DYNAMICS OF A RIGID BODY. 



where 0, $ are the angles through which the string and the disc 

 have turned at a time t, a is the radius, and k'= - + t m, p 

 being the masses of the disc and particle. 



1536. Two equal circular discs lying flat on a smooth hori- 

 zontal table, are connected by a fine string coiled round each 

 which is wound up till the discs are in contact with each other, 

 and are on the same side of the tangent string. One of the discs 

 has its centre fixed and can move freely about it, the other disc is 

 projected with a velocity u at right angles to the tangent string; 

 prove that the angle through which either disc will have turned 



I vW 

 after a time t ia ./ 1 + ^ - 1, and that the angle through which 



the string will have turned is -^- tan' 1 p ; a being the radius 



a^o 



of either disc. 



1537. A smooth tube, mass w, lying on a horizontal table, 

 contains a particle, mass/?, which just fits it; the system is set in 

 motion by a blow at right angles to the tube : prove that 



r being the distance of the particle from the centre of the tube, 

 when the tube has turned through an angle 0, c tin; initial value 



of r, A - -, where m, p t are the masses of the tube and 

 particle, and 2a the length of the tube. 



1538. A circular disc of mass m and diameter d t can move on 

 a smooth horizontal plane about a fixed point A in its cimimfe- 

 rence, and a fine string is wound round it carrying a particle of 

 mass/), which is initially projected from the disc, at the otlu 



diameter through A t with a velocity u normal to the disc, 

 the disc being then at rest. Prove that the angular velocity of 



n i 



