Statics/Geometric Properties of Solids

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Mass Moments Of Inertia Of Common Geometric Shapes[edit]

Slender Rod[edit]

 I_x = 0

 I_y = I_z = \frac {1}{12} ml^2

Thin Quarter-Circular Rod[edit]

 I_x = I_z = mr^2 (\frac {1}{2} - \frac {4}{\pi^2})

 I_y = mr^2 (1 - \frac {8}{\pi^2})

Thin Ring[edit]

 I_x = I_y = \frac {1}{2}mr^2

 I_z = mr^2

Sphere[edit]

 I_x = I_y = I_z = \frac {2}{5} mr^2

Hemisphere[edit]

 I_x = I_y = \frac {83}{320} mr^2

 I_z = \frac {2}{5} mr^2

Thin Circular Disk[edit]

 I_x = I_y = \frac {1}{4} mr^2

 I_z = \frac {1}{2} mr^2

Rectangular Prism[edit]

 I_x = \frac {1}{12} m \left ( b^2 + c^2 \right )

 I_y = \frac {1}{12} m \left ( a^2 + c^2 \right )

 I_z = \frac {1}{12} m \left ( a^2 + b^2 \right )

Right Circular Cylinder[edit]

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

 I_z = \frac {1}{2} mr^2

Right Half Cylinder[edit]

 I_x = \frac {1}{12} mh^2 + mr^2( \frac {1}{4} - \frac {16}{9\pi^2})

 I_y = \frac {1}{12} mh^2 + \frac {1}{4}mr^2

 I_z = mr^2( \frac {1}{2} - \frac {16}{9\pi^2})

Thin Rectangular Plate[edit]

 I_x = \frac {1}{12} mb^2

 I_y = \frac {1}{12} ma^2

 I_z = \frac {1}{12} m(a^2 + b^2)

Right Circular Cone[edit]

 I_x = I_y = \frac {3}{80} m ({4}{r^2} + h^2)

 I_z = \frac {3}{10} mr^2

Right Tetrahedron[edit]

 I_x = \frac {3}{80} m (b^2+c^2)

 I_y = \frac {3}{80} m (a^2+c^2)

 I_z = \frac {3}{80} m (a^2+b^2)

further reading[edit]