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



of the acceleration of P parallel to the axes are 



u wy f w?x r , and v + wx ofy . 



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 

 2m (u wy o&amp;gt;V) = Mu, 



and Sm (v + &d V) = ^i) ; 



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 



{of (v + mx - &) Y) y (u- u&amp;gt;y - &&amp;gt;V)j 



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 M&w. (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 



