Angular velocity -velocity conversion

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SUMMARY

The discussion centers on the conversion between angular velocity and linear velocity, specifically addressing the formula v = rw and its validity. The participant seeks clarification on calculating angular velocity (ω) using the expression ω = (r × v) / r², where v is the linear velocity and r is the radius from the reference point. The conversation emphasizes the importance of understanding the relationship between linear and angular motion in physics.

PREREQUISITES
  • Understanding of basic physics concepts, particularly linear and angular motion.
  • Familiarity with the relationship between linear velocity and angular velocity.
  • Knowledge of vector cross product operations in physics.
  • Basic trigonometry, specifically sine functions related to angles.
NEXT STEPS
  • Study the derivation and applications of the formula v = rw in rotational dynamics.
  • Learn about the vector cross product and its role in calculating angular momentum.
  • Explore the implications of angular velocity in circular motion scenarios.
  • Investigate the relationship between angular velocity and centripetal acceleration.
USEFUL FOR

Physics students, educators, and professionals in engineering or mechanics who need to understand the conversion between angular and linear velocities for practical applications.

torquemaster
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angular velocity --velocity conversion

I am a bit confused about angular velocity --velocity conversion . I thought of a problem in my mind which is as follows

There is a particle moving with velocity v in certain direction as shown in the figure.and I want to calculate the angular velocity wrt the reference point. is it vsin@/r.

and also is v=rw valid in any condition for angular velocity --velocity conversion . please explain the validity of this formulae I didnt understand what this formulae( v=rw ) actually means
 

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You can use the expression ω=(rxv)/r^2.
 

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