good day (daytime greeting)How to calculate the moment of inertia (inertia) of a rotating body and the calculation excel"Memo for.
Many websites explain the moment of inertia, but here we specialize in the moment of inertia of rotating bodies, and you can download an Excel file for calculating the moment of inertia explained in this article. Please take advantage of this service.
- Moment of inertia (inertia) of a rotating body
- Formula for calculating the moment of inertia when the axis of rotation of a rotating body passes through the center of gravity
- Formula for calculating the moment of inertia when the axis of rotation of a rotating body does not pass through the center of gravity
- Formula for calculating the moment of inertia of a cylinder
- Equation for the moment of inertia of a rectangular rotating body with its center of rotation away from the center of inertia
- Equation for calculating the moment of inertia of a rectangular rotating body with its center of rotation on its side
- Moment of Inertia Calculation Excel Download
Moment of inertia (inertia) of a rotating body
The moment of inertia is a physical quantity that expresses numerically the "hardness to turn" or "hardness to stop," which is necessary mainly to determine the required capacity of a drive source. Therefore, the following formula can be used to calculate the moment of inertia with a margin in the early stages of design to prevent significant time loss in the latter half of the design process. Here, we will calculate two units of inertia moment, "kg-m2" and "GD2".
Formula for calculating the moment of inertia when the axis of rotation of a rotating body passes through the center of gravity
Formula for calculating the moment of inertia of a cylinder
J moment of inertia (kg・m2)=1/8*(M*D^2)
GD2 moment of inertia (kgf-m2)=1/2*(M*D^2)
Formula for calculating the moment of inertia of a hollow cylinder
J moment of inertia (kg・m2)=1/8*(M*(D1^2+D2^2))
GD2 moment of inertia (kgf-m2)=1/2*(M*(D1^2+D2^2))
Formula for the moment of inertia of a rectangular rotating body
J moment of inertia (kg・m2)=1/12*(M*(a^2+b^2))
GD2 moment of inertia (kgf-m2)=1/3*(M*(a^2+b^2))
Formula for calculating the moment of inertia when the axis of rotation of a rotating body does not pass through the center of gravity
Formula for calculating the moment of inertia of a cylinder
J moment of inertia (kg-m2)=M/4*((1/2*D^2)+(4*R^2))
GD2 moment of inertia (kgf-m2)=M*((1/2*D^2)+(4*R^2))
Equation for the moment of inertia of a rectangular rotating body with its center of rotation away from the center of inertia
J moment of inertia (kg・m2)=M/4*(((b^2+a^2)/3)+(4*R^2))
GD2 moment of inertia (kgf-m2)=M*(((b^2+a^2)/3)+(4*R^2))
Equation for calculating the moment of inertia of a rectangular rotating body with its center of rotation on its side
J moment of inertia (kg-m2)=1/12*(M*((4*b^2)+(a^2)))
GD2 moment of inertia (kgf-m2)=1/3*M*((4*b^2)+(a^2))
Moment of Inertia Calculation Excel Download
Here you can download an Excel file containing the above formula for calculating the moment of inertia. Please feel free to use it.
This Excel formula is for the PTC Division of Sumitomo Heavy Industries, Ltd.MaterialsThe following table was prepared in reference to the following table.
That's it.