A uniform rod of mass `m` and length `l_(0)` is rotating with a constant angular speed `omega` about a vertical axis passing through its point of suspension. Find the moment of inertia of the rod about the axis of rotation if it make an angle `theta` to the vertical (axis of rotation).

Explanation

To find the moment of inertia of a uniform rod of mass \( m \) and length \( l_0 \) rotating about a vertical axis at an angle \( \theta \) to the vertical, we can follow these steps:

### Step 1: Define the Rod and its Orientation
Consider a uniform rod of length \( l_0 \) suspended at one end and making an angle \( \theta \) with the vertical. The axis of rotation is vertical and passes through the point of suspension.

### Step 2: Set Up the Element of Mass
We can consider a small element of the rod of length \( dl \) at a distance \( l \) from the point of suspension. The mass of this small element \( dm \) can be expressed as:
\[
...