When to use this calculator
Find rotational inertia of a uniform solid sphere about its centre. Uniform solid sphere rotating about a diameter.
Explore the force, energy & machines calculators for other questions in this topic. For a related calculation, use the Spring Energy Calculator: Find elastic energy stored in a linear spring.
PUTTING IT INTO PRACTICE
Solid Sphere Moment of Inertia: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Sphere mass (kg) | 10 |
| Radius (m) | 2 |
| Result | 16 kg·m² |
- Check the input labels and enter the example values above.
- Apply the relationship: I = 2 × mass × radius²/5.
- The result is 16 kg·m², rounded for display.
How to interpret your result
Uniform solid sphere rotating about a diameter.
Distinguish net force from individual forces and specify the direction of displacement. Work can be negative. Force multiplication does not create extra energy because motion distance and losses also matter.
Frequently asked questions
Is mechanical advantage the same as efficiency?
No. Mechanical advantage compares forces; efficiency compares useful output energy or power with the corresponding input.
When is the solid sphere moment of inertia calculator useful?
Find rotational inertia of a uniform solid sphere about its centre. Uniform solid sphere rotating about a diameter.
How do I use the solid sphere moment of inertia calculator?
Enter sphere mass (kg), radius (m). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
I = 2 × mass × radius²/5.
What should I check before using the result?
Uniform solid sphere rotating about a diameter.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see OpenStax: work and energy ↗. This is a topic reference, not an external review or endorsement of this tool.
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