APPENDIX. 



443 



APPENDIX 0. 



Centrifugal Force. (See 77.) Let a body placed at A re- 

 ceive an impulse which would push it in one second to D, while 

 it is acted upon by a second 

 force which in the same time 

 would draw it to B. Then 

 (see 82) it will move through 

 the diagonal AE. Inertia 

 would then carry it in the line 

 EF but the centripetal force 

 draws it toward H and it de- 

 scribes a second diagonal EG. 

 But the action of the cen- 

 tripetal force is continuous 

 instead of intermittent as we 

 have described it. Conse- 

 quently, the moving body will 

 change its direction at every 

 point and describe a curve. 

 Since ED, the distance that FIG. 345. 



the body would have receded 



in one unit of time, is equal to AB, the two central forces are equal 

 and the curve is a circle. If the arc AE.be sufficiently small it will 

 not sensibly differ from the diagonal AE. Since the triangles 

 ABE and AEO are similar, we have 



AB : AE :: AE : AO. 



AB = 



But AB represents the centripetal force and its equal the cen- 

 trifugal, while AE represents the velocity, and AO the diameter 

 or twice the radius. 



Hence the formula : C. F. = 

 2r 



(1.) 



In this formula, C. F. represents a line, the distance over which 

 the centrifugal force will move the given body. If we wish to 

 measure this force by pounds or weight, we must compare it with 

 the force of gravity, which is the cause of weight. A body , whose 

 weight may be represented by w, will fall, when acted upon by 

 gravity alone, 16.08 feet in one second. Hence : 



10 : C. F. .: : 16.08 : . 



r P - 

 ' 



wv * 

 32.16r 



(2-) 



