Degrees of Freedom: Square & Triangular Lamina

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Discussion Overview

The discussion revolves around the degrees of freedom for a square sheet and a triangular lamina moving in the XY plane. Participants explore the implications of constraints on the movement of these shapes and how they relate to degrees of freedom in a mechanical context.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the degrees of freedom for a square sheet, suggesting that it has three degrees of freedom based on the constraints of fixed distances between particles.
  • Another participant challenges the notion that three degrees of freedom account for the movement of the square, implying that additional factors related to movement should be considered.
  • A participant introduces the concept of generalized coordinates and their relation to calculating coordinate velocities, referencing the example of a simple pendulum to illustrate the principle of degrees of freedom.
  • There is a suggestion that the same reasoning applied to the square should also apply to the triangular lamina, although this is not universally accepted.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the degrees of freedom for the square and triangular lamina. There are competing views regarding the implications of constraints and movement, and the discussion remains unresolved.

Contextual Notes

Participants express uncertainty about the relationship between constraints and degrees of freedom, and there are unresolved questions regarding the movement of the shapes in the XY plane.

Jhansi1990@gma
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What are the number of degrees of freedom of
1)a square sheet moving in XY plane
2)a triangular lamina moving freely in XY plane
 
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This looks like homework: What did you find out so far?
 
A square is composed of many particles with the constraint that distance between every particle is the fixed.so such a square is moving in XY plane.

if i consider two particles they have 4-1 =3degree of freedom(one is subtracted due to constraint that distance between particles are fixed).if i consider third particle it is defined by two co-ordinates and two constraints and therefore no degree of freedom...the same for fourth fifth and so on...

so my answer is three

and i don't find any difference in this respect with a triangular lamina...



I do not know the answer to the question...please comment on this and say if you have any other opinion.
 
Those 3 degrees of freedom just fix the current position of the square. What about its movement?
 
if i get generalized co-ordinates i can calculate co-ordinate velocities from it
 
Is that related to the original question?
What do you mean with "get"?
 
The question does not ask that .But i told a general principle.For example a simple pendulum which is oscillating in a plane.since its moving along the arc of a circle(distance from orgin is fixed) it has only one degree of freedom...theta...which is the angle dat the string makes with vertical...so if i know theta as a function of time...i can differentiate "theta" to find generalised co-ordinate velocity
 

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