Relation between radius of gyration and centre of mass

[sane123]

In a book the radius of gyration is defined as

 

"Radius of gyration may be defined as the distance from the axis of rotation of a mass point whose mass is assumed to be equal to the mass of the whole body and whose moment of inertia is equal to the moment of inertia of the body about the axis"

 

So can that mass point be considered as the centre of mass of the body? Acoording to me it has to be the COM. Please do correct me if i am wrong

[imatfaal]

In a book the radius of gyration is defined as

 

"Radius of gyration may be defined as the distance from the axis of rotation of a mass point whose mass is assumed to be equal to the mass of the whole body and whose moment of inertia is equal to the moment of inertia of the body about the axis"

 

So can that mass point be considered as the centre of mass of the body? Acoording to me it has to be the COM. Please do correct me if i am wrong

 

If you are being pernickity; I guess it could be any point that is on a line parallel to the axis of rotation and which passes through the Centre of Mass

And the more I think about it the more I think it might be only very likely to the centre of mass rather than always the centre of mass

[studiot]

On 9/17/2015 at 2:19 PM, sane123 said:

In a book the radius of gyration is defined as

 

"Radius of gyration may be defined as the distance from the axis of rotation of a mass point whose mass is assumed to be equal to the mass of the whole body and whose moment of inertia is equal to the moment of inertia of the body about the axis"

 

So can that mass point be considered as the centre of mass of the body? Acoording to me it has to be the COM. Please do correct me if i am wrong

We don't usually resurrect old threads, but since I see a new member is looking at this,

The answer is no. The mass point is not the COM of the system.

The axis of rotation is independent of the body and may be placed anywhere.
Hence the comment in your definition "whose moment of inertia is equal to the moment of inertia of the body about the axis".

It is also worth noting that there are two properties, moment of inertia and product of inertia.

The moment of inertia only tells you the numerical value, it does not describe the configuration of the mass within the body or system.
And many different distributions will lead to the same moment of inertia about any particular axis.

The product of inertial provides the distribution information and is unique to the body or system.