Consider a thin square plate on the z = 0 plane with mass density given by o(x, y) = C ((x - 1)²y² + x¹y²), 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 = 0 o(x, y) dxdy
Consider a thin square plate on the z = 0 plane with mass density given by o(x, y) = C ((x - 1)²y² + x¹y²), 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 = 0 o(x, y) dxdy
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Transcribed Image Text:Consider a thin square plate on the z = 0 plane with mass density given by
o(x, y) = C ((x - 1)²y² + 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:
1-L L
I
=
r²o(x, y)dxdy
(6)
You may leave your final answer as the sum of two fractions.
4. Now find the moment of inertia along the (x = 2, y = 0) axis.
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