238 Dynamics. 



FG 



We hence derive the proportion, 



.xra JOCLXJW x ro ::FO: re. 



/ G ^ ?/i r 2 



which gives 



/mr2 y m r a 



'a v 



""" "~ **" ^ -- ** i- F-? rr n AN ~" - 



w x L X FHxFG L x 



357. which is the same as the expression for the centre of percussion. 



362. Since all the forces which act upon the body L, or up- 

 on a system of bodies that admit only of a motion of rotation 

 about a point or a fixed axis, cause in this body such a velocity 

 that, for any given point Jlf, we have 



and since it is evident, that if this body were to turn in the op- 

 posite direction with the same velocity, there would be an equi- 

 librium among all these forces ; we infer, that if a body, turning 

 with a velocity which for a determinate point M is equal to v 9 

 would have its motion counterbalanced by a power p, the direc- 

 tion of which passes at a distance from F equal to 7), this power 

 taken in connection with its distance Z), must be such that the 

 moment p X D shall be equal to the velocity of the point M, di- 

 vided by the distance FM^ and multiplied by the sum of the pro- 

 ducts of the .particles into the squares of their distances respect- 

 ively from F, or from the axis passing through F. Indeed this 

 power must be such as will be sufficient to produce the same ve- 

 locity in the body L, supposed at rest ; and this velocity would 

 be 



v = -^ x FM, 

 which gives 



FM 



