183_notes:torquediagram

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183_notes:torquediagram [2016/03/14 16:39] – [A balanced situation] caballero183_notes:torquediagram [2021/05/31 16:37] – [Torque Diagrams] stumptyl
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 ===== Torque Diagrams ===== ===== Torque Diagrams =====
  
-To investigate situations in static equilibrium more throughly, you can make use of an extended free-body diagram that shows the "point of application" of the force. That is, you won't crush the system down to a [[183_notes:point_particle|point particle]] and [[183_notes:freebodydiagrams|treat all the forces as acting at the center of mass]]. Instead, you will consider where the forces are applied because doing so will be necessary for determining [[183_notes:torque|the torque]] (or, rather, exploiting the fact that the sum of all the torques about any rotation point is zero). +To investigate situations in static equilibrium more thoroughly, you can make use of an extended free-body diagram that shows the "point of application" of the force. That is, you won't crush the system down to a [[183_notes:point_particle|point particle]] and [[183_notes:freebodydiagrams|treat all the forces as acting at the center of mass]]. Instead, you will consider where the forces are applied because doing so will be necessary for determining [[183_notes:torque|the torque]] (or, rather, exploiting the fact that the sum of all the torques about any rotation point is zero). 
  
-In these notes, you will read through an example where we will apply the ideas that the net force and net torque are zero and make use of the torque diagram to construct a mathematical representation of the problem.+**In these notes, you will read through an example where we will apply the ideas that the net force and net torque are zero and make use of the torque diagram to construct a mathematical representation of the problem.**
  
 ==== Lecture Video ==== ==== Lecture Video ====
  
-Forthcoming...+{{youtube>rQUWKAKlc2U?large}}
  
 ==== A balanced situation ==== ==== A balanced situation ====
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 == Let's use Location 4 (Pivot location) == == Let's use Location 4 (Pivot location) ==
  
-In this case the pivot force is not included in the analysis and the only unknown is mass 2. We can perform a torque analysis around this location noticing that the weight of the plank and mass 1 will contribute to an out-of-the-page torque (positive torque) while mass 2 will contribute to an into-the-page torque (negative torque). [[183_notes:torque|Torque directions are defined by the right-hand rule]]. Our analysis of the net torque gives,+In this case the pivot force is not included in the analysis and the only unknown is mass 1. We can perform a torque analysis around this location noticing that the weight of the plank and mass 1 will contribute to an out-of-the-page torque (positive torque) while mass 2 will contribute to an into-the-page torque (negative torque). [[183_notes:torque|Torque directions are defined by the right-hand rule]]. Our analysis of the net torque gives,
  
 $$\vec{\tau}_{net} = 0 \longrightarrow \tau_{net,z} = 0$$ $$\vec{\tau}_{net} = 0 \longrightarrow \tau_{net,z} = 0$$
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 Here, you obtain $m_1$ without any additional work. So, to summarize, every pivot location can be used -- it's just that some make the work a little easier than others. You would not have been wrong to choose any of the other locations. Here, you obtain $m_1$ without any additional work. So, to summarize, every pivot location can be used -- it's just that some make the work a little easier than others. You would not have been wrong to choose any of the other locations.
  
 +===== Examples =====
 + 
 +  * [[:183_notes:examples:statictorque|Calculating Static Torque]]
  • 183_notes/torquediagram.txt
  • Last modified: 2021/11/15 17:25
  • by pwirving