1. What is Rotational Moment of Inertia?

The rotational moment of inertia (I) is a measure of an object's resistance to changes in its rotational motion. For a hollow rectangle, it depends on the outer and inner dimensions of the shape.

2. How Does the Calculator Work?

The calculator uses the formula for hollow rectangular sections:

Where:

• \( b \) — Outer width (m)
• \( h \) — Outer height (m)
• \( b_i \) — Inner width (m)
• \( h_i \) — Inner height (m)
• \( I \) — Rotational moment of inertia (kg·m²)

Explanation: The formula calculates the difference between the inertia of the outer rectangle and the inner hollow portion.

3. Importance of Rotational Moment of Inertia

Details: Rotational moment of inertia is crucial in mechanical engineering for designing rotating components, analyzing structural stability, and predicting rotational behavior under torque.

4. Using the Calculator

Tips: Enter all dimensions in meters. Outer dimensions must be larger than inner dimensions. For solid rectangles, set inner dimensions to zero.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between solid and hollow rectangle inertia?
A: Hollow sections typically have higher inertia-to-weight ratios, making them more efficient for many structural applications.

Q2: How does orientation affect the moment of inertia?
A: The moment of inertia depends on the axis of rotation. This formula assumes rotation about the centroidal axis parallel to the width.

Q3: What are typical applications of this calculation?
A: Used in designing beams, columns, machine frames, and any structural component with hollow rectangular cross-sections.

Q4: How does wall thickness affect the result?
A: Thicker walls (smaller inner dimensions relative to outer) increase the moment of inertia for a given outer dimension.

Q5: Can this be used for non-rectangular hollow sections?
A: No, different formulas apply for circular, elliptical, or other shaped hollow sections.