134 



KINEMATICS. 



[246. 



at 



at 



dt 



dt 



= cox. 



246. Next, taking an arbitrary origin O (Fig. 54), let x, y be 

 the co-ordinates of P and x l ', y' those of any other point O r of 



the moving figure with re- 

 spect to fixed rectangular 

 axes through O ; and let 

 rj be the co-ordinates of P 

 with reference to rectangu- 

 lar axes through O' fixed in 

 the figure but moving with 

 it. Then, if be the angle 

 between the axes Ox and 

 O'g, we have 



X' 



- 54 - 



xx ] r + f cos 77 sin0, y=y' 



sn 



cos#. 



Differentiating we find for the component velocities of 

 parallel to the fixed axes Ox, Oy : 



dx' 



dO 



Now, d6/dt is the angular velocity o> about the point O' while 

 dx' /dt, dy' /dt are the velocities of O' parallel to the fixed axes, 

 say v*, v y -. Considering moreover that f sin 6 + 77 cos 6 =yy', 

 f cos 6 ?; sin 0=x x', we have 



(3) 



velocity of P consists, therefore, <?/" /ze/^ parts, a velocity of 

 translation equal to that of O' and a velocity of rotation equal to 

 t.'i.itof? about O'. 



