DYNAMICS OF A RIGID BODY. 307 



1469. Tn a triangular lamina any one of the sides is a 

 principal axis at the point bisecting the distance between its 

 middle point and the foot of the perpendicular on it from the 

 opposite angle. 



1 170. If straight lines be drawn in the plane of a given 

 lamina through a given point, the locus of the points at which 

 they are respectively principal axes is a curve of the third degree. 



1471. The locus of the straight lines drawn through a given 

 point, each of which is at some point of its course a principal axis 

 of a given rigid body, is the cone 



A y B, C being the principal moments of inertia at the given point, 

 a, b, c the co-ordinates of the centre of gravity ; and the principal 

 axes at the given point the axes of reference. 



Prove that the locus of the points at which these straight liiu-s 

 are principal axes is the curve 



cy -z az- ex 



\\1'1. If the principal axes at an; l-e parallel to the 



principal axes through tin* centre of gravity, tin- point nm>t lie oil 

 one of the principal axes at the centre of g 



II. Motion about a Fixed Axis. 



1 17 vular dise rolls in one plane on a fixed plane, its 



(l-scril)in^ a straight line with uniform aeeel< i rati<>n /': find 



the magnitude and p the impressed 



1 171. A pieoc i 00 Irnirtli into tli 



i axis through its 



jM-ndinilar t. pr\ t liat tin- o-nt iv of oscilla- 



tion will In- at tin- least possible tin- axis of r 



tiii when ' 



117 . i ! M I., a\ y r,.,l of radius 



'In- one about a h and tin- other 



-2 



