Match the diagram conditions, then follow the example inputs and results. Change numerical values in the calculator.
1. Match the diagram to your question
円板を中心軸のまわりに回す例です。回転軸の方向が変わると式も変わります。
外径Dと質量mを使います。この例は重心軸と回転軸が一致し、ずれeは0です。
回転する形状
円柱・円板（中心軸）
質量 m
10 kg
外径 D
100 mm
平行な回転軸までの距離 e
0 mm
Jは回しにくさです。梁のIではありません。同じ質量でも軸から離れて分布すると大きくなります。
指定軸の質量慣性 J
0.0125 kg·m²
重心軸の質量慣性 Jc
0.0125 kg·m²
平行軸による増分 me²
0 kg·m²
This disc rotates about its central axis. A different axis changes the formula.
Use outside diameter D and mass m. Here the rotation axis passes through the centroid, so offset e is zero.
Rotating shape
Solid cylinder / disk, centre axis
Mass m
10 kg
Outside diameter D
100 mm
Parallel-axis offset e
0 mm
J is rotational inertia, distinct from a beam’s I. Mass distributed farther from the axis increases J.
Mass inertia about the selected axis
0.0125 kg·m²
Centroidal mass inertia Jc
0.0125 kg·m²
Parallel-axis addition me²
0 kg·m²
Blue marks inputs; orange marks outputs. These diagrams explain the fixed example below; dimensions and deformation are not drawn to physical scale.
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2. Example inputs
Rotating shapeWhat goes here?
Choose the option matching your mechanism and diagram. A different model can change required inputs and applicable results.
Solid cylinder / disk, centre axis
Mass mWhat goes here?
This is mass, including fixtures or loads that move with it where required. Kilograms describe mass; newtons describe force.
10 kg
Outside diameter DWhat goes here?
Use the dimension marked in the diagram. Distinguish radius from diameter, bore from outside diameter, and overall length from support span.
100 mm
Parallel-axis offset eWhat goes here?
Use the dimension marked in the diagram. Distinguish radius from diameter, bore from outside diameter, and overall length from support span.
0 mm
These are fixed teaching inputs. Coefficients, properties and comparison limits are not recommendations. Enter your conditions in the calculator.
3. Results for this example
Mass inertia about the selected axis
0.0125 kg·m²
Centroidal mass inertia Jc
0.0125 kg·m²
Parallel-axis addition me²
0 kg·m²
Read J about the chosen axis first. Mass farther from the axis increases J. This differs in units and purpose from a beam’s second moment of area I.
4. Which formula is used?
Jc = mD²/8; J = Jc + me²
Table units are not always the units required in the formula. The calculator converts selected units to its internal base units before computing.
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Assumptions and exclusions
Uniform rigid bodies and the stated axis direction; a point mass has Jc=0. Mass inertia is different from the area second moment (mm⁴). Gear-ratio reflection is performed in the drive calculator.
