How Do You Calculate the Moment of Inertia for an Off-Center Pivot?

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Homework Help Overview

The problem involves calculating the moment of inertia for a solid door with specific dimensions, focusing on a pivot point that is off-center. The subject area pertains to rotational dynamics and moment of inertia calculations.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the moment of inertia for a pivot point at the edge of the door and consider how to adjust the formula for an off-center pivot. There are attempts to clarify the relationship between angular momentum and moment of inertia.

Discussion Status

Some participants have offered hints and guidance on how to approach the problem, including breaking the door into sections and considering the distance between axes. There is an acknowledgment of potential misunderstandings regarding the equations involved.

Contextual Notes

There are indications of incomplete equations and potential typos in the discussion, as well as a need for clarification on the correct application of the moment of inertia formulas.

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Homework Statement


A 20 kg solid door is 220 cm tall, 93 cm wide.

Homework Equations


What is the door's moment of inertia for rotation about a vertical axis inside the door, 14 cm from one edge?

The Attempt at a Solution


I know that if the pivot point is at the edge of the door, the equation is 1/3ML^2, but I don't know how to find the formula for this question...
 
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Hint: Think of the door as two doors, joined at the axis 14cm in...
 
Oops thinking of angular momentum
 
Do you know how the equation for the pivot point of the edge of the door is calculated?
It is done by using the moment of inertia of an axis thru the center of the door plus M * R^2 where R is the perpendicular distance between the two axes. You can confirm this equation by starting with the moment of inertia of a thin rectangular plane thru the center and adding the M * R^2 to get the moment of inertia of a thin rectangular plane on the edge.

BTW: The equation you have for the pivot point at the edge of the door is wrong (rather, incomplete). You need to have another term for the length of the door.
 
djeitnstine said:
Moment of inertia is L = I \omega I meaning inertia and omega meaning angular velocity

Might be a typo. L is angular momentum, and I is the Moment of Inertia. Just follow the PF Library link that was automatically added to your term moment of intertia:

https://www.physicsforums.com/library.php?do=view_item&itemid=31
 
berkeman said:
Hint: Think of the door as two doors, joined at the axis 14cm in...

Or you could do that :P
 

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