i6i .] ACCELERATION. 



By composition, we have of course 



7 = 



(5) 



161. For polar co-ordinates r, 0, we may resolve the accelera- 

 tion j into a component j v along the radius vector r and 

 a component j e at right 



angles to r. Expressions 3y 



for these components are 

 readily found by projecting 

 the components 



on r and at right angles to 

 r (Fig. 39) 



Fig. 39. 



Differentiating the relations x=rcos6, y = rsin6, we find 



dx dr /! 

 = cos# 

 dt dt 



and differentiating again : 



dQ dv dr 



, -^- = 



dt dt dt 



* 



r cos 6- ; 

 dt 



dt* 



dt dt 



Substituting these expressions for ^ and 

 equations for j n j B , we find : 



in the above 



d 



,~ 



