284-] PLANE MOTION. 







J y = ay + ax+ cou. 



The co-ordinates x^ y Q of the centre of acceleration / must 

 fulfil the conditions 



o, (10) 



whence * = /^' Jo= ~/^' (ll>1 



The equations (10) evidently represent the two lines CI and HI. 



282. Let %=x-x Qt 77=7-^/0 be the co-ordinates of P with 

 respect to parallel axes through /; then, combining (10) and 

 (9), we find 



These expressions show that the total acceleration/ of P is 



since Vf 2 +7 ? 2 =/=// > , as in Art. 280. 



283. The tangential and normal components of the accelera- 

 tion j are readily obtained from Fig. 74, as follows : 



.?, A-v * ds> 



The loci of the points having only normal, and only tangential, 

 acceleration at any moment are therefore the circles : 



uy = Q. (14) 



284. Exercises. 



(i) A wheel of radius a rolls on a straight track. Find the centre 

 of angular acceleration H, (a) when the velocity v with which the axis 

 of the wheel moves along the track is constant ; (&) when v is uniformly 

 accelerated as when the wheel rolls down an inclined plane ; (c) when v 

 is uniformly retarded, as in rolling up an inclined plane. 



