l.YNAMICS OF A RIGID BODY. 



2a being the length of the rod. If 4<o f cos a = 3^, prove that the 

 time of a small oscillation is 



a\ 



J' 



1 "--. A number of concentric spherical shells of equal inde- 

 finitely small thickness revolve with uniform angular velocities 

 about a common axis through the centre, each with an angular 

 roportional to the ?t th power of its radius; the shells 

 suddenly rigidly united, prove that the subsequent angular 

 velocity is to the previous angular velocity of the outer shell as 

 5 : n + 5. 



1523. An infinite number of concentric spherical shells of 

 equal small thickness are rotating about diameters all in one 

 plane with equal angular velocities, the axis of any one who>e 



radius is r being inclined at an angle cos" 1 - to the axis of the 

 shell ; if they become suddenly united into a solid sphere, the 



rt 



new axis of rotation will make an angle tan"' , with the 

 former axis of the -outer shell. 



Any possible state of motion of a rigid rod may be 

 I by a single rotation about any one of an infinite 

 number of axes lying in a certain plain-. 



1 '>- ee rigid body is in motion about its centre of 



ICO another p,,ii,t -!' th.- ri-id body is suddnily li.\.-d, and 

 >dy assumes a state of permanent rotation abou 

 through that poinl ; prove that tin- point must lie on a c 



r hyperbola. 



- r >. A rL'i'l body is in motion u: 



forces, and iU centre of gr:. ;;inta- 



neous ^idly con- 



, 1 tho new inat. 



