23 4 MOTION OF A RIGID BODY IN TWO DIMENSIONS. [CHAP. XI. 



of the acceleration of P parallel to the axes are 



u wy' w?x', and v + fax 1 ufy ' . 



Fig. 56. 



The kinetic reactions may be reduced to a vector localised in 

 a line through the centre of inertia and a couple. The vector in 

 question has resolved parts parallel to the axes 

 Sm (u a>y' - &> V) = Mu, 



and 2m (v + ax' - &>y ) = Mv ; 



and the couple is the moment of the kinetic reactions about a 

 line through the centre of inertia perpendicular to the plane of 

 motion ; this moment is 



Sm \x' (v + fax' ft) 2 !/ 7 ) y'(u coy' 



The moment of the kinetic reactions about any axis perpen- 

 dicular to the plane of motion is the moment about that axis of the 

 kinetic reaction of a particle of mass equal to the mass of the 

 body and moving with the centre of inertia, together with the 

 moment of the couple Mk z co. (Article 103.) 



The formulae for the acceleration of a point show that at each 

 instant there is a point which has zero acceleration. This point 



