Question

Find Moment of Inertia @ XX and YY centroidal axes of a composite figure

consisting of a rectangle of 3m base and 4m height and a isosceles triangle of same

base as rectangle and of 6m height ,The triangle is kept on the top of the rectangle.

Answer 1

The moment of inertia, otherwise known as the angular mass or rotational inertia, of a rigid body is a tensor that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for a desired acceleration

SI unit of moment of inertia is kgm^2

it appears in the relationships for the dynamics of rotational motion. The moment of inertia must be specified with respect to a chosen axis of rotation. For a point mass the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis,

moment of inertia=I = mr^2

moment of inertia=i=6×4×3

moment of inertia=i=24×3

moment of inertia=i=72

moment  of inertia=i=72kgm^2