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Here I have understood the solution but just have a doubt regarding the last question about the vector force at B.

The solution says that as the y axis is a principal axis of inertia,so rotation about this axis will not cause any force to be exerted on the pivots. I do not understand why rotation about a Principal axis will not cause any force to be exerted. Moreover, if the rigid body rotates about that axis,there must be some centripetal force acting upon it. Where does this force come from?

Subsequently,the solution says that the only force on the pivots will be due to the rotating point mass which has a centrifugal force in the rotating frame. Well, what is the source of the necessary centripetal force to the point mass for its rotation?

I am at a very preliminary stage of classical mechanics,I know nothing about the Lagrangian or Hamiltonian mechanics. Please help.

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There is no resultant centripetal force due to the disk itself because the force on any one part of the disk is balanced by the force on an equal mass diametrically opposite to it on the other side side of the axis of rotation. If the pivots were not there, the disk (without the point mass) would still spin about the same axis.

The point mass is the only part which has no opposite partner of equal mass. Because of this, centripetal force must be supplied by the pivots to make up for the lack of a balancing mass. Centripetal force is required because the object is not rotating about an axis through its combined centre of mass.

If the pivots were not there, the disk and point mass would rotate about an axis parallel to AB but through its combined centre of mass, which does not lie on AB. Not external centripetal force is required for such a rotation.

The centripetal force on the point mass comes from the normal reactions from the pivots. If the pivots are not smooth there will also be a friction force which slows the disk.

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  • $\begingroup$ Thank You.If no external Centripetal Force is required for rotation about an axis passing through the centre of mass. $\endgroup$
    – Alice
    Commented May 26, 2017 at 4:01
  • $\begingroup$ If no external Centripetal Force is required for rotation about an axis passing through the centre of mass, the how does the body rotate? To start a body rotating,we need to apply some torque after all!Doesn't rotation always need a necessary Centripetal Force? $\endgroup$
    – Alice
    Commented May 26, 2017 at 4:18
  • $\begingroup$ Yes, an external force is required to start/stop rotation, but not to keep it going. When an object rotates about an axis through its centre of mass, the centripetal forces required are supplied by internal forces between the constituent parts of the object. $\endgroup$
    – sammy gerbil
    Commented May 26, 2017 at 19:08