Moment of inertia of a thin uniform rod

[Apashanka]

I was thinking that if a uniform rod of mass M and length L remains static ,then it's centre of mass will be at L/2 from one end (e.g total mass assumed to be concentrated at L/2 )
But if this rod is moving with uniform angular velocity ω about an axis passing through it's one end and perpendicular to the rod ,it's moment of inertia is ML²/3 so we can think that the total mass is now rotating at a distance L/√3 from the rotating end.
Hence the total mass is now concentrated at a distance L/√3 from the rotating end as opposed to the static case for which the total mass is concentrated at L/2 from the same end.
Am I right??

 

[Ibix]

Hence the centre of mass shifts a little if the rod is rotating??

No. The moment of inertia is what it is regardless of whether or not the rod is rotating. And the centre of mass is what it is regardless of whether or not the rod is rotating.

It's true that the moment of inertia of a rod is the same as a point mass on the end of a massless rod. But the centre of mass is not the same.

 

[Apashanka]

No. The moment of inertia is what it is regardless of whether or not the rod is rotating. And the centre of mass is what it is regardless of whether or not the rod is rotating.It's true that the moment of inertia of a rod is the same as a point mass on the end of a massless rod. But the centre of mass is not the same.

Yes sir but for a uniform rod of mass M and length L,we can assume that the total mass is concentrated at the midpoint L/2(e.g from centre of mass concept).
Similarly if we calculate the moment of inertia of the same rod about an axis passing through it's one end and perpendicular to the rod the it comes out be ML²/3
So we can imagine that a mass is situated at a distance L/√3 from the axis we have taken for reference.
Hence total mass assumed to be concentrated at L/2 from centre for mass concept but from the moment of inertia concept it will produce the same effect if the total mass is situated at L/√3 ??

 

[A.T.]

(e.g total mass assumed to be concentrated at L/2 )

This interpretation of centre of mass ignores the rotational inertia, so it's not surprising that it's inconsistent with moment of inertia interpretations.

 

[reterty]

Apashanka,
your interpretation is correct, but there is another version: the point mass m / 3, located at the distance of L. Both these interpretations yield the same result for the value of moment of inertia for this case

 

[Apashanka]

Apashanka,
your interpretation is correct, but there is another version: the point mass m / 3, located at the distance of L. Both these interpretations yield the same result for the value of moment of inertia for this case

Yes that is the case ,also to be taken
Thanks