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Does anyone know what the rotational inertia of a cube of uniform density is when it is rotated about an edge? Any help is appreciated!
I suggest you start with the definition of rotational inertia of a rigid body of uniform density.Does anyone know what the rotational inertia of a cube of uniform density is when it is rotated about an edge? Any help is appreciated!
You need to be able to derive the equation; you can't look it up (in your textbook, etc.)?I'd use the parallel axis theorem but I don't know how to find the rotational inertia for a cube about it's center of mass.
So would it be [tex][tex]
I = \int r^2 \,dm = \rho \int r^2 \,dV
[/tex]
where [itex]\rho[/itex] is the density of the cube (assumed to be uniform).
You can then convert r into a Cartesian equivalent, then split dV into dx, dy, dz and do a triple integral.
You can use the rotational inertia of a thin plate around the axis perpendicular to the plane of the plate to derive the moment of inertia of a cube around an edge.Does anyone know what the rotational inertia of a cube of uniform density is when it is rotated about an edge? Any help is appreciated!