279-] PLANE MOTION. 



157 



these have the components c* 2 r and ar* opposite sense. There 

 exists therefore only one centre of acceleration /, and its radii 

 vectores satisfy the conditions 



279. The appropriateness of the name centre of acceleration 

 for the point / appears in particular when the acceleration of 

 any point P is referred to this point 7. For it can be shown 

 that, if/ be the distance of P from /, the acceleration of P can 

 be resolved into two components, one o> 2 p along PI, the other ap 

 at right angles to IP (Fig. 74), similarly as in the case of rota- 

 tion about a fixed axis (see Art. 273). 



74. 



To prove this we resolve the component eoV of the acceler- 

 ation of P along PI and parallel to IC\ it appears from the 

 figure that these components are aPp and &>V . The other 

 component ar f of the acceleration of P is due to the infini- 

 tesimal. angular velocity dw about H. Replacing this dw about 

 H by an equal angular velocity du> about / in combination with 

 the infinitesimal velocity of translation r Wo> at right angles to 



