The intermolecular reason for an object rotating and translating at the same time for force applied elsewhere than the center of mass

Question

Suppose a rigid body is lying in space with no external forces. Now when a force is applied on it, the force can introduce either a translation when applied towards the center of mass or both translation and rotation when off the center of mass, and for the same force the linear acceleration will be same. But how does this force introduce these motions from the molecular levels of the rigid body? How does the force when applied towards the center of mass cause all the molecules to have the same velocity at an instant? How does this acceleration introduced by the force propagate through all the molecules causing a equal acceleration for all of the particles? Again when applied off the center of mass, how do the molecules where the force has been applied get more acceleration but the rotational axis passing through center of mass get the same acceleration to that of when the force was applied towards the center of mass? (here by the acceleration I mean the instantaneous acceleration as a sum of both tangential acceleration caused by the torque and also the linear acceleration by the force causing translation). I found this on the internet ---

Answer to When we apply a force to the point of the center of mass, the object moves in the direction of force. Imagine we apply a force 'not' in the center of mass. Then what will happen? Will it accelerate by F/m? This means the center of mass will move? What about the rotation? by Dean Carpenter https://www.quora.com/When-we-apply-a-force-to-the-point-of-the-center-of-mass-the-object-moves-in-the-direction-of-force-Imagine-we-apply-a-force-not-in-the-center-of-mass-Then-what-will-happen-Will-it-accelerate-by-F-m-This-means-the-center-of-mass-will-move-What-about-the-rotation/answer/Dean-Carpenter-1?ch=15&oid=9145005&share=8ebaec35&srid=0Vxbe&target_type=answer

But could not understand the molecular imaging of it. Sorry I might be unclear about the concept so any answer will be appreciated. Thanks in advance.

Answer 1

If you are asking about the rigid body motion, by assuming that all distances between particles in the body remain fixed, then you apply Newton-Euler laws of motion

• Sum of force on body relate to the motion of the center of mass (point).
• Sum of torques about the center of mass relate to the rotation of the body.

But instead, if you want to consider the elasticity the object and how individual molecular bonds might stretch on compress under different loads then you need a simulation environment that can model all the degrees of freedom each molecule has and that is almost impossible to do currently.

So instead some idealization of the situation is implemented where some reduced number of degrees of freedom representing some gross bending or stretching of the whole object, but still under a simulation environment.

Even this approach has subclasses on how to deal with this problem. One being a modal analysis that breaks down the deformation shapes by each natural frequency of vibrations and then assembles the combined motion that fits the boundary conditions. The other approach is a explicit FEA solver that breaks down the overall body into smaller elemental shapes (like cubes) and then applies the equations of motion and deflection to each element.

In summary, there are no general equations of motion for flexible bodies.