DYNAMICS OF A POINT. 2!>7 



through a small fixed ring in the table; the 

 re ;tt di-tancrs <(, a from the ring, and are projected 

 with velocities r. r' at right angles to the string, so that the parts 

 of the string revolve in the same sense ; prove that, if 



cither particle will describe a circle uniformly; and that, if 



their second apsMal distances will be a, a respectively. 



Two particles m, m connected by a string which 

 S through a small fixed ring are held so that the string is 

 horizontal, their distances from the ring being a, a', and are 

 simultaneously let go ; prove that 



m m' 111 _1 



p-p" p + p'~ + ' ; 

 p, p being the initial radii of curvature of their paths. 



1 125. Two particles A and B are connected by a fine strinir : 

 A rests on a rough horizontal table, and // h.-r .-ally at a 



ice a below the edge of the table. A being on the point of 

 motion, I: i< ]>n>i"ctr.l horizontally with a velocity u in tin- piano 



ndicular to the edge of the table; prove that A will begin t> 



move with acceleration ~ , and that the initial radius of 

 /x+ 1 a 



curvature of J5*s path will be (/x -f I) a, /x being the coefficient 



111''-. A smooth win- in tin- form of a circle is made to 

 volvc uniformly in a lioi-i/'.ntal plain- about a point A in its 

 droomferenoe, \vitli angular v-lo \ small riiiLT /' sli ; 



th- wire and is initially at rest at its | <listance r fn.jn A ; 



it its distance from A at a time t is - - , nn-1 



- C"* 



I-sith in space bisects the angle between PA 



and th radius to P. 



