Cl It VI. 



M OF A COS8TILAIXE 



86. To M the amditio*, of eqmhTmmm of fore* acting 

 on a rigid body when one point ujized. 



Let the fixed point be taken an the origin of co-ordinates. 



bodr will produce a pressure 



on th<- fixed jH.int; 1 /' be the rewired pa: 



this pressure parn! - axes. Then the fixed point will 



exert forces - A , - ) the bodjr; and if we 



take the*e forcee in oonnex . the giren forces, we may 



-He the body to be free, and the equations of equilibrium 

 nr- 



--Y'-O, SI'- )' ' = " r-0, 



L - 0, Mm 0, 0. 



first three conation* give the resolved parts of the 

 pressure on the fixed point; and the last three are the onljr 



tions to be satisfied by the given forces. Thus the forces 

 will be in equilibrium it' the aum* of the momtnt* of tk* firm 



t*ptct to three ttraighi line* at right angle* to ack other, 

 and pasting through the fixed point, vanuh. 



Convcrsrlv. if the forces are in equilibrium the sum of the 

 forces with respect to any straight line 

 throu \cd point will va 



From the equations A' '--: lows 



ressure on the fixed ]>oint is equal to the resultant 

 of nil the irivrn forces of the system moved parallel to then* 

 cs up to the fixed poi 



11 the forces are lurallcl, we may take the axis of s 



passing through the fixed point parallel to the forces. Them 



forces included in 1 A \anish. and so do all the forces 



..-,1 in 1 :> .. s. M reduces to -SZr, and 



vanish and the eqia- 

 of equilibrium reduce to 

 -/ - 



