236 ANSWERS. 



have / a ' = / 8 ' = $/!, and /2 = / 3 = /i'+i/i. Hence, 7 2 = 7 3 = 

 \ a 2 ) . At the centroid the squares of the principal radii are 



(4) A = JS=C=lMa\ D = E = F=\Ma?; hence momental 

 ellipsoid : 4 (JT + f -f s 2 ) 3 (jys + 2* + ^) = 6 ^ ; squares of prin- 

 cipal radii : \ a 2 , { a 2 , |i a 2 . 



(5) ? 2 = itf 



(6) /= 



(8) The centroid may be such a point ; or if the central ellipsoid be 

 an oblate spheroid, the two points on the axis of revolution at the dis- 

 tance V(/i I<?)IM from the centroid. 



(9) The ellipsoid must have the same central ellipsoid as the given 



body ; its equation is - + *-. -j -- - = -5_ t where M is the mass, and 



A Jj G JM 



A\ B', C are the moments of inertia for the principal planes of the 

 body at the centroid. 



\ 





Pages 163, 164. 



(2).fV2. (4) 



(5) 375 oo foot-pounds. 



(6) - - , where r and r* are expressed in feet. 

 3600^ r 1 



(7) 4 m. 22 s. (8) 



Pages 203-207. 

 > = F/Ma. 



(8) The body begins to turn about an axis through the fixed point, 

 parallel to the instantaneous axis before impact, with angular velocity 



