I79-] MOTION ON A FIXED CURVE. 3^ 



The equations of motion (see Art. 67) can then be written in 

 the form 



m = P t -F t \ 



o 



m = resultant of F n and F n ', 

 P 



where v is the velocity and p the radius of curvature of the 

 path at the time t. It should be noticed that the components 

 F n and F n ' t though both situated in the normal plane, do not 

 in general have the same direction. But in the important 

 special case of plane motion, i.e. when the path is a plane curve 

 and the resultant F of the given forces lies in this plane, F n and 

 F^ are both directed along the radius of curvature so that the 

 right-hand member of the second equation becomes the sum or 

 difference of F n and F n . 



169. The normal component F n ' of the constraining force 

 is generally denoted by the letter N and is called the resistance 

 or reaction of the curve; a force N, equal and opposite to 

 this reaction, represents the pressure exerted by the particle 

 on the curve. 



The tangential component F t ' of the constraint will exist only 

 when the constraining curve is rough, i.e. offers frictional resist- 

 ance ; we have then, denoting the coefficient of friction by //,, 



We shall therefore write the equations of motion as follows : 



V 



m = resultant of F n and N. (2) 



170. The normal component, mv^/p, of the effective force 

 is sometimes called the centripetal force (see Art. 67) ; it is 

 directed along the principal normal of the path towards the 





