277-] PLANE MOTION. ! 55 



277. Another important method for finding the components 

 of the acceleration of any point P of the body consists in 

 resolving (according to Art. 254) the rotor w + dw through \ 

 into two parallel rotors, &> through C, and du> through a point H 

 (Fig. 72) on the tangent CC l whose distance CH=h from C is 

 given by the relations 



CC 1== C 1 H = CH 

 dw a) &) + da) 



Putting again CC^dcr, da-/dt=u, du>/dt=cx, ) we find for the 

 distance CH=h : 



k = . (4) 



a 



The body can therefore be regarded as having, during the 

 second element of time dt, the same angular velocity w about 

 the same axis throu-gh C as during the first element of time, 

 but in addition an angular velocity dw about a parallel axis 

 through H. As the magnitude of the angular velocity about 

 C does not change, the rotation about C produces at any point 

 P (Fig. 72) only a normal acceleration o>V towards C, but no 



H h Ci C 



Fig. 72. 



tangential acceleration. The infinitesimal angular velocity day 

 .about H, on the other hand, produces only a tangential acceler- 

 ation ar 1 , perpendicular to HP=r 1 . 



The acceleration of any point P can therefore be resolved 

 into two components, one o>V directed towards the centre of 

 rotation C and proportional to the distance r from this centre, 



