Why Does Rotational Inertia Depend on Mass Distance from the Axis?

[Bashyboy]

Hello,

I was curious to know if there was some intuitive out-look on why rotational inertia depends on the distance of the mass from the axis of rotation; and why is this distance have to be squared?

 

[sankalpmittal]

Hello,

I was curious to know if there was some intuitive out-look on why rotational inertia depends on the distance of the mass from the axis of rotation; and why is this distance have to be squared?

Moment of Inertia I = mr²

Moment of inertia do same work for rotational motion as , inertia for linear motion.

Since moment of inertia is tendency of body to maintain its initial state of rotation , so it has to depend on distance from axis of rotation also. Remember , torque is force times perpendicular distance of line of action from axis of rotation. As torque depends on the distance "r" , so body's tendency to maintain its rotation has also to depend on distance "r".

And this distance is squared due to dimensional analysis.

Let torque T depend on moment of inertia and angular acceleration. (You know it!)

Equate the dimensions. You'll see that distance has to be squared in moment of inertia.