How is the moment of inertia related to the square of the distance?

AI Thread Summary
The moment of inertia (I) is defined by the equation I = MR², indicating that it is directly proportional to both mass (M) and the square of the distance (R) from the axis of rotation. An increase in mass results in greater inertia, while a decrease leads to less inertia, provided the distance remains constant. The relationship to the square of the distance arises because the torque needed to achieve a certain rotational acceleration increases with the distance of the mass from the axis. This means that the further the mass is from the axis, the more difficult it is to rotate the object. Understanding this relationship is crucial for analyzing rotational dynamics.
Hardik Batra
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Moment of inertia is
I = MR2
object has more mass means more inertia and less mass means less inertia.
That means moment of inertia is directly proportional to mass.
But how the moment of inertia is directly proportional to the square of the distance.?
 
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Hardik Batra said:
Moment of inertia is
I = MR2
For a point mass, not in general.

Hardik Batra said:
object has more mass means more inertia and less mass means less inertia.
OK.

Hardik Batra said:
That means moment of inertia is directly proportional to mass.
Only if the distance to the axis--the R--is fixed.

Hardik Batra said:
But how the moment of inertia is directly proportional to the square of the distance.?
It's a measure of the torque required to produce a given rotational acceleration. Loosely: The further the mass is from the axis, the harder it is to get it to rotate.
 
but why it is square of the distance rather than only distance.
 
Thanks. It helpful for me.
 

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