Moment of Inertia of a Sphere

Moment of Inertia of a Sphere Formula, Solid Sphere
$I \;=\; \dfrac{2}{5} \cdot m \cdot r^2$
Symbol	English	Metric
$\large{ I }$ = Moment of Inertia	$lbm\;/\;ft^2-sec$	$kg\;/\;m^2$
$\large{ m }$ = Mass	$lbm$	$kg$
$\large{ r }$ = Radius	$in$	$mm$

This calculation is for the moment of inertia of a sphere. There are three separate calculations: a solid sphere, a hollow sphere and a hollow core sphere. The difference between a hollow sphere and a hollow core sphere is a hollow sphere has a thin shell, or a thickness that is neglible. Because a sphere is the same dimensions in every dimension, the moment of inertia is the same about every axis.

Moment of Inertia of a Sphere Formula, Hollow Sphere
$I \;=\; \dfrac {2}{3} \cdot m \cdot r^2$
Symbol	English	Metric
$\large{ I }$ = Moment of Inertia	$lbm\;/\;ft^2-sec$	$kg\;/\;m^2$
$\large{ m }$ = Mass	$lbm$	$kg$
$\large{ r }$ = Radius	$in$	$mm$

Moment of Inertia of a Sphere Formula, Hollow Core Sphere
$I \;=\; \dfrac{2}{5} \cdot m \cdot r^2 \cdot \dfrac{ r_2^5 - r_1^5 }{ r_2^3 - r_1^3 }$
Symbol	English	Metric
$\large{ I }$ = Moment of Inertia	$lbm\;/\;ft^2-sec$	$kg\;/\;m^2$
$\large{ m }$ = Mass	$lbm$	$kg$
$\large{ r }$ = Radius	$in$	$mm$
$\large{ r_1 }$ = Radius	$in$	$mm$
$\large{ r_2 }$ = Radius	$in$	$mm$

Moment of Inertia of a Sphere

Moment of Inertia of a Sphere Formula, Solid Sphere

Moment of Inertia of a Sphere Formula, Hollow Sphere

Moment of Inertia of a Sphere Formula, Hollow Core Sphere

Similar Articles

Latest Articles

Login Form

Moment of Inertia of a Sphere

Moment of Inertia of a Sphere Formula, Solid Sphere

Moment of Inertia of a Sphere Formula, Hollow Sphere

Moment of Inertia of a Sphere Formula, Hollow Core Sphere

Similar Articles

Latest Articles