IiYNAMICS OF A RIGID BODY. 31 1 



1490. A uniform rod, capable of motion about one extre- 

 mity, has attached to it at the other extremity a particle by 

 means of a string, and the system is abandoned freely to the 

 action of gravity, whon the rod makes an angle a with the ver- 

 tical ; prove that the radius of curvature of the particle's initial 

 path is 



2p 



m cos a ('2 3 sin* a) ' 



1 the masses of the rod and particle, and I the length of 

 i ing. 



1491. A uniform rod is moveable about one extremity on a 

 smooth horizon til table, and to the other extremity is fastened a 

 particle by means of a string. Initially, the rod and string are in 

 one straight line, the particle is at rest, and the rod has an angu- 

 lar velocity w; prove that when the rod and string are next in a 

 straight line, the angular velocity of the rod is to that of the 

 string as b : a, or as 



b[3p(a-b)'-ma'} : a [3p (a - b) 9 + ma (a - 2b)} ; 



in, p bring the masses of the rod and particle, and a, b the lengths 

 of the- rod and string. 



III. .Motion in Two Dimensions. 



1 I'.IL*. T\v., r.ju.il uniform rods AB, EC, freely jointed at B 

 and iiiovrabl.r about J, start fr.-in r.-st in a liori/oiital position, 

 ^ over a smooth prg whose < :'rom A is 



f 8 "\ 

 4asm(>--J; 



n EC leaves the peg, the angul-ir velocity of AB is 



//3y co a \ 

 V \** 1+cos" W' 



2a being tin- 1 tli r rod. 



