Why is moment of inertia varyiing with the square of the radius?

In summary, moment of inertia is defined as the product of mass and the square of the radius. This definition is derived from an energy method, as explained in the general principles section for moment of inertia in the PF library.
  • #1
gnanasenthil6
1
0
why is moment of inertia varyiing with the square of the radius??

hello,
where ever i search moment of inertia on the web or on textbooks ,it starts with a definition saying that it is the product of mass the square of the radius.

my question is why is moment of inertia defined like mass times square of the radius.
if someone can help me to understand moment of inertia intutively please??
 
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  • #2


If you read the general principles section for moment of inertia (click on 'moment of inertia') in the PF library, they have a proof as to how they arrived at I= ∫r2 dm using an energy method.
 

FAQ: Why is moment of inertia varyiing with the square of the radius?

Why does the moment of inertia vary with the square of the radius?

The moment of inertia is a measure of an object's resistance to rotational motion. It depends on the mass and distribution of mass around the axis of rotation. Since the distribution of mass increases as the square of the distance from the axis of rotation, the moment of inertia also increases with the square of the radius.

What is the formula for calculating moment of inertia?

The formula for moment of inertia is I = mr^2, where m is the mass of the object and r is the distance from the axis of rotation.

How does moment of inertia affect an object's rotational motion?

An object with a higher moment of inertia will require more torque to accelerate its rotational motion compared to an object with a lower moment of inertia. This means that the object with a higher moment of inertia will be more difficult to rotate.

Can the moment of inertia be negative?

No, the moment of inertia cannot be negative. It is a physical property that reflects an object's resistance to rotational motion and therefore must be a positive value.

How does the moment of inertia vary for different shapes?

The moment of inertia varies for different shapes because the distribution of mass around the axis of rotation is different. For example, a solid sphere has a higher moment of inertia compared to a hollow sphere of the same mass and radius, since more mass is distributed farther from the axis of rotation in a solid sphere.

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