Description
Apply the parallel-axis theorem to two parallel rotation axes separated by an explicit distance.
A mechanics calculation needs a coordinate frame, sign convention, and consistent force, length, mass, and time units. Vector projections, local balance terms, and ideal motion equations describe particular parts of a physical model. They do not automatically establish all equilibrium conditions or the validity of the model.
Apply the parallel-axis theorem to two parallel rotation axes separated by an explicit distance.
When to use this tool
Use Inertia Parallel Axis Contribution when you need this particular projection, balance, frame conversion, or ideal-model component from supplied physical quantities.
How to use the tool and how it works
- Enter centroidInertia, mass, offset. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read increment, shiftedInertia. Use the output convention below.
For nonnegative centroidInertia and mass return increment=mass*offset^2 and shiftedInertia=centroidInertia+increment.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| centroidInertia | Centroid Inertia | Required. Finite number; minimum 0. |
| mass | Mass in a consistent unit for the stated model. | Required. Finite number; minimum 0. |
| offset | Offset | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| increment | Increment | Required. Finite number. |
| shiftedInertia | Shifted Inertia | Required. Finite number. |
{
"input": {
"centroidInertia": 2,
"mass": 3,
"offset": 2
},
"output": {
"increment": 12,
"shiftedInertia": 14
}
}Limitations and assumptions
- The parallel-axis theorem requires parallel axes and a centroidal starting inertia. Offset is a length, and geometry, axis identification, and the supplied centroidal inertia are not checked.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Use a complete force, motion, or energy model when a single contribution is insufficient. Check coordinate frames, idealizations, and dimensional consistency before combining calculated terms.
References
Similar or alternative tools
- Rotational Inertia Single Mass Contribution
Return the point-mass inertia contribution about a supplied nonzero axis through the origin.
- Angular Momentum Axis Share
Project a supplied three-component angular momentum onto a declared axis; a zero momentum has no directional share.