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top12eaper

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In summary, the conversation is about calculating the inertia for a cylinder and subtracting it from the inertia of a rectangle. However, the person is having trouble finding an equation for the inertia of a rectangle when the plane is spinning perpendicular to the rotation axis. They ask for help and are told to refer to a wiki page or look for information elsewhere. The person then explains that the equation for the inertia is given for the x and y axis, but in their case, the axis pierces the plane of the rectangle. They are asked if they know how to do double integrals, and if so, the formula can be derived from first principles. If not, they are left with no solution.

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top12eaper

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sophiecentaur

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Which axis do you want?

Does this wiki page help? Have you looked anywhere else for this info?

Does this wiki page help? Have you looked anywhere else for this info?

- #3

top12eaper

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dont think so, they give me the equation for the inersia about the x and y axis, in my case the axis pierces the plane of the rectangel.sophiecentaur said:Which axis do you want?

Does this wiki page help? Have you looked anywhere else for this info?

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Nidum

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Do you know how to do double integrals ?

If yes then we can derive the formula from first principles .

If no then :

or

If yes then we can derive the formula from first principles .

If no then :

or

Last edited:

The moment of inertia of a cylinder with a rectangular hole refers to the resistance of the object to changes in its rotational motion. It is a measure of the distribution of mass around the axis of rotation and is affected by both the shape and size of the hole.

The moment of inertia for a cylinder with a rectangular hole can be calculated by summing the individual moments of inertia of the solid cylinder and the rectangular hole. The formula for moment of inertia is I = mr², where m is the mass and r is the distance from the axis of rotation.

The size of the rectangular hole has a direct impact on the moment of inertia of the cylinder. A larger hole will result in a smaller moment of inertia, meaning that the object will be easier to rotate. On the other hand, a smaller hole will result in a larger moment of inertia, making it more difficult to rotate the object.

Calculating the moment of inertia for a cylinder with a rectangular hole is important in understanding the object's rotational behavior. It can help predict how the object will respond to external forces and how much torque is needed to rotate it.

Yes, the moment of inertia for a cylinder with a rectangular hole can be changed by altering the size and shape of the hole. For example, increasing the size of the hole or changing it from a rectangle to a circle will decrease the moment of inertia, while decreasing the size or changing it to a more complex shape will increase the moment of inertia.

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