I5 6 KINEMATICS. [278. 



the other ar r perpendicular and proportional to the distance r r 



of P from a point H on the tangent at C, such that CH= wu/a. 



The point H may be called the centre of angular acceleration. 



278. The resolution of the acceleration given in the last article 

 enables us to show the existence, at any time t, of a point 

 having at this instant no acceleration. This point is called the 

 instantaneous centre of acceleration; we shall denote it by the 

 letter 7, and its distances from C and //", respectively, by r 

 and r Q f . 



For a point of acceleration zero the components ar f and co 2 r 

 must be equal and opposite. Now it is evident that these 



Fig. 73. 



components fall into the same straight line only for points 

 whose radii vectores r, r' are at right angles. The centre / 

 must therefore lie on the circle described over CH as diameter 

 (Fig. 73). In addition to this the radii vectores of / must fulfil 



the condition 



a>\ = ar Q '. (5) 



The locus of all points for which at any instant the ratio r/r 1 is 

 constant and equal to a/co? is a circle whose centre lies on CH 

 and whose intersections A, A' with CH divide this distance 

 internally and externally in the ratio /o> 2 . 



The two circles intersect in two points ; but only for one of 



