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
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 dont 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.
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