Question

why does moment of inertia increases when we stretch our hands on rotating chair​

Answer 1

When we stretch our hands on rotation, the radius of us, as a rotational body, increases.

We have the formula for moment of inertia,

I = mr²

where m is the mass of our body and r the radius.

Since our mass, m, is a constant, we can say that the moment of inertia is directly proportional to the second power of radius. This is why the moment of inertia increases.