Solving a Moment Equation: Understanding the Relationship with AD

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Homework Help Overview

The discussion revolves around understanding a moment equation involving vectors and their relationships in a mechanical system. The original poster presents a scenario with a dot product equation involving moments and questions how different vectors relate to the resultant moment about a point D.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the implications of the moment equations and the role of various vectors, particularly questioning the necessity of certain terms and the relationships between the forces and moments. There is a focus on understanding why specific vectors are used and how they contribute to the equilibrium condition.

Discussion Status

The conversation is ongoing, with participants seeking clarification on the relationships between the vectors involved in the moment equation. Some guidance has been offered regarding the equilibrium condition and the use of dot products to eliminate terms, but confusion remains about the interpretation of the vectors and their roles in the equation.

Contextual Notes

Participants express uncertainty about the assumptions regarding the directions of forces and moments, particularly concerning the resultant force at point A and its relationship to the vector rDA. There is also a discussion about the order of terms in cross products and their implications for the moment calculations.

  • #31
goldfish9776 said:
because when rE x W and rb xTB are not perpendicular to u , then i can't say that u . (rE x W) and u .(rb xTB ) = 0
Nobody is saying those two dot products are individually zero.
The balance of torques gives us that rE x W + rb x TB + rDA x force_at_A = 0.
We take the dot product of that with u to obtain the equation u.(rE x W) + u.(rb x TB) + u.(rDA x force_at_A) = 0.
We then observe that since u is parallel to rDA the triple product u.(rDA x force_at_A) must be zero.
From that we conclude u.(rE x W) + u.(rb x TB) = 0.
This does not tell us anything about whether u is parallel to any of the four other vectors in that equation.
 

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