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Why the object actually rotates ?

When I researched about this topic , I have gotten satisfying answer from here: Why do object rotate at all?

All the atoms and molecules of the object are connected with each other by intermolecular force. So when we apply force on the object other than its centre of mass these force oppose the motion and result in the rotation.

My question is : if all the atoms and molecules are bind by intermolecular forces , then why the half of the portion of the object moves in opposite direction (i.e , why the half the part of object rotates in the direction of force and other half rotates in the opposite direction of force)

So what am I missing here?

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All the individual molecules are connected by strong bonds so each molecule wants to stay at a particular distance with respect to its neighbours. If you were to change this distance by a little bit it would cost a lot of energy.

So a natural question to ask is, which transformations can I apply to a set of points such that the distances between each pair of point stays the same? The answer is translations and rotations. If I apply an arbitrary force to a solid object you can expect the result to be a combination of translation and rotation. (or you would produce a sound wave which is basically an excitation of the bonds in the solid but that's not really relevant here).

To answer your question more specifically you can image a molecule of just two atoms connected by a bond. If you give one of the atoms a push at 90 degrees to the bond it will start rotating (and translating, i.e. moving). To rotate an object around a circle it needs a centripetal force and this force is provided by the bond between the particles. The momentum of each particle tends to move each particle further away from its center of mass but the centripetal force keeps them together, resulting in rotation.