Solving Moment and Cross-Product Problems with R

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SUMMARY

This discussion addresses the correct application of the moment and cross-product in statics problems, specifically focusing on the calculation of moments about a point using the formula 𝑀 = 𝑟 × 𝐹. The vector 𝑟 must be defined as the vector from the point of interest to the point of force application. The right-hand rule is recommended for verifying the direction of the resulting moment vector. Misinterpretations regarding the direction of vectors and the forces involved are common among students, as highlighted by the original poster, Astrit Imeri.

PREREQUISITES
  • Understanding of vector mathematics
  • Familiarity with the right-hand rule in vector cross-products
  • Basic knowledge of statics and forces
  • Ability to interpret vector diagrams
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  • Study the application of the right-hand rule in vector cross-products
  • Learn about moment calculations in statics using examples
  • Explore vector representation in 3D space for statics problems
  • Review common mistakes in calculating moments and forces in engineering statics
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Engineering students, particularly those studying statics, mechanical engineers, and anyone involved in solving moment and force problems in physics and engineering contexts.

bigu01
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Dear friends, and science lovers,

I am doing some statics problems with moment( cross-product).And I've been having some problems solving them.I am getting the result but in opposite sign. I mean I know we have to do R x F , but looks like I am taking R in the wrong a. For example we have to determine the moment of a force at A about point P.Should I find the vector from A to P or from P to A.Same thing in the couple forces, where we have to find the vector R between the couple forces and to multiply with one of the forces.I am getting that vector but I don't know with which force to multiply.If you can help me clear this thing on my mind I would be really thankfull.

Kind regards,

Astrit Imeri

ME student
 
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Moments are taken about a point. In the expression ##\vec{M} = \vec{r} \times \vec{F}##, the vector ##\vec{r}## is from the point you are taking moments about to the point of application of the force ##\vec{F}##. The following graphics (borrowed from Wiki) should illustrate this:
Torque_animation.gif

512px-Torque%2C_position%2C_and_force.svg.png


You can check your results using the right hand rule (assuming you're using a right-handed coordinate system!).
 

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