32-35] FORMULAE FOR ACCELERATION, 35 



for them an abbreviated notation. We shall therefore denote 

 the differential coefficient of any quantity q with regard to the 



time t by placing a dot over the q, thus q stands for -p . 



Now suppose x, y, z are the coordinates of a moving point 

 at time t, then its component velocities parallel to the axes are 

 denoted by x, y, z. 



Again suppose u, v, w are the component velocities of a point 

 parallel to the axes, then its component accelerations are denoted 

 by u, v, w. 



~. dx dii dz . . 



bmce u = -j- , v = ~ , w = -j- it is convenient to write for 

 dt dt dt 



them x, y, z respectively. This recalls the fact that the com- 

 ponent accelerations parallel to the axes are the second differential 

 coefficients of the coordinates. 



In the same way when we have to deal with any function 



of the time, say q, we may write q for -^ > as we write q for -~ , 



dt dt 



where as usual ~ is written for -=- ( -^ J . Also, following the 



analogy of the case where q is x, y, or z, we may call q the velocity 

 with which q increases, and q the acceleration with which q 

 increases. 



35. Acceleration of a point describing a plane curve. 



Suppose that the moving point describes a plane curve which 

 occupies a fixed position with reference to the axes. To fix 

 ideas we may take it to be in the plane of (x, y). 



Let v be the velocity at any point P of the curve, 1/ the 

 velocity at a neighbouring point Q, and A< the angle QTA 



Fig. 27. 



32 



