Dynamics: Relative Motion Analysis

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SUMMARY

The discussion focuses on the analysis of relative motion in a dynamics problem involving bar AB with an angular velocity of 6 rad/s. The user calculates the velocity of slider block C using the equation vB = vA + wAB × rB/A, resulting in vB = -0.8485i + 0.8485j. Further calculations yield wBC = -1.96 rad/s and vC = 3.30 m/s, which conflicts with the expected answer of 2.32 m/s. The user seeks clarification on the steps taken to identify the source of the discrepancy in the final velocity of block C.

PREREQUISITES
  • Understanding of angular velocity and its application in dynamics.
  • Familiarity with vector operations in physics.
  • Knowledge of relative motion concepts in mechanics.
  • Proficiency in using equations of motion for rigid bodies.
NEXT STEPS
  • Review the principles of angular velocity and its effects on linear motion.
  • Study vector addition and subtraction in the context of dynamics problems.
  • Learn about the kinematic equations for rigid body motion.
  • Explore common pitfalls in relative motion analysis to avoid calculation errors.
USEFUL FOR

Students studying dynamics, mechanical engineers, and anyone involved in analyzing motion in mechanical systems.

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Homework Statement


[/B]
If bar AB has an angular velocity of 6 rad/s, determine the velocity of the slider block C at the instant shown.

2. Homework Equations

The Attempt at a Solution



vB=vA+wABxrB/A

vA=0

vB= -0.8485i+0.8485j

So then C relative to B:
vC=vB+wBCxrC/B
-vCi= -0.8485i+0.8485j+0.25wBCi+0.433wBCj

After equating i and j terms...
Solved for wBC= -1.96 rad/s

and vC=3.30 m/s

The solution I'm looking at has 2.32 m/s as the answer! I'm not sure what I'm doing wrong!
 

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Please exaplain your reasoning for each step.
 

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