Calculate the moment of inertia of the steel plate in

Step 1 of 2

We have to calculate the moment of inertia of the steel plate for rotation about a perpendicular axis passing through the origin.

The moment of inertia of the steel plate can be found using the equation.

\(I=\int\left(x^{2}+y^{2}\right) d m\)

\(d m\) is the mass of region of small area \(d A\)

\(d m=\frac{M}{A} d A\)

The area of the steel plate (triangular in shape) is

\(A =\frac{1}{2}(0.20)(0.30)\)

\(=0.030 \mathrm{~m}^{2}\)

Thus,

\(\frac{M}{A} =\frac{0.800 \mathrm{~kg}}{0.030 \mathrm{~m}^{2}}\)

\(=26.67 \mathrm{~kg} \mathrm{~m}^{2}\)