Moment of Inertia I: Simple Laminae

mathmos.net > useful data > moment of inertia i: simple laminae

Name	Picture	Dimensions	Defining Equation	Principal Moments about O
Name	Picture	Dimensions	Defining Equation	`I`_x	`I`_y	`I`_z
Uniform Rod		length, 2`a`	`x` = `y` = 0 -`a` < `z` < `a`	¹/₃`Ma`²		0
Circular Rim		radius, `a`	`x`² + `y`² = `a`² `z` = 0	¹/₂`Ma`²		`Ma`²
Circular Disk		radius, `a`	`x`² + `y`² < `a`² `z` = 0	¹/₄`Ma`²		¹/₂`Ma`²
Rectangular Lamina		width, 2`a` length, 2`b`	-`a` < `x` < `a` -`b` < `y` < `b` `z` = 0	¹/₃`Mb`²	¹/₃`Ma`²	¹/₃`M`(`a`²+`b`²)
Elliptical Disk		principal semi-axes, `a` and `b`	(`x`/`a`)² + (`y`/`b`)² < 1 `z` = 0	¹/₄`Mb`²	¹/₄`Ma`²	¹/₄`M`(`a`²+`b`²)
Annulus		radii, `b` < `a`	`b`² < `x`² + `y`² < `a`² `z` = 0	¹/₄`M`(`a`²+`b`²)		¹/₂`M`(`a`²+`b`²)