36 THE HUMAN MOTOR 



which means F = mf for the duration of a second. In the 

 element of time dt, the force has an "impulse" Fxdt, equivalent 

 to trie product M X dv. From the instant zero to the instant t, 

 the equation Fdt = mdv, will be the sum of several similar pro- 

 ducts. This sum has as its sign, in the integral calculus, 



/*Fdt = MV MV . 



This equation expresses that, in a rectilineal movement, the 

 "impulse" F/ develops a momentum mv. Therefore, to stop a 

 wagon of 60 kilogrammes, travelling at a speed of 5 metres, in the 

 space of 3 seconds, a force of 10 '2 K is necessary because : 



MV _ 60 

 3 ~ 9-81 



In a curvilinear movement the equation stiil holds but F will 

 only designate the tangential force. 



Consider now the projection of a point belonging to a material 

 system on a plane perpendicular to the axi:, OZ. If the direction 

 of the force which acts on that point passes through a similar 

 point during the movement, for example, through the point O, 

 the moment of the force will be zero, at any time. In short. 



5 



X o = 



F/&. (tl 



the sum of the moments of the impulse F<//, in relation to the 

 fixed axis, will always be zero, and in consequence the sum of the 

 moments of the momentums of a system will not be modified 

 and will not be increased. This sum is constant. It can be seen 

 (fig. 63) that the masses sweep out, with the radii Om', O/Wj . . . 

 areas proportional to the time, and that the sum of the products 

 of the masses iorming the system, into the areas remains con- 



