240 Dynamics. 



u JV X ti X FH JV X u' X FH 



2 9 



_ 

 FH fmr 2 fmr 



u f X fm r 2 Nxu'xFH _ N X u X FH 

 /mr 2 X F 



fmr 2 X FH 



= JV ' XU - 

 J f m 



x FH 



,2 



f NxuX FH fmr 2 X FH 



FH 



fmr 2 + 



From this the value of T, or the velocity of rotation, is readily 

 obtained. But the equation v = , or i> FJaT = u'FT, since 



it gives the proportion 



u' : v : : FH : FT, 



makes it evident, that u' is the velocity of rotation of the point H; 

 from which it will be seen, that the point H turns with the veloc- 

 ity that remains to JV after collision. 



364. We hence perceive, that in order to find the motion of 

 bodies that turn about a fixed point or axis, we must be able to 

 determine the value ofj*m r 2 . This will always be easy, as we 

 shall soon show, when the bodies are such as admit of being ex- 

 pressed by equations. We may, indeed, in any case consider 

 the body as composed of parallelepipeds, pyramids, &c., which 

 are capable of being thus expressed ; and finding for each com- 

 ponent part the value ofjmr 2 , take the sum of these as the to- 

 tal value oijm r a 2 for the entire body or system of bodies. 



When the body is such as admits of being expressed by an 

 equation, we proceed thus in finding the value oij'm r 2 . 



