Degrees of Freedom: Square & Triangular Lamina

[Jhansi1990@gma]

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

 

[mfb]

This looks like homework: What did you find out so far?

 

[Jhansi1990@gma]

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.

 

[mfb]

Those 3 degrees of freedom just fix the current position of the square. What about its movement?

 

[Jhansi1990@gma]

if i get generalized co-ordinates i can calculate co-ordinate velocities from it

 

[mfb]

Is that related to the original question?
What do you mean with "get"?

 

[Jhansi1990@gma]

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