Kinematics using vector analysis

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SUMMARY

The discussion focuses on kinematics using vector analysis, specifically addressing the velocity components of point D in a system involving points A, B, C, and D. The equations provided, Va = Vb + Va/b and Va = Vb + (wab x ra/b), are essential for understanding the relationships between the velocities of these points. The confusion arises from the observation that point D has only an i component of velocity and is not stationary despite being a fixed point in the system. This is clarified by noting that point D moves along a circular path around point C, which influences its velocity vector.

PREREQUISITES
  • Understanding of vector analysis in kinematics
  • Familiarity with rotational motion concepts
  • Knowledge of fixed points in mechanical systems
  • Proficiency in using vector equations for velocity
NEXT STEPS
  • Study the principles of rotational dynamics and fixed points in mechanics
  • Learn about circular motion and tangential velocity
  • Explore vector decomposition in kinematic equations
  • Investigate the role of pivot points in determining motion paths
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and vector analysis, as well as educators seeking to clarify concepts related to rotational motion and fixed points in mechanical systems.

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Homework Statement



4e9b23fa04e6e173e3f349493846bf58.png


Homework Equations



Va = Vb + Va/b
Va = Vb + (wab x ra/b)

The Attempt at a Solution



OK so here is part of my solution:

e86f179e151f512dd5808025f06a411c.png


My velocity for B is correct according to the book. But I'm confused about D. The only problem here is that the velocity of D only has an i component, no j component. How do we know that and why is that? Also, how come the velocity of D isn't zero since it's a fixed point?
 
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Why do you think that D is a fixed point? At the time shown, D is at the end of CD and must move along the circle with center C since CD pivots about C. At the time shown, CD is vertical so the tangent vector to the circle is horizontal at that time.
 

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