Moment of Inertia of a Cylinder

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Moment of Inertia of a Cylinder Index

 

 

 

 

 

 

Moment of Inertia of a Cylinder Formula, Hollow Cylinder

\( I_z = m \; r^2 \) 
Symbol English Metric
\( I \) = moment of inertia \(lbm \;/\; ft^2-sec\) \(kg \;/\; m^2\)
\( m \) = mass \( lbm \) \( kg \)
\( r \) = radius \( in \) \( mm \)

 

Moment of Inertia of a Cylinder Formulas, Solid Cylinder

\( I_z = \frac{1}{2}\; m \; r^2 \) 

\( I_x = I_y = \frac {1}{12} \;m \; ( 3\;r{^2} + l^2 ) \) 

Symbol English Metric
\(\large{ I }\) = moment of inertia \(lbm \;/\; ft^2-sec\) \(kg \;/\; m^2\)
\(\large{ l }\) = length \( in \) \( mm \)
\(\large{ m }\) = mass \( lbm \) \( kg \)
\(\large{ r }\) = radius \( in \) \( mm \)

 

Moment of Inertia of a Cylinder Formulas, Hollow Core Cylinder

\( I_z = \frac {1}{12}\; m \; ( r_1{^2}  + r_2{^2} ) \) 

\( I_x = I_y = \frac {1}{12} \;m \; ( 3 \; ( r_2{^2}  + r_1{^2} )  + l^2 )  \) 
Symbol English Metric
\(\large{ I }\) = moment of inertia \(lbm \;/\; ft^2-sec\) \(kg \;/\; m^2\)
\(\large{ l }\) = length \( in \) \( mm \)
\(\large{ m }\) = mass \( lbm \) \( kg \)
\(\large{ r_1 }\) = radius \( in \) \( mm \)
\(\large{ r_2 }\) = radius \( in \) \( mm \)

 

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Tags: Moment of Inertia