1 62 



KINEMATICS. 



[287. 



edges concurring in P are evidently dr, rd6, rsin0d<f); hence 

 the components of the velocity are 



dr 

 ' dt' 



dt 





X 



Fig. 76. 



287. The components of the acceleration / in polar co-ordi- 

 nates are readily obtained by considering that the accelerations 

 of the point P in the direction at right angles to Ox in the 

 plane xOP and in the direction at right angles to this plane 

 are the same as the accelerations of the point Q (Fig. 76); they 

 are therefore, by Art. 161, (6), since RP=OQ = 



in the direction RP, and 

 i 



r sin 6 dt 



dt 



at right angles to the plane of the angle 0. The component of 

 j parallel to the axis Oz is, of course, d\r cos 0)/dt 2 , Resolv- 

 ing these three components parallel to the three rectangular 

 directions along r, at right angles to r in the plane xOP, and 



