Rotational Inertia of a triangle

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Homework Help Overview

The problem involves determining the rotational inertia of a right triangle-shaped vane about a specified vertical axis. The context includes the triangle's dimensions, specifically its base width and mass.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the interpretation of the axis of rotation, questioning whether it is perpendicular to the triangle's plane or coplanar with it. There are differing views on the correct distance to consider when calculating rotational inertia.

Discussion Status

The discussion is ongoing, with participants providing insights and clarifications regarding the axis of rotation. Some guidance has been offered about the implications of the term 'vane' and its relevance to the axis position.

Contextual Notes

There is ambiguity regarding the definition of the vertical axis and its relation to the triangle's vertices, which may affect the calculation of rotational inertia. Participants are navigating these assumptions without reaching a consensus.

rpthomps
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Homework Statement



A thin, uniform vane of mass M is in the shape of a right triangle, as shown. Find the rotational inertia about a vertical axis through its apex, as shown in the figure. Express your answer in terms of the triangle’s base width b and its mass M.

Homework Equations

The Attempt at a Solution



Question.jpg


The answer in the back is just ##b^2M/2## without the second term.
 
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It's not clear what is meant by "a vertical axis through the apex". Your answer looks correct if the vertical axis is perpendicular to the plane of the triangle and passes through the lower left vertex of the triangle in your drawing. The answer in the back of the text appears to be correct if the axis is in the plane of the triangle, passes through the lower left vertex, and is perpendicular to the base b.
 
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Okay, thanks for looking it over.
 
The word 'vane' implies to me that the axis is coplanar with the lamina.
rpthomps, your r is wrong. You want the distance from the axis, not the distance from the apex.
 

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