GENERAL PRINCIPLES 



41 



Knowing the mass M and the angular speed, we obtain the 

 radius of gyration for various bodies. For example :- 



1. For a thin rectilineal rod, having the axis of rotation per- 

 pendicular to its length / : 



2. For a cylinder of radius r, turning round its axis : 



r 2 



If turning round a diameter of the base, the height being h : 



P = 



12 



3. For the rim of a wheel of rectangular section, of which 

 the external and internal radii are r and r' : 

 ^ _ ^ -M; 2 

 ~"~2 



4. For the frustrum of a solid cone, with radii r and r' and 

 height h, having for axis a straight line situated in one of the 

 base and at the centre of the figure, and : 



P lss! T( 1+ rT7') +J r ~^~ 



d being the difference r r '. 



5. For a Rectangular parallelepiped having as sides a, b, c, 

 and turning round an axis drawn through the middle of the 

 side b parallel to a : 



1 / 2 1 2 \ 



3 \ 4 / 



The preceding values of the moment of inertia, or, more 

 exactly, of the radius of gyration, are for 

 homogeneous bodies. They do not apply, 

 _ strictly speaking, in the case of non-homo- 

 ~ geneous parts, such as the parts composing 

 the animal locomotive apparatus. 



32. Energy. The fact that live power 

 comes from stored-up work, and can be 

 restored, has led the natural philosophers 

 to identify that live power J mv 2 with a 

 sort of immaterial substance capable of 

 concealing itself and of appearing in the 

 body ; it has been called energy. Energy 

 is therefore the capacity for work ; it can 

 be in reserve, that is, potential, or it can 

 translate itself into work and become kinetic. 



Fio. 67. 



