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montreal1775
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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!
montreal1775 said: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!
montreal1775 said: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.
Saketh said:[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.
montreal1775 said: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!
Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. It is a property that depends on an object's mass, shape, and distribution of mass.
The rotational inertia of a cube can be calculated using the formula I = (1/6) * M * (a^2 + b^2), where I is the rotational inertia, M is the mass of the cube, and a and b are the length of two adjacent sides.
The shape of a cube plays a significant role in determining its rotational inertia. A cube with a larger mass and longer sides will have a greater rotational inertia compared to a cube with a smaller mass and shorter sides.
Rotational inertia is directly proportional to rotational motion. This means that objects with a higher rotational inertia will require more torque to accelerate or decelerate their rotational motion compared to objects with a lower rotational inertia.
The rotational inertia of a cube can be changed by altering its mass, shape, or distribution of mass. For example, increasing the mass or length of the sides will increase the rotational inertia, while decreasing these factors will decrease the rotational inertia.