67 



Table 34. 



MOMENTS OF INERTIA, RADII OF GYRATION, AND WEIGHTS. 



In each case the axis is supposed to traverse the centre of gravity of the body. The axis is 

 one of symmetry. The mass of a unit of volume is w. 



Body. 



Sphere of radius r 



Spheroid of revolution, po- 

 lar axis 2a, equatorial di- 

 ameter 2r 



Ellipsoid, axes za, 2b, 2c 



Spherical shell, external ra- 

 dius r, internal r' 



Ditto, insensibly thin, ra- 

 dius r, thickness dr 



Circular cylinder, length 2a, 

 radius r 



Elliptic cylinder, length 2a, 

 transverse axes 2b, 2c 



Hollow circular cylinder, 

 length 2a, external ra- 

 dius r, internal r' 



Ditto, insensibly thin, thick- 

 ness dr 



Circular cylinder, length 2a, 

 radius r 



Elliptic cylinder, length 2a, 

 transverse axes 2a, 2b 



Hollow circular cylinder, 

 length 2a, external ra- 

 dius r, internal r' 



Ditto, insensibly thin, thick- 

 ness dr 



Rectangular prism, dimen- 

 sions 2a, 2b, 2c 



Rhombic prism, length 2a, 

 diagonals 2b, 2c 



Ditto 



Diameter 



Polar axis 



Axis 2a 

 Diameter 



Diameter 



Longitudinal 

 axis 2a 



Longitudinal 

 axis 2a 



Longitudinal 

 axis 2a 



Longitudinal 

 axis 2a 



Transverse 

 diameter 



Transverse 

 axis 2b 



Transverse 

 diameter 



Transverse 

 diameter 



Axis 2a 

 Axis 2a 

 Diagonal zb 



Weieht. 



3 



i^-Kwar"^ 



\Trwabc 



2inva{7-'^—r'-) 



^irwardr 



2Tr2var^ 

 2irwabc 



2irwa{r^ — r'^) 



4trwardr 

 Swabc 

 \wabc 

 A^wabc 



Moment of Inertia lo 



Square of Ra- 

 dius of Gyra- 

 tion (?. 



15 



i^irwabc(P-\-fi ) 



IS 

 8ir7v{r^ — r'5) 



IS 



Sinvr^dr 



3 



invar* 



irwabc{b^-\-<:^) 

 2 



nwa[r*—r'^) 



4irwar^dr 



'K7uar^(T)r'^-\-4a'^) 



6 

 irwabc(y'^-\-jfi'^) 



6 



■mua < 2{r* — r'^) ) 



6 \ +4^2(^2 



irwa (2r^-\ — a'^r)dr 



?,wabc(b'^-\-fi) 



3 



2wabc{b''-\-c'^) 



3 



2wabc(c'^-\-2a'^) 



2f^ 



5 



S 

 <^2.ff2 



5 



2(r5— r ^S) 

 2r2 



3 



y2 



2 



^2-fr2 

 4 



y2_l_^'2 



r^ cfi 



^2_j_^'2 (fi 

 "4 '"3 



^2 /z2 

 2 +^ 

 ^2-1-^2 



3 



6 



^2 a2 



(Taken from Rankine.) 



Smithsonian Tables. 



