Introduction

The Moment of Inertia Calculator allows users to compute the moment of inertia for various geometric shapes by inputting their properties. Supported shapes include rectangles, polygons, circles, and circle sectors.

Getting Started

Open the App: Navigate to the application page.
Select a Shape: Choose the shape you want to analyze.
Enter Input Values: Input the required coordinates and dimensions.

Use the Action Buttons:
- Add Area: Adds a new geometric area to the calculation.
- Add Gap: Adds a void or cut-out in the shape.
- Clear All: Resets the entire calculation.
View Results: The app calculates the moment of inertia and updates the display dynamically.

Results Table

Each area added to the calculation is listed in a table displaying the following parameters: Gx, Gy, A, Ix, Iy, Ixy, and I0. These values represent the geometric properties of each area used in the moment of inertia calculation. To remove an area, simply click the delete icon in its row.

Calculation of Moment of Inertia

The total moment of inertia is determined using the parallel axis theorem:

Ix = Σ (Ix + A * dx²)

Iy = Σ (Iy + A * dy²)

Ixy = Σ (Ixy + A * dx * dy)

I0 = Σ (I0 + A * r²)

IxG = Σ (IxG + A * dxG²)

IyG = Σ (IyG + A * dyG²)

IxyG = Σ (IxyG + A * dxG * dyG)

IG = Σ (IG + A * rG²)

Graphical Representation

Each time you add or remove an area, the figure is dynamically redrawn to reflect the updated shape. The final combined structure is displayed for reference.

Note:

Ensure all values are entered correctly.
For polygons, enter coordinates in counter-clockwise order.
The application updates calculations dynamically based on the inputs.

Troubleshooting

If the moment of inertia does not display, check if all required inputs are provided.
Ensure valid numerical values are entered for each field.

Conclusion

This app provides an intuitive interface for determining the moment of inertia of various shapes. If you encounter any issues, refer to the input guide or reach out for support.