KEVOS® MAKEOS · Mechanics
Mass Moment of Inertia
What is the mass moment of inertia of this body about the chosen axis?
Mass moment of inertia and radius of gyration of common solids, with the parallel-axis transfer to an offset axis, for drive sizing and acceleration.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Body and axis | choice | The body and the axis it rotates about. |
| Mass | kg | Mass of the body. |
| Dimension A (outer diameter, or side a, or rod length) | mm | Outer diameter (disc, ring, cylinder, sphere), side a (block) or length (rod). |
| Dimension B (inner diameter, length, or side b) | mm | Inner diameter (ring), length (cylinder across), side b (block); not used for disc, sphere or rod. |
| Offset of rotation axis from centre (parallel axis) | mm | Distance between the body’s own central axis and the actual (parallel) rotation axis; 0 if it rotates about its centre. |
Method and formulas
- Disc ½mr²; ring ½m(rₒ² + rᵢ²); cylinder across m(3r² + L²) ÷ 12; block m(a² + b²) ÷ 12; sphere ⅖mr²; rod about end mL² ÷ 3.
- Parallel axis: J = J_c + m d².
- Radius of gyration k = √(J ÷ m).
- Example: a 10 kg, 300 mm disc has J = 0.1125 kg·m².
Limitations
- Uniform density and the idealised shape are assumed; holes and features change the result.
- The rod formula already refers to the end axis; the offset is added from that axis.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a motor for a rotary table, roller or disc
- Find inertia of a part about a pivot
- Compare inertia of design options
Who it is for
- Automation engineers
- Design engineers
What you get
- Moment of inertia about the body axis
- Moment of inertia about the offset axis
- Radius of gyration
Interpreting the result
- Use the inertia with the motor’s rotor inertia and any gear ratio to check acceleration.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 228–240. Topic reference; no source tables or recommended settings are reproduced.
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