Area Moment Of Inertia Formulas For Different Shapes

Moment of inertia of a cylinder shell.

Area moment of inertia formulas for different shapes. I ρ2 da. Ix area moment of inertia related to the y axis m4 mm4 inches4 x the perpendicular distance from axis y to the element da m mm inches. For example if two disks have the same mass but one has all the mass around the rim and the other is solid then the disks would have different moments of inertia. The moment of inertia plays the same role in angular motion as the mass in linear motion.

Moment of inertia of hoop. The moment of inertia or more accurately the second moment of area is defined as the integral over the area of a 2d shape of the squared distance from an axis. Here s the list of formulas of the moment of inertia of different shapes. Da an elemental area m2 mm2 inches2 the moment of inertia for bending around the y axis can be expressed as.

I iint a y 2 da where a is the area of the shape and y the distance of any point inside area a from a given axis of rotation. It may be noted that moment of inertia depends not only on mass m but also on r. Moment of inertia formulas. The notation ρ rho corresponds to the coordinates of the center of differential area da.