PHYIC CALCULATOR
Rotational Inertia of a Sphere Calculator
A precise tool.
What is the Rotational Inertia of a Sphere Calculator & How does it work?
The moment of inertia is a measure of an object’s resistance to changes in its rotation. For a solid sphere, the moment of inertia about an axis through its center is given by the formula:
I = frac{2}{5}mr^2
I = Moment of Inertia, m = Mass, r = Radius
This formula is derived from the integration of mass elements over the volume of the sphere, considering their distances from the axis of rotation.
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Result
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Frequently Asked Questions
What is the formula for the moment of inertia of a solid sphere?
The formula for the moment of inertia of a solid sphere about an axis through its center is I = (2/5)mr^2, where m is the mass and r is the radius.
How do I use this calculator to find the moment of inertia?
Enter the mass and radius of the sphere into the respective fields, then click calculate to get the moment of inertia.
What units should I use for mass and radius?
Use kilograms (kg) for mass and meters (m) for radius to get the moment of inertia in kilogram-square meters (kg·m²).
Can this calculator be used for hollow spheres?
No, this calculator is specifically for solid spheres. For hollow spheres, a different formula would apply.
Why is the moment of inertia important in physics?
The moment of inertia is crucial as it determines how difficult it is to change an object’s rotational motion, affecting angular acceleration and torque calculations.
Results are for informational purposes only and do not constitute professional advice.