The formula to calculate Moment of Inertia (I) is:
\[ I = \frac{M \cdot L^2}{12} \]
Where:
Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
Mass of body is the quantity of matter in a body regardless of its volume or of any forces acting on it.
The length of rod is the size of the rod from one end to another end (how long the rod is).
Let's assume the following values:
Using the formula:
\[ I = \frac{M \cdot L^2}{12} \]
Evaluating:
\[ I = \frac{12.6 \cdot 10^2}{12} \]
The Moment of Inertia is 105 kg·m².
| Mass of Body (M, kg) | Length of Rod (L, m) | Moment of Inertia (I, kg·m²) |
|---|---|---|
| 10 | 8 | 53.3333 |
| 10 | 9 | 67.5000 |
| 10 | 10 | 83.3333 |
| 10 | 11 | 100.8333 |
| 10 | 12 | 120.0000 |
| 11 | 8 | 58.6667 |
| 11 | 9 | 74.2500 |
| 11 | 10 | 91.6667 |
| 11 | 11 | 110.9167 |
| 11 | 12 | 132.0000 |
| 12 | 8 | 64.0000 |
| 12 | 9 | 81.0000 |
| 12 | 10 | 100.0000 |
| 12 | 11 | 121.0000 |
| 12 | 12 | 144.0000 |
| 13 | 8 | 69.3333 |
| 13 | 9 | 87.7500 |
| 13 | 10 | 108.3333 |
| 13 | 11 | 131.0833 |
| 13 | 12 | 156.0000 |
| 14 | 8 | 74.6667 |
| 14 | 9 | 94.5000 |
| 14 | 10 | 116.6667 |
| 14 | 11 | 141.1667 |
| 14 | 12 | 168.0000 |
| 15 | 8 | 80.0000 |
| 15 | 9 | 101.2500 |
| 15 | 10 | 125.0000 |
| 15 | 11 | 151.2500 |
| 15 | 12 | 180.0000 |