Moment of Inertia of a Disk and mass

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Homework Help Overview

The problem involves determining the mass of a disk based on its moment of inertia as a function of the distance from the center of the disk to the axis of rotation. The context includes the application of the parallel axis theorem and the relationship between mass and moment of inertia.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of the parallel axis theorem and the implications of the axis of rotation not being at the edge of the disk. There is an exploration of how to relate the given moment of inertia values to the mass of the disk.

Discussion Status

Some participants have provided guidance on how to approach the problem using the parallel axis theorem, while others have clarified the relationship between the variables involved. The discussion reflects a mix of interpretations regarding the setup of the problem.

Contextual Notes

There is a noted confusion regarding the relationship between the distance h and the length L, as well as the specific values of moment of inertia at different points. The original poster expresses uncertainty about their calculations and seeks further assistance.

drj1
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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.
 
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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.
 

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