Description
Return the point-mass inertia contribution about a supplied nonzero axis through the origin.
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.
Return the point-mass inertia contribution about a supplied nonzero axis through the origin.
When to use this tool
Use Rotational Inertia Single Mass 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 mass, axis, position. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read perpendicularSquared, inertia. Use the output convention below.
Require nonnegative mass and three-component position and nonzero axis vectors. Compute perpendicularSquared=max(0,dot(position,position)-dot(position,axis)^2/dot(axis,axis)) and inertia=mass*perpendicularSquared.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| mass | Mass in a consistent unit for the stated model. | Required. Finite number; minimum 0. |
| axis | Nonzero three-component direction of the axis through that origin. | Required. Array of finite number; maximum items 256. |
| position | Three position components relative to an origin on the axis. | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| perpendicularSquared | Perpendicular Squared | Required. Finite number. |
| inertia | Inertia | Required. Finite number. |
{
"input": {
"mass": 2,
"axis": [
0,
0,
1
],
"position": [
3,
4,
5
]
},
"output": {
"perpendicularSquared": 25,
"inertia": 50
}
}Limitations and assumptions
- The axis passes through the position origin; position uses one length unit and inertia uses mass times length squared. The zero clamp limits cancellation artifacts but is not a geometric tolerance or a complete body's inertia calculation.
- 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
- Inertia Parallel Axis Contribution
Apply the parallel-axis theorem to two parallel rotation axes separated by an explicit distance.
- Buoyancy Apparent Mass Density Factor
For nonnegative mass and fluidDensity and positive objectDensity return displacedMass=mass*fluidDensity/objectDensity and apparentMass=mass-displacedMass.