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Homework Statement
Consider the curve y=(2/9)x^2 revolved around the y-axis. Find the moment of inertia about the y-axis
Homework Equations
I=\int r^2 dm
The Attempt at a Solution
So I considered a cylindrical element of width dy and radius x, so that it's volume is
dV=(\pi x^2)dy
Now the moment of inertia of this element about the y-axis is
dI= \frac{1}{2} x^2 \rho (\pi x^2)dy
so to get the moment of inertia of this entire curve, I just need to integrate like so
I= \int_{0}^{\frac{2x^2}{9}} \frac{1}{2} \rho \pi x^4 dy
Where x=\sqrt{4.5y}
is this correct??