Finding Angular and Linear Velocity in a Sliding Bar System

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SUMMARY

The discussion focuses on calculating the angular velocity and linear velocity of a slender bar system with fixed ends. The established results are an angular velocity (ω) of 1.394 rad/s and a linear velocity (VA) of 0.408 m/s directed downwards. The key equations utilized include Va=Vb + Va/b and V=rw, alongside the law of sines. The challenge lies in correctly applying these equations to find the velocities based on the given angles and conditions.

PREREQUISITES
  • Understanding of angular velocity and linear velocity concepts
  • Familiarity with the law of sines in trigonometry
  • Knowledge of rotational motion equations, specifically V=rw
  • Basic principles of rigid body dynamics
NEXT STEPS
  • Study the application of the law of sines in rigid body motion problems
  • Learn about the relationship between linear and angular velocities in mechanical systems
  • Explore examples of velocity components in constrained motion scenarios
  • Investigate advanced topics in dynamics, such as the inertia of rigid bodies
USEFUL FOR

Students in mechanical engineering, physics enthusiasts, and professionals dealing with dynamics and kinematics of rigid bodies will benefit from this discussion.

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Homework Statement



The ends of the slender bar remain in contact with their respective support surfaces. If end has a velocity in the direction shown, determine the angular velocity of the bar and the velocity of end.

Answers:
ω=1.394 rad/s VA=0.408 m/s down

attachment.php?attachmentid=57030&stc=1&d=1364086950.png

Homework Equations



Va=Vb +Va/b
law of sines
V=rw

The Attempt at a Solution



I've tried using the angles given to use the law of sines and the velocity given into find Va/b or Va and then using V=rω to find the angular velocity but have had no luck. Any help would be appreciated
 

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Hint: Each end of the rod has a component of it's velocity in the direction of the rod. These components must be the same or the length of the rod would change.
 

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