# Wolfram Language™

## Moment of Inertia

Explore new capabilities covering physical parameters of a rigid body, including rotational inertia.

In:= `wrench = ExampleData[{"Geometry3D", "Wrench"}, "Region"]`
Out= Pick a point for the wrench to rotate about.

In:= `point = {-8, -0.168, 0};`
In:= ```Show[wrench, Graphics3D[{PointSize[Large], Point[point]}], ViewPoint -> {0, -\[Infinity], 0}]```
Out= The inertia matrix centered at this point.

In:= `\[ScriptCapitalI] = MomentOfInertia[wrench, point]`
Out= Find the principal axes, the axes a body tends to rotate about.

In:= `principalaxes = Eigenvectors[\[ScriptCapitalI]]`
Out= Find the inertia ellipsoid whose radii indicate the relative resistance to accelerate about a principal axis.

In:= `inertiaellipsoid = Ellipsoid[point, 1000 Inverse[\[ScriptCapitalI]]]`
Out= Show the wrench with its principal axes and inertia ellipsoid. The wrench arm stretches the ellipsoid along its axis.

show complete Wolfram Language input
In:= ```axes = Graphics3D[{Opacity, Arrowheads[{-0.04, 0.04}], {Specularity[Gray, 10], Gray, inertiaellipsoid}, MapThread[{RGBColor[#2], Arrow[Tube[{point - 4 #, point + 4 #}, .06]]} &, {principalaxes, IdentityMatrix}]}];```
In:= `Show[wrench, axes, BaseStyle -> Opacity[0.3]]`
Out= 