Newtonian Mechanics – Work Done by Internal Forces of a Rigid Body Explained

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I am reading Goldstein's Classical Mechanics book, and I came across that:

In a rigid body the internal forces do no work

Is this statement based on the assumption that the internal forces are central?
Or, is it true even when the internal forces not central?

Goldstein defines a rigid body as a system of particles in which the distance between the particles remain constant, and does not require that the internal forces to be central.

Best Answer

Recall the difference between the weak and strong Newton's third law, cf. e.g. this Phys.SE post.

  1. If the internal forces satisfy the weak Newton's third law (but not the strong Newton's third law, i.e. without the collinarity assumption), then it is not guaranteed that the internal forces do no work, cf. e.g. Fig. 1.

    ^ F
|
|                  2
x------------------x
1                  |
                   |
                   v F

    $\uparrow$ Fig. 1: A rigid body consisting of 2 point-particles with a pair of non-collinear internal forces $F$. Note that there in principle could be other internal forces holding the 2 point-particles together.

  2. If the internal forces satisfy the strong Newton's third law, then the internal forces do no work, cf. e.g. this Phys.SE post.

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