational dynamics or kinematics will benefit from this discussion.

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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