### Moment Of Inertia And Theorems Of Perpendicular And Parallel Axes

**Moment of Inertia, Perpendicular and Parallel Axes Theorems:**

**Parallel Axis Theorem**:

- Moment of inertia about an axis = Moment of inertia about parallel centroidal axis + (total mass) x (square of distance between the two axes)

**Perpendicular Axis Theorem**:

- Moment of inertia about axis perpendicular to a line through COM = Sum of moments of inertia about two axes parallel to the line through the COM

**Parallel Axis Theorem for a Uniform Rod**:

- Moment of inertia of a rod about an axis perpendicular to the rod through one end = (1/3) x (mass of rod) x (length of rod)^2

**Important Points:**

- Moment of inertia depends on mass distribution and rotation axis.
- It measures the resistance of an object to angular acceleration.
- Moment of inertia of a system of particles equals the sum of individual particle moments of inertia.
- A hollow object’s moment of inertia is greater than a solid object of the same mass and shape.