# Moment of Inertia of a Quarter Disc

• utsav55
In summary, the conversation discussed finding the Moment of Inertia of a Quarter Disc with mass M and radius R about the axis passing through the center and perpendicular to the plane. The attempt at a solution involved dividing the Moment of Inertia by 4, but initially gave the wrong answer. It was discovered that the incorrect mass was used, and after correcting it, the solution was found to be correct.
utsav55
1. Find the Moment of Inertia of a Quarter Disc which has mass M and radius R about the axis passing through the center (of original disc) and perpendicular to the plane.

2. The attempt at a solution
I found the Moment of Inertia (I) of a disc about the axis passing through the center, perpendicular to the plane and divided by 4. It gave the wrong answer.

So, please tell me that why dividing by 4 is giving me the wrong answer for the quarter disc.

Also, a hint of how should I start the problem.

Dividing by 4 is correct. Did you use the correct mass? (I suspect that's the problem.)

Doc Al said:
Dividing by 4 is correct. Did you use the correct mass? (I suspect that's the problem.)

Yes, I got it correct now.

Thanks

## 1. What is the moment of inertia of a quarter disc?

The moment of inertia of a quarter disc is a measure of its resistance to rotational motion. It takes into account the mass distribution and shape of the disc.

## 2. How is the moment of inertia of a quarter disc calculated?

The moment of inertia of a quarter disc can be calculated using the formula I = 1/2mr^2, where m is the mass of the disc and r is the radius of the disc.

## 3. Why is the moment of inertia of a quarter disc important?

The moment of inertia of a quarter disc is important because it helps in understanding the rotational motion of the disc and can be used in various engineering and physics applications.

## 4. How does the moment of inertia of a quarter disc compare to that of a full disc?

The moment of inertia of a quarter disc is generally smaller than that of a full disc because it has a smaller mass and radius. However, the exact value depends on the specific dimensions and mass distribution of the disc.

## 5. How does the moment of inertia of a quarter disc change with respect to its radius?

The moment of inertia of a quarter disc increases as the radius increases. This is because the farther the mass is distributed from the axis of rotation, the greater the resistance to rotational motion.

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