# Moment of Inertia: Proving Mass, Side & Axis | 1/12 md²

• Chadi B Ghaith
In summary, we have a uniform square of mass m and side d, and we need to prove that its moment of inertia about an axis through its centre, parallel to a side, is equal to 1/12 md². The proof involves integrating the definition of moment of inertia and the outcome of the calculation will serve as our proof.
Chadi B Ghaith
I need help to prove that the moment of inertia of a uniform square of mass m and side d about an axis through its centre, parallel to a side is 1/12 md²

Chadi B Ghaith said:
I need help to prove that the moment of inertia of a uniform square of mass m and side d about an axis through its centre, parallel to a side is 1/12 md²
OK, what kind of help ? You know the definition of moment of inertia ? It amounts to an integration; does that pose a problem ? Write it out and we'll help you further.

BvU said:
OK, what kind of help ? You know the definition of moment of inertia ? It amounts to an integration; does that pose a problem ? Write it out and we'll help you further.
Hi,
Yes I know the definition of inertia. What I am asking is how to prove the above statement. I am bit confuse in procedure.

Good you know it. Write down the integral and attempt to do the integration in your next post. The outcome of your calculation is your 'proof'.

## What is moment of inertia?

Moment of inertia is a physical property of a rotating object that describes its resistance to changes in its rotational motion.

## How is moment of inertia calculated?

Moment of inertia is calculated by multiplying the mass of the object by the square of its distance from the axis of rotation.

## What is the significance of proving mass, side, and axis when calculating moment of inertia?

Proving the mass, side, and axis is important because these factors directly affect the calculation of moment of inertia. Without accurate values for these parameters, the moment of inertia calculation will be incorrect.

## What are some real-world applications of moment of inertia?

Moment of inertia is used in various engineering and physics applications, such as designing vehicles and machines that involve rotating components, analyzing the stability of structures, and understanding the motion of celestial bodies.

## How does changing the mass, side, or axis affect the moment of inertia?

Changing the mass or the distance from the axis of rotation will directly affect the moment of inertia, while changing the axis of rotation will require a more complex calculation. Generally, increasing the mass or distance from the axis will increase the moment of inertia, making the object more resistant to changes in rotational motion.

### Similar threads

• Mechanics
Replies
2
Views
679
• Mechanics
Replies
12
Views
628
• Mechanics
Replies
2
Views
1K
• Mechanics
Replies
5
Views
2K
• Mechanics
Replies
3
Views
2K
• Mechanics
Replies
10
Views
1K
• Mechanics
Replies
2
Views
1K
• Mechanics
Replies
10
Views
1K
• Mechanics
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
21
Views
2K