GENERAL PRINCIPLES 



13 



8. Composition of Movements. A point, or a material system.. 

 jv| ( can have various movements : in that case it 

 is possible to compose them on the principle 

 of a parallelogram. Thus if a piece of metal 

 is let fall from a boat it will fall vertically 

 from M to M' ; if the boat is moving so that 

 it reaches first the point M^ in the same time, 

 the piece of metal will reach the point M' x , 

 having followed the diagonal of the parallel- 

 ogram MM X M'M'j (fig. 19). From this can 

 be determined the resultant of any two vectors 

 expressing speed, acceleration, etc. 



19. 



FIG. >( 



We may have 3, 4 or more movements or vectors to deal with. 

 It is just as simple to get the resultant of the first two with the 

 third, this new resultant with the fourth, and so on until the 

 final resultant OR is obtained (fig. 20). 



Conversely, two directions OX and OY being given, a move- 

 ment or a vector can be resolved in either of these two directions 

 as shown in fig. 21. 



Generally a given vector can be 

 resolved in the three dimensions of 

 space (see 3). 



Thus vectors of speeds and accelera- 

 tions are composed and resolved in 

 \ the same way as movements. 



\ The vectors representing movements 



of rotation are composed in the same 



Y way. We have seen that a uniform 



Fro - 21 - rotation and translation combined pro- 



duces helicoidal movement ( 7). If, however, the motion is com- 

 pounded of rotation around an axis and translation in a direction 

 at right angles to that axis, as in fig. 22, where the circle O rolls 



