What is the Moment of Inertia for a Door Rotating Around a Vertical Axis?

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Homework Help Overview

The discussion revolves around calculating the moment of inertia for a door, specifically a 32 kg door that is 107 cm wide, rotating around a vertical axis. The original poster is attempting to determine the moment of inertia at a point 10 cm inside the door.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to use the moment of inertia formula, considering both the center of mass and the parallel axis theorem. Some participants question the specifics of the door's rotation, including the orientation and plane of rotation.

Discussion Status

The discussion is ongoing, with participants clarifying the setup of the problem and suggesting relevant concepts such as the parallel axis theorem. There is no explicit consensus yet, as different interpretations of the door's orientation are being explored.

Contextual Notes

There are uncertainties regarding the exact orientation of the door during rotation, which may affect the calculation of the moment of inertia. The original poster has provided some calculations but is unsure about the next steps.

JMUkid
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Homework Statement



A 32kg door that is 107 cm wide. What is the moment of inertia 10 cm inside the door with rotation around a vertical axis?

Homework Equations



L=Iω

The Attempt at a Solution



I=1/3mL^2
I= Icm+ md^2

1/3(32)(107)^2
Im not sure what to do after I find the I center of mass
 
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Your question is confusing.Give more details.Whether the door is rotating in vertical plane or horizontal plane??
 
It is rotating around a vertical axis
 
JMUkid said:
It is rotating around a vertical axis
But in which plane?
I mean that whether the door is on floor and rotating about vertical axis or in an erect position rotating about vertical axis.Moment of inertia in both cases is different.
 
It seems fair to assume from the question that the door is mounted to a vertical pole 10cm from its longest edge and parallel to that edge.
JMUkid you should try doing a search for the "parallel axis theorem" :)

EDIT: Looking at your working it looks like you've already got the formula there for your moment of inertia, you just need to add the second term in your second formula to your answer :)
 

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