Moment of Inertia in Applied Calculus
Saad Habib · Digital Commons - University of South Florida (University of South Florida) · 2021
This paper demonstrates the usefulness of calculus in structural/continuum mechanics. Calculus in structural/continuum mechanics is used to calculate mass, volume, centre of mass, moment of inertia and in solutions of differential equations. In this paper, we will use calculus to calculate moment of inertia. The area moment of inertia of a surface measures the resistance to deflection of the cross section to bending or buckling. Moment of inertia is used by engineers of inertia to determine the state of stress in a cross section and the amount of inertia. It represents a mathematical concept that depends on the size and shape of the cross section of the element. The cross section’s bending axis is also the central axis, so the ability to maintain the centroid of the shape is closely related to the moment of inertia.