Mass Moment Of Inertia Of Cuboid About Y Axis Passing Through Centroid Calculator

Formula Used:

\[ I_{yy} = \frac{M}{12} \times (L^2 + w^2) \]

Mass Moment of Inertia about Y-axis (I_yy):

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1. What is Mass Moment of Inertia about Y-axis?

The Mass Moment of Inertia about Y-axis (I_yy) of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis. For a cuboid, it represents the resistance to rotational motion about the y-axis passing through its centroid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ I_{yy} = \frac{M}{12} \times (L^2 + w^2) \]

Where:

\( I_{yy} \) — Mass Moment of Inertia about Y-axis (kg·m²)
\( M \) — Mass of the cuboid (kg)
\( L \) — Length of the cuboid (m)
\( w \) — Width of the cuboid (m)

Explanation: This formula calculates the moment of inertia for a cuboid about the y-axis passing through its centroid, considering both the length and width dimensions.

3. Importance of Mass Moment of Inertia Calculation

Details: Calculating mass moment of inertia is crucial in mechanical engineering and physics for analyzing rotational dynamics, designing rotating machinery, and predicting the behavior of objects under rotational forces.

4. Using the Calculator

Tips: Enter mass in kilograms, length and width in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between mass moment of inertia and area moment of inertia?
A: Mass moment of inertia relates to rotational motion and depends on mass distribution, while area moment of inertia relates to bending and depends on cross-sectional geometry.

Q2: Why is the formula divided by 12?
A: The factor of 1/12 comes from the integration of the mass distribution over the cuboid's volume when calculating the moment of inertia about the centroidal axis.

Q3: Can this formula be used for other shapes?
A: No, this specific formula applies only to rectangular cuboids. Different shapes have different moment of inertia formulas.

Q4: What are the typical units for mass moment of inertia?
A: The SI unit is kilogram-square meter (kg·m²). Other units include slug-ft² in the imperial system.

Q5: How does mass distribution affect moment of inertia?
A: Mass further from the axis of rotation contributes more to the moment of inertia. Objects with mass distributed farther from the axis have higher moment of inertia.