98 .:. rnonm UNO 







! N; an : lly we may inlrr 



very sy^' <>ne plain 



a single resultant has a centre; or, in other words, it there 

 be a system of forces acting in a plane and having a BJ 



kn.w i ';itude of each force, the 



I tin- diivetinns 'f the forces make with each < 

 no point in the direction of each, then < 



nitnde of the resultant, the anirle its dir. 

 makes with those of the c t forces, and one p ;int in 



.. 



105. If a system of forces maintain a body in equilibrium, 

 and equilibrium also subsist after the b.dy h. ; in. d 



through ay ffifi'-n anirle which is not a multiple, of 1w> ri-ht 

 angles, about any axis, then equilibrium will still s 



i the body is turned about the same axis tlmiuirh "//.>/ 

 (inrjlc >'/,, , f, ,rr, the forces beinp: sii]ijM.st-d to act with the 

 same intensity and in parallel directions throughout. 



Take the axis of z to coincide with the straight line about 

 which the body is turned. Since there is equilibrium in its 

 first position, w- '. 



n. ^)' = 0, 2Z=0 ............... (1), 



? ^ }'.r-T V ) = ..... 



uilibrium subsist when the body is turned ihrou 

 angle 0, tin- is (1) and (2) must hold when we put 



.c cos 6 y sin 6 for #, and a; sin 6 + y cos 6 for y. 1 fence (2) 

 become 



M0:(Zx)+cos0:(/3/)-2(F*) = ...... (I 



Q ...... (4), 



...... 



By means of (2), equations (3) and (1) Income 

 sin 2 (Az) - (1 - cos 0) 2 ( Yz) = 0, 



' }'z) = 0. 



tions hold for SOL of sin different from 



we must have 



,;)=0, and 2(3V'=0 



