Moment of inertia of a triangular plate

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Discussion Overview

The discussion revolves around the moment of inertia of a triangular plate, including calculations for various configurations and the implications of symmetry. It also touches on related problems involving oscillations and rotational dynamics of different shapes.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents a set of answers for the moment of inertia calculations, suggesting that the integration may involve double or triple integrals across the thickness and surface of the triangle.
  • Another participant introduces a problem regarding the frequency of small oscillations for a thin homogeneous triangular plate suspended from different points, indicating a potential application of the moment of inertia in dynamics.
  • A third participant describes a scenario involving a square sheet rotating about an axis and asks for the rate of precession of its axis of symmetry, which may relate to the concepts of moment of inertia and angular momentum.
  • A later post expresses urgency for responses, indicating a need for assistance with the homework problems presented.

Areas of Agreement / Disagreement

The discussion does not appear to have a consensus, as multiple distinct problems are presented without resolution or agreement on the methods or answers. Participants are seeking help and clarification on different aspects of the topics discussed.

Contextual Notes

There are limitations in the clarity of the integration methods proposed, as well as the assumptions regarding the thickness of the plate and the specific configurations for oscillation and rotation. These factors may affect the accuracy of the calculations and the applicability of the results.

Who May Find This Useful

This discussion may be useful for students or individuals studying mechanics, particularly those interested in the moment of inertia, oscillatory motion, and rotational dynamics of various geometric shapes.

xzibition8612
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Homework Statement



see attachment

Homework Equations



integration

The Attempt at a Solution



answers:
a. mH2/6 + mt2/12
b. mB2/2 + mt2/12
c. mH2/6 + mB2/2
d. -mBH/4
e. 0, 0
If the plate were thin t can be ignored.

Ok so e is because of symmetry so I get that. a-d on the other hand...seems like a bunch of complicated integrals. So double/triple integrals? I know integration needs to be done across the thickness, and then across the surface of the triangle, so 2 integrals? Any help would be appreciated.
 

Attachments

Physics news on Phys.org
Find the frequency of small oscillations for a thin homogeneous plate if the motion takes
place in the plane of the plate and if the plate has the shape of an equilateral triangle and
is suspended (a) from the midpoint of one side and (b) from the apex.
 
A square sheet is constrained to rotate with an angular velocity ! about an axis passing
through its center and making an angle with the axis through the center of mass and
normal to the sheet (i.e. its axis of symmetry). At the instant the axis of rotation lies in
the plane determined by the axis of symmetry and a diagonal, the body is released. Find
the rate at which the axis of symmetry precesses about the constant direction of the angular
momentum.
 
Is anybody there can reply these?
I need help
they are due tomorrow...
 

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