Understanding Particle Degree of Freedom: 3N dof for N Particles Explained

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A particle is considered to have three degrees of freedom (dof) due to its translational motion in three-dimensional space. The discussion clarifies that while one might think of including rotational motion, classical mechanics treats particles as having zero spatial extent, rendering rotation about their center of mass irrelevant. Therefore, for N particles, the total degrees of freedom remain at 3N, focusing solely on translational motion. The concept of rotational energy does not apply to infinitesimal particles in classical mechanics. This understanding is crucial for accurately analyzing the dynamics of systems in classical physics.
babbar.ankit
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A particle has 3 degree of freedom (dof) , so we write 3N dof for N particles...
But I have a fundamental doubt: 3 dof means we consider only transitional motion of particle?
... why can't we say 6 dof?
 
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Because, in classical mechanics, a particle is said to have zero spatial extent, and hence, insofar it rotates about an axis going through its C.M, the whole particle lies on the axis of rotation and thus do not have any rotational energy in addition to its translational energy.

Thus, in classical mechanics, rotation of infinitesemal particles is dynamically irrelevant.
 
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