Degree of freedom of a block of wood sliding on a horizontal plane

[sudipmaity]

Homework Statement

Find out the degrees of freedom of a block of wood sliding on a horizontal plane.

Homework Equations

DoF=Nn-k
N=no. of dimensions. n=no. of particles.k= no. of constraints.

The Attempt at a Solution

I am considering the block of wood as a rigid body made of n no. of particles.
But it will move with respect to a center of mass.
I will need 3 points on the body to define the CM.
As the body is constrained to move on a plane each of these 3 points can be denoted with 2 coordinate points.
Each of these 3 points has fixed distance from each other so there will be 3 constraints if these points are non collinear.
So i think the answer should be 3×2-3=3.
Are my deductions correct??
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[BvU]

So you have 2 dimensions. One particle with no constraints would have two degrees of freedom ? Not 4 (x, y, v_x, v_y) ?

I also don't quite follow how you need 3 points to define the CM. Wouldn't e.g. two corners be enough ? Could you explain ? (It may be correct, I just wonder)

 

[sudipmaity]

Please BvU clarify one thing, should i consider the block of wood a rigid 3d body or a point particle??

 

[BvU]

It's a block of wood. To me that sounds closer to a rigid body than to a point particle.
You said you need three points to pinpoint the block. Why three ?

What is the basis for your relevant equation ? Does a particle on a plane with no further constraints have 2 degrees of freedom in your book ?