02:00 681BB T Problem 3 Consider a thin plate on the z = 0 plane with mass density given by o(x, y) = C ((x - 1)²³y² + x

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02 00 681bb T Problem 3 Consider A Thin Plate On The Z 0 Plane With Mass Density Given By O X Y C X 1 Y X 1 (41.25 KiB) Viewed 22 times

02:00 681BB T Problem 3 Consider a thin plate on the z = 0 plane with mass density given by o(x, y) = C ((x - 1)²³y² + x¹y²), (4) and whose total mass is M. The plate has a side length of two meters, and its center lies at the origin. The infinitesimal mass element is given by: dM = o(x, y)dxdy (5) 1. What are the units of C? Find an expression for C in terms of M. 2. Find the coordinates of the center of mass XCM. 3. Find the moment of inertia around the z-axis: I: = [₁ [₁ r²o(x, y)dady You may leave your final answer as the sum of two fractions. 4. Now find the moment of inertia along the (r = 2, y = 0) axis. @0.99% +0