Moment of Inertia of a Cylinder

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

moment of inertia Cylinder 2moment of inertia Cylinder 1Hollow Cylinder formula

(Eq. 1)  \(\large{ I_z = m \; r^2 }\)        

Solid Cylinder formula

(Eq. 2)  \(\large{ I_z = \frac {1}{2}\; m \; r^2 }\)        

(Eq. 3)  \(\large{ I_x = I_y = \frac {1}{12} \;m \; \left( 3\;r{^2} + l^2  \right) }\)        

Hollow Core Cylinder formula

(Eq. 4)  \(\large{ I_z = \frac {1}{12}\; m \; \left( r_1{^2}  + r_2{^2}  \right) }\)        

(Eq. 5)  \(\large{ I_x = I_y = \frac {1}{12} \;m \; \left( 3 \; \left( r_2{^2}  + r_1{^2}  \right)  + l^2 \right)  }\)        

Where:

\(\large{ I }\) = moment of inertia

\(\large{ l }\) = length

\(\large{ m }\) = mass

\(\large{ r }\) = radius

\(\large{ r_1 }\) = radius

\(\large{ r_2 }\) = radius

 

Tags: Equations for Moment of Inertia