# What is the meaning of radius of gyration and its relation to rotation?

• MHB
• harpazo
Haha, well, in summary, the radius of gyration, as taught in Calculus 3, is a measure of the distribution of mass around an axis of rotation. It answers the question of how far a point mass would need to be from the axis of rotation to have the same angular momentum as the entire object. So yes, there is a connection between gyration and rotation.
harpazo
In simple terms, what exactly is the radius of gyration as taught in Calculus 3? Is gyration connection in any way to rotation?

Yes, it is. The "radius of gyration" answers the question "If the mass of this object were reduced to a single point, how far from the axis of rotation would that point be so that the angular momentum of that single point mass would be the same as the object itself were rotated around the axis?"

HallsofIvy said:
Yes, it is. The "radius of gyration" answers the question "If the mass of this object were reduced to a single point, how far from the axis of rotation would that point be so that the angular momentum of that single point mass would be the same as the object itself were rotated around the axis?"

This is deep, very deep...

## What is the radius of gyration?

The radius of gyration is a measure of how far a particle or object is from its center of mass or axis of rotation. It is a property of an object that describes its distribution of mass around its axis.

## How is the radius of gyration calculated?

The radius of gyration can be calculated using the formula Rg = √(I/m), where I is the moment of inertia and m is the mass of the object.

## What is the significance of the radius of gyration?

The radius of gyration is important in understanding an object's rotational motion and stability. It is also used in various fields such as physics, engineering, and sports to analyze the behavior of rotating objects.

## How does the radius of gyration differ from the radius of gyration tensor?

The radius of gyration refers to a single value that characterizes an object's rotational properties, while the radius of gyration tensor is a mathematical representation of the object's distribution of mass in different directions. The tensor provides more detailed information about an object's rotation, while the radius of gyration is a simpler measure.

## Can the radius of gyration change?

Yes, the radius of gyration can change depending on how the mass is distributed within an object. For example, if an object's mass is closer to its axis of rotation, the radius of gyration will decrease, and if the mass is farther away, the radius of gyration will increase.

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