List of moment of inertia tensors

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This list of moment of inertia tensors is given for principal axes of each object.

Description Figure Moment of inertia tensor
Solid sphere of radius r and mass m Image:moment of inertia solid sphere.png I = \begin{bmatrix} \frac{2}{5} m r^2 & 0 & 0 \\ 0 & \frac{2}{5} m r^2 & 0 \\ 0 & 0 & \frac{2}{5} m r^2 \end{bmatrix}
Hollow sphere of radius r and mass m Image:moment of inertia solid sphere.png

I = \begin{bmatrix} \frac{2}{3} m r^2 & 0 & 0 \\ 0 & \frac{2}{3} m r^2 & 0 \\ 0 & 0 & \frac{2}{3} m r^2 \end{bmatrix}

Right circular cone with radius r, height h and mass m, about the center of the base Image:moment of inertia cone.png I = \begin{bmatrix} \frac{1}{10} m h^2 + \frac{3}{20} m r^2 & 0 & 0 \\ 0 & \frac{1}{10} m h^2 + \frac{3}{20} m r^2 & 0 \\ 0 & 0 & \frac{3}{10} m r^2 \end{bmatrix}
Solid cuboid of width w, height h, depth d, and mass m Image:moment of inertia solid rectangular prism.png I = \begin{bmatrix} \frac{1}{12} m (h^2 + d^2) & 0 & 0 \\ 0 & \frac{1}{12} m (w^2 + d^2) & 0 \\ 0 & 0 & \frac{1}{12} m (w^2 + h^2) \end{bmatrix}
slender rod of length l and mass m about end Image:Moment of inertia rod end.png

I = \begin{bmatrix} \frac{1}{3} m l^2 & 0 & 0 \\ 0 & \frac{1}{3} m l^2 & 0 \\ 0 & 0 & 0 \end{bmatrix}

Slender rod of length l and mass m about center Image:Moment of inertia rod center.png

I = \begin{bmatrix} \frac{1}{12} m l^2 & 0 & 0 \\ 0 & \frac{1}{12} m l^2 & 0 \\ 0 & 0 & 0 \end{bmatrix}

Solid cylinder of radius r, height h and mass m Image:Moment of inertia solid cylinder.png

I = \begin{bmatrix} \frac{1}{12} m (3r^2+h^2) & 0 & 0 \\ 0 & \frac{1}{12} m (3r^2+h^2) & 0 \\ 0 & 0 & \frac{1}{2} m r^2\end{bmatrix}

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