Talk:Radius of gyration

Comments from User:Tastemyhouse (21 April 2006)

The radius of gyration of an area with respect to a particular axis is the square root of the quotient of the area moment of inertia divided by the area. It is the distance at which the entire area must be assumed to be concentrated in order that the product of the area and the square of this distance will equal the moment of inertia of the actual area about the given axis.

I found this article next to useless - I have to assume that anyone who can understand this article already knows what radius of gyration means. So the article only really serves to refresh physicists, and give them a sense of verisimilitude. It would be a great improvement if someone could provide an explanation that wasn't in the physics equivalent of leagalese, and provide some meaningful examples of how this concept applies to the real world.

Here's an answer to your question. From a physical sense, and in simple terms, gyration measures the rotational instability of an object along its axis of rotation. The radius of gyration is a measure of this instability, the smaller the gyroradius, the small is the instability, so radius of gyration is zero for a body whose center of gravity is located on the axis of rotation. But, if the radius of gyration of a rotating body along a particular axis is getting larger with time, the rotational instability will grow very wild leading to rotational vibrations that breakdown the mechanical system (rotating body + fixed axis).

What is actually 'gyrating' ?

We need an explanation of the physical meaning of this! Something is presumably gyrating about something else, at a particular radius. One explanation might be as follows:

1)Take some complicated shape, where we know the mass (M) and the Moment of Inertia (I) about some axis. 
2)By definition, I = M.Rg^2.
3)Thus, Rg is the distance from the axis at which, if we put a point of mass M, we would have the same I as our original shape.

[This is similar to the way to analyse pendulums with non-point masses, i.e. as a point mass, but with a "dodgy" moment of inertia] RichardNeill 21:35, 15 July 2007 (UTC)

Chain length

This article seems to use N as the length of the chain in monomers, rather than the length of the chain in steps. Do you think this definition is common enough not to warrant a mention? Shinobu 11:14, 14 November 2007 (UTC)

Comments from chemistry student, april 2010

"Hydrodynamic volume" redirects to this article, though it dosen't describe the effect at all (as far as I know hydrodynamic volume is the volume of a large molecule/colloid + the water that is ordered/caged around it). I think it would be appropriate with an explanation of the effect and the things that influence on the hydrodynamic volume (ionic strength, temperature etc.). The definitions are meaningless geometrics without the physical chemistry behind. 212.88.73.9 (talk) 09:52, 19 April 2010 (UTC)

Derivation of identity

The derivation shows how the first definition can be simplified, it does NOT show why the second definition is equivalent. —Preceding unsigned comment added by 129.16.110.138 (talk) 10:29, 14 December 2010 (UTC)

Ambiguity

We have an article Radius of Gyration stating "Radius of gyration or gyradius refers to distribution of the components of an object around an axis..." as well as an article Gyroradius stating "The gyroradius (also known as radius of gyration, Larmor radius or cyclotron radius) is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field..." In neither of these two, which treat completely unrelated phenomena, the other meaning of "radius of gyration" is mentioned. I think we would at least need a pointer "For the other physical effect named radius of gyration see...", if not a full disambiguation page for "Radius of gyration". — Preceding unsigned comment added by Seattle Jörg (talk • contribs) 13:36, 19 January 2017 (UTC)

Error in first paragraph

The first paragraph of the page ends ubruptly

Ambiguity due to less information and no reference in the end of the second paragraph

One can represent a trajectory of a moving point as a body. Then radius of gyration can be used to characterize the typical distance travelled by this point.

The first few thoughts that came in my mind after reading this were:

1. Does it mean that assuming the trajectory of any moving point as a body and finding its radius of gyration (about what axis?) can help us find the distance travelled by that body? and
2. How to calculate the distance travelled by a particle using the radius of gyration of its trajectory (represented like a body)?

There isn't further explanation nor a reference for further reading.

If my comprehension of this is correct, will this example help ease the comprehension of these lines:

Let's take a ring. Its moment of inertia is MR2 about the axis passing through its center and perpendicular to its plane. This is the same for any particle of mass M located R distance from the same axis. So, according to the two sentences I quoted above, we can represent the trajectory of this point we assumed, ie circular around the axis. This trajectory can be represented as the body, which is the ring in this case, and the radius of gyration, which is R can be used to calculate the distance travelled by the point (2πR, the length of the body).

The best approach would be to derive it for a general case. But I am not able to do so. If anyone of you can, please edit this page/add a reference.

Full description of my doubt on Stackexchange

Vinamrsachdeva (talk) 07:55, 9 May 2020 (UTC)