I know that torque will cause an object to rotate about its centre of mass. I am curious why this is so.
Suppose we have a string of particles that are held in a line by electromagnetic forces of attraction such that they resemble a rod. The rod is floating in space. If we were to apply a perpendicular force at one end of the rod, it should start rotating about its centre of mass.
As such: Why does the object rotate about its centre of mass? I know that this is intuitive if there is a pivot supporting the centre of the rod. However, in this case there isn't, yet the object still behaves as though it is pivoted at the centre.
Why are the particles at both ends of the rod accelerating in opposite directions? If a perpendicular force was applied at one end of the rod, shouldn't the rod experience translational motion, as though it is being dragged forward by the end where the force was applied?
More specifically, I would like to know how the individual particles in the rod are "pulling and pushing" each other when the rod is rotating.