Problem $10\mathrm{.}99-$ Enhanced $-$ with Hints and Feedback

Consider the thin plate shown in $($Figure $1).$ Suppose that a$=150$mm$,$b$=490$mm$,$

r$=50$mm$.$ The material has a mass per unit area of $20$k$($g$)/($m$^(2)).$

Part A

Determine the mass moment of inertia of the thin plate about an axis perpendicular to the page and passing through point O$.$

Express your answer to three significant figures and include the appropriate units.

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I$\_($O$)$

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Figure