How Do You Calculate the Reaction at Point A in a Rotating Rod Problem?

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SUMMARY

The discussion focuses on calculating the reaction force at point A in a rotating rod problem involving a 4-kg uniform rod ABD attached to crank BC. The crank rotates with an angular velocity of 6 rad/s clockwise and an angular acceleration of 15 rad/s² counterclockwise. Participants emphasize the application of Newton's 2nd Law and kinematic equations, specifically the use of cross products in deriving the necessary equations for the problem. The primary challenge identified is the formulation of kinematic equations that yield results in vector components.

PREREQUISITES
  • Understanding of Newton's 2nd Law in the context of rigid body dynamics
  • Familiarity with kinematic equations for rotational motion
  • Knowledge of vector cross products and their application in physics
  • Ability to draw and interpret Free Body Diagrams (FBDs)
NEXT STEPS
  • Study the application of vector cross products in rotational dynamics
  • Learn how to derive kinematic equations for rotating bodies
  • Review examples of Free Body Diagrams in rigid body problems
  • Explore advanced topics in dynamics, such as angular momentum and torque
USEFUL FOR

This discussion is beneficial for students in mechanical engineering, physics enthusiasts, and anyone tackling problems related to dynamics and rotational motion in rigid bodies.

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Homework Statement


The 4-kg uniform rod ABD is attached to the crank BC and is fitted with a small wheel that can roll without friction along a vertical slot. Knowing that at the instant shown crank BC rotates with an angular velocity of 6 rad/s clockwise and an angular acceleration of 15 rad/s^2 counterclockwise, determine the reaction at A.
D1.jpg



Homework Equations


Newton's 2nd Law (Shown in FBDs)
Acceleration and velocity kinematic equations
aa = ab + aa/b
va = vb + vc/b


The Attempt at a Solution


I've drawn FBDs and written out Newton's 2nd Law, but I'm at a loss on how to write the kinematics equations I need. I know that they involve a cross product, but I don't really know how to use them to make an equation that will come out to all i's and j's. Please help!
D2.jpg

D3.jpg


Thank you.
 
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