Number of degrees of freedom of two particles connected by a rigid rod moving freely in a plane is?

Question

Hi respected researchers and scholars,

I have a question regading degrees of freedom

Number of degrees of freedom of two particles connected by a rigid rod moving freely in a plane is _______ ?

I have in my mind is: For a single particle it is 2 in a plane,

Q. 1 What if two or three independent particles in a plane? Is it 4

Q. 2 if two particles connected by a rigid rod moving freely in a plane ?

Need your kind attention. Thanks

Answer 1

Three real parameters, 2 for center of mass of whole thing, one for rotation angle would do it. Don't know if that's what you mean by degree of freedom...

Answer 2

Think of DOF as the number of parameters to completely define the position of the particles

You need two parameter for the first particle, the $x$ and $y$ coordinate.

After specifying the position of the first particle, then specify the angle of the rigid rod.

Thus 3 DOF in total