For a rigid body, can we substitute the work done on the point of application of force by the work done on the center of mass so that we can use the work-energy theorem for rigid as well as non-rigid bodies?


In short, generally, no, except for the weight.

To understand this, you just have to consider a solid as a set of punctual masses. Since a solid is... solid, these masses don't move relative to each other: internal forces don't work. Then, since energy is extensive, you just have to sum all the work of external forces on their point of application to find the change of kinetic energy.

In the case of weight, when you sum all the weights of the masses which form the solid, you find that everything is as if the weight was applied on the center of mass of the rigid body.

While solids are really easy to study, since internal forces don't work, non rigid bodies are really complex: indeed, it's much more difficult to know what internal forces are.


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