A. TWO-DIMENSIONAL CASES 



1. Circular cylinder in translation perpendicular to its axis: 



(^7^iL 



fj =— pn a^ f/^, as in Equation [68i], 



M/ = pn a , 



k = l. 



2a Elliptic cylinder in translation parallel to an axis, called the o-axis, either a>b as shown 

 or b> a: 



+-3^ 



T, =—pn b^U^, 



M/ = pn ab. 



from Equation [841], 

 k = b/a. 



3. Plane lamina in translation perpendicular to its faces 



J. 

 2 



u 



T^ ^-^pn a^U^ 



as in Equation [86b], 



kM/ = pn 



4« Elliptic cylinder rotating about its axis: 



T'l = — p7T{a^-b^)^ co^, as in Equation [106z] 

 16 



/j = — pn ab{a^ + b^), k ' 



2ab (a^ + b^) 



5o Plane lamina rotating about its central axis: 



7\ Axis of 

 Rotation 



3 



T^ = pn at), as in Equation [106a'], 



16 



A//= 077 a^ 



1 Q '^ 



6o Plane lamina rotating about one edge: 



r, = pn a cj^. as in Equation [106b'] 



^16 



with /3 = 1, 



' Axis of 

 , Rotation 



; / 



' / Apparent increase in moment of inertia 9 pn a^/8 3 



W\ Moment of inertia of fluid displaced by a o n^/o ^ 



cylinder of radius a rotating as if rigid 

 about a generator 



viy- 



385 



