15_5_28 - about the z-axis is I = σ ZZ ( x 2 + y 2 ) dS =...

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28. The surface area element for a conical surface , z = h 1 - p x 2 + y 2 a ! , having base radius a and height h , was determined in the solution to Exercise 23 to be dS = a 2 + h 2 a dx dy . The mass of , which has areal density σ , was also determined in that exercise: m = πσ a a 2 + h 2 . The moment of inertia of
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Unformatted text preview: about the z-axis is I = σ ZZ ( x 2 + y 2 ) dS = σ √ a 2 + h 2 a Z 2 π d θ Z a r 2 r dr = 2 πσ √ a 2 + h 2 a a 4 4 = πσ a 3 √ a 2 + h 2 2 . The radius of gyration is D = √ I / m = a √ 2 ....
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