Moment of Inertia of a Circle

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

moment of inertia Flat Solid Disk 1Formulas that use Circle, Hollow Plane

\(\large{ I_z = m \; r^2 }\)   

Where:

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

\(\large{ m }\) = mass

\(\large{ r }\) = radius

  

Formulas that use Circle, Solid Plane

\(\large{ I_z = \frac {1}{2}\; m \; r^2 }\)   
\(\large{ I_z = \frac {1}{2}\; \pi \; r^4 }\)   
\(\large{ I_x = I_y = \frac {1}{4} \;m \; r^4 }\)   
\(\large{ I_x = I_y = \frac {1}{4}\; \pi \; r^4 }\)  
\(\large{ I_x = I_y = \frac {1}{64}\; d^4 }\)  

Where:

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

\(\large{ d }\) = diameter

\(\large{ m }\) = mass

\(\large{ \pi }\) = Pi

\(\large{ r }\) = radius

 

Tags: Equations for Moment of Inertia