MOI Of Disc about center | Rotation Motion | Class 11th | PHYSICS | JEE MAINS | NEET | DERIVATION

MOI Of Disc about center | Rotation Motion | Class 11th | PHYSICS | JEE MAINS | NEET | DERIVATION CBSE | HP Board |

The moment of inertia (MOI) of a disc (or cylinder) about its central axis (axis of rotation) is:

MOI = (1/2) × M × R²

where:

M is the mass of the disc
R is the radius of the disc

This formula is similar to the one for a ring, but with a factor of 1/2. This is because the disc has a more uniform distribution of mass across its radius, whereas a ring has all its mass concentrated at the edge.

Note that this formula assumes a uniform density and a thin disc. If the disc has a non-uniform density or a thick cross-section, the formula would be more complex.

Also, keep in mind that the MOI about the center is different from the MOI about other axes, like the MOI about a diameter or a tangent to the disc. Each axis has its own unique MOI value!

Here are some more MOI formulas for discs:

MOI about a diameter: (1/4) × M × R²
MOI about a tangent: (1/2) × M × R² + M × R² = (3/2) × M × R²

Let me know if you have any other questions!