Why Does Moment Act Perpendicular to Force?

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Discussion Overview

The discussion revolves around the concept of moment in relation to a force applied to a cantilever beam. Participants explore why the moment is considered to act perpendicular to the applied force, referencing diagrams and calculations related to bending moments.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant presents a diagram of a cantilever beam with a downward force and questions why the moment acts perpendicular to this force.
  • Another participant suggests considering the vector cross product r x F and provides a mnemonic related to a right-hand coordinate system.
  • A different participant challenges the relevance of the provided diagram, implying it may not adequately illustrate the concept of moment and questioning its intended meaning.
  • A later reply calculates the bending moment at the fixed support due to the applied force, stating that the moment is a twisting force about an axis that is perpendicular to both the applied force and the moment arm.
  • There is a note on the proper representation of moment vectors in diagrams, indicating that straight moment vectors should have a double arrowhead, while those normal to the page should be drawn with a curved symbol and a single arrowhead.

Areas of Agreement / Disagreement

Participants express differing views on the relevance and clarity of the diagrams presented, and there is no consensus on the explanation of why the moment acts perpendicular to the force.

Contextual Notes

Some assumptions about the definitions of moment and force may not be explicitly stated, and the discussion includes unresolved questions regarding the interpretation of the diagrams.

paddles069
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Hi all, please view the file I have attached which contains the diagram of the question. The picture is a cross section of a cantilever beam in which a force is applied downwards at the tip of the beam, as shown in the upper diagram. The solutions then conclude that the moment is acting in a perpendicular direction to the force, as shown in the bottom diagram. Why is this?

Thanks!
 

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Think about what the vector r x F means in terms of its components.

As a memory aid: i j k | i j which means: i X j = k; j x k = i; k x i = j
got a right-hand coordinate system.
 
That moment has nothing to do with that force. That looks like half of an illustration to draw stress squares and Mohr's circles. Where did you get that? What is it supposed to mean?
 
paddles069 said:
The solutions then conclude that the moment is acting in a perpendicular direction to the force, as shown in the bottom diagram. Why is this?
paddles069: The 10 kN force is applied at the cantilever tip, 10 m from the fixed support. Therefore, the bending moment at the fixed support is M = (10 m)*(10 kN) = 100 000 N*m, which is a twisting force about (around) an axis perpendicular to the applied force, and perpendicular to the moment arm.

By the way, straight moment vectors should always be drawn with a double arrowhead (not a single arrowhead). However, if the moment vector is normal to the page, then the moment symbol should be drawn curved, with a single arrowhead.
 

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