Analytical mechanics, comprising the kinetics and statics of solids and fluids (1911)
Barton, Edwin Henry · London, Longmans · leaf 252
equal to L Hence the laminatheorem applied to the disc yields 2l=K (6). It is simpler now to determine Kdirectly by integration and deduce /,thus reversing the procedure followedfor the rectangular lamina. For our element we take a ring ofradius r and radial width dr, as shownin Fig. 91. The area… … Fig. 91. Moment of Inertiaof Disc. K-- rfrdr-- Jo 27r<ra %Ma (7). Whence by (6) we see that I=lMa2 (8). It is obvious that (7) will apply also to a cylinder of any lengthrotating about its geometrical axis. For a cylindrical tube of radii aand b outside and inside and density />, we have from…
Mechanics
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