Rotation of Bodies unconfined. 257 



the formula gives 



,,, - 86400 - 



- y 40-0^ 



the sign indicating that the clock loses. 



Rotation of Bodies unconfined. 



379. It has been demonstrated that when a body L re-Fig.is. 

 ceives an impulse in a direction HZ, not passing through its 

 centre of gravity G, this impulse is transmitted entirely to 124t 

 the centre of gravity, which moves in a direction parallel to HZ 

 according to which the body has received the impulse ; and that 

 the parts of this body, in the mean time, turn about the centre 

 of gravity in the same manner as if it were fixed. Therefore, if 

 the figure of this body, arid the forces impressed upon it (of 

 which I suppose p to represent the resultant) are such that it can 

 turn only about a single axis ; as this axis will necessarily pass 

 through the centre of gravity, all that we have said on the 

 subject ot the moment of inertia, is applicable to this case, 

 understanding by r in fm r 2 , the distance of any particle from 354^. 

 the axis which passes through the centre of gravity, and by p x D 

 the moment of the force HZ, taken with respect to the same axis, 

 or the sum of the moments of all the forces which act upon the 

 body, taken with respect to this same axis. That is, the centre 

 of gravity will move parallel to the direction of the force p, with 



a velocity = -y-, L being the mass of the body ; and if we draw 



JL/ 



GZ perpendicular to HZ, and call v the velocity of rotation of 

 the point Z, we shall have 



or 



Of this we shall give a few applications. 



380. Let us suppose that the body JV* impinges upon the 

 body L, according to any direction whatever J2Q,m such a man-Fig.186. 



Mech. 33 



