1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Static Equilibrium Conditions

  1. Aug 25, 2012 #1
    1. The problem statement, all variables and given/known data
    we know that, every force systems can be generally replaced by a resultant force(R) and a couple(M) at a point O and the position of point O is optional.
    but magnitude and direction of M is dependent to this point while magnitude and direction of R is independent.
    In static equilibrium R and M are zero at an optional point O. now this is the question:
    While M is zero at an optional point O, why should we conclude that M would be zero at every point chosen( infinite in number of points)...please pay attention that " magnitude and direction of M is dependent to the point chosen"....
    I mean we don't know the object is in static equilibrium or not and we want to determine it... why do we consider that if M is zero about a point, it means that it is zero about any point? is there a theorem about this? is it provable?


    2. Relevant equations
    Static equilibrium conditions.



    3. The attempt at a solution
    In fact I have no answer to the question...it's not a numerical problem.
     
  2. jcsd
  3. Aug 25, 2012 #2
    Let us suppose net torque (couple M)

    M = r1 X F1 +r2 X F2 ......
    where ref. point is O

    Take another ref point O'
    then

    M'=(r1 + r) X F1 +(r2 + r )X F2 ......
    Simplifying

    M' = r1 X F1 +r2 X F2 ...... + r X ( F1 + F2 .....)
    However F=F1 + F2 ......... =0
    Hence M=M'
     
  4. Aug 25, 2012 #3
    The above can be compactly phrased this way: if R = 0, then M is independent of O. So R = 0 and M = 0 about any O imply equilibrium.
     
  5. Aug 25, 2012 #4
    Thank You all...that's right...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Static Equilibrium Conditions
  1. Statics: Equilibrium (Replies: 3)

  2. Statics (Equilibrium) (Replies: 1)

Loading...