# Moment of Inertia of a Disk and mass

• drj1
In summary, the conversation discusses a problem involving a rotating disk with a given moment of inertia at a certain distance from the center. The question is to determine the mass of the disk using the parallel axes theorem. The conversation goes through a solution involving the equation for moment of inertia and the parallel axes theorem, and ultimately arrives at the correct answer.
drj1

## Homework Statement

Figure (a) shows a disk that can rotate about an axis at a radial distance h from the center of the disk. Figure (b) gives the rotational inertia I of the disk about the axis as a function of that distance h, from the center out to the edge of the disk. The scale on the I axis is set by IA = 0.010 kg·m2 and IB = 0.210 kg·m2. What is the mass of the disk?
Here's a link to the image --> http://www.webassign.net/hrw/10-35.gif

## Homework Equations

Inertia=Icom + Mh^2
=(mL^2)/2 + Mh^2

## The Attempt at a Solution

I set .010= (mL^2)/2 and solved for L^2 which turns out to be (.02/m). I then plugged this term into L^2 variable of the equation I=(mL^2)/2 + Mh^2. Then I plugged in .210 for I and .2 for h and solved for m which came out to be about 5.25. I thought I had it right but I don't. Help would be great I appreciate it.

You know that at the edge of the disk the moment of inertia is 0.210 kg m2 and that h = L = 0.2 m. Put everything in the parallel axes theorem and solve for the mass. You don't have to guess what the moment of inertia at h = 0 is.

Yes but in this case h does not equal L because the axis of rotation is not at the edge of the disk it is somewhere between the center of mass and the edge of the disk.

Oh okay I just read the problem over again and that makes sense now. Thanks a lot for your help.

## What is the formula for calculating the moment of inertia of a disk?

The formula for calculating the moment of inertia of a disk is I = 1/2 * m * r^2, where I is the moment of inertia, m is the mass of the disk, and r is the radius of the disk.

## How does the distribution of mass affect the moment of inertia of a disk?

The moment of inertia of a disk is directly proportional to the distribution of mass. This means that the farther the mass is from the axis of rotation, the greater the moment of inertia will be.

## Can the moment of inertia of a disk change?

Yes, the moment of inertia of a disk can change if the mass or distribution of mass changes. For example, if more mass is added to the disk or if the mass is shifted farther from the axis of rotation, the moment of inertia will increase.

## How does the mass of a disk affect its moment of inertia?

The mass of a disk has a direct effect on its moment of inertia. The greater the mass of the disk, the greater the moment of inertia will be.

## What is the significance of calculating the moment of inertia of a disk?

The moment of inertia of a disk is an important calculation in physics and engineering. It helps determine the resistance of a disk to changes in its rotational motion and is used in the design of machines and structures that involve rotating disks.

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