Question

Explain, in your own words, the difference between the first moments and the second moments with respect to the x and y axis of a variable density sheet.

Answer 1

The first moment or first moment of area is also known as the mass moment of inertia. It quantifies how much torque is applied for unit angular acceleration about a particular axis.

The second moment or second moment of area is also known as the area moment of inertia. It represents the resistance of a particular shape/area offers against bending and deflection about a particular axis. For a variable density sheet/plate, if second moment is about x axis it quantifies the sheet resistance to bending and deflection about x-axis. A similar explanation can be given for y axis.

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