How to find the moment of inertia of a cube?

In summary, to find the moment of inertia for a rigid cube rotated about an axis with dimensions L x W x H centimeters, you can use the formula I_P = \int_V \rho(\mathbf{r})\,\mathbf{r}^2 \, dV, where \mathbf{r} is the radius vector to a point in the cube from the axis passing through P. Alternatively, you can refer to a list of moments of inertia for common bodies and axes.
  • #1
geekie weekie
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Hello,

If I have a rigid cube rotated about an axis with dimensions L x W x H centimeters, how can we find the moment of inertia?

Thank you.
 
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  • #2
You can calculate the moment of rotational inertia of a body rotating about an axis passing through a point [itex]P[/itex] using the formula:[tex] I_P = \int_V \rho(\mathbf{r})\,\mathbf{r}^2 \, dV[/tex] where [itex]\mathbf{r}[/itex] is the radius vector to a point in the body from the axis passing through [itex]P[/itex]. See here: http://en.wikipedia.org/wiki/Moment_of_inertia

You can often look up the moments of inertia for some typical bodies rotating around typical axes:
http://en.wikipedia.org/wiki/List_of_moments_of_inertia
 

1. What is the formula for finding the moment of inertia of a cube?

The formula for finding the moment of inertia of a cube is I = (1/6) * m * a^2, where m is the mass of the cube and a is the length of one side.

2. How do I determine the mass of the cube?

The mass of the cube can be determined by weighing it on a scale or by using the formula m = ρ * V, where ρ is the density of the material and V is the volume of the cube.

3. Is the moment of inertia the same for all axes of rotation?

No, the moment of inertia for a cube will differ depending on which axis of rotation is being considered. The formula for moment of inertia is different for each axis.

4. Can I use the same formula to find the moment of inertia for any cube, regardless of its size?

Yes, the formula for finding the moment of inertia of a cube is applicable to all cubes, regardless of their size. However, the mass and length of one side must be measured accurately for the formula to be accurate.

5. How does the moment of inertia of a cube affect its rotational motion?

The moment of inertia of a cube determines how easily it can be rotated around an axis. A larger moment of inertia means the cube will resist rotational motion more, while a smaller moment of inertia means the cube will rotate more easily.

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