Deriving Angular velocity from Euler's?

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SUMMARY

The discussion centers on deriving angular velocity from Euler's theorem, specifically the relationship between angular displacement and time. The equation w = dθ/dt is identified as a key formula, but participants express uncertainty about the approach to take. The suggestion is made to differentiate Euler's theorem with respect to time to find the connection to angular velocity. Clarity and additional context are requested to facilitate better understanding and responses.

PREREQUISITES
  • Understanding of Euler's theorem in rotational dynamics
  • Familiarity with angular displacement and angular velocity concepts
  • Basic calculus, specifically differentiation
  • Knowledge of the relationship between time and angular motion
NEXT STEPS
  • Study the derivation of angular velocity from Euler's theorem
  • Learn about the application of differentiation in physics
  • Explore examples of angular motion in rotational dynamics
  • Review the relationship between angular displacement and time in various contexts
USEFUL FOR

Students studying physics, particularly those focusing on rotational dynamics, as well as educators seeking to clarify concepts related to angular velocity and Euler's theorem.

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Homework Statement


To go from Euler's theorem :
2k0how.png


to angular velocity as shown:
25qzymv.png


Homework Equations

The Attempt at a Solution



I'm curious how to begin. I can not see the connection! I know w = dtheta/dt, but not sure how to approach this. It has to be more than just differentiate the first equation.
 
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Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
I guess that you should take derivative wrt time of the Euler theorem.
You really should be givinig the full context, my telepathy doesn't work that good nowadays.
 

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