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Radius of gyration
Intermediate
Distance at which all mass would give the same I.
I = mk²k = √(I/m) is the distance at which a point mass would have the same I. It's an alternative way to give rotational inertia.
I = 0.5 kg·m², m = 2 kg: k = 0.5 m.
k isn't a physical dimension of the body.
In more detail
The radius of gyration k is defined by I = Mk². It gives an effective distance from the axis at which the total mass could be concentrated to give the same moment of inertia.
Real-world uses
- Engineers quote radii of gyration to compare rotational inertia of different machines.
- Aircraft designers use radius of gyration to assess handling in rolls and turns.
- Mechanical engineers use the radius of gyration to describe how a shaft or a flywheel resists angular acceleration.
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Frequently asked questions
Is the radius of gyration a real distance?
It is an effective distance, not a physical radius of the body.
How is it related to moment of inertia?
It is the square root of I divided by M.
Is the radius of gyration a real radius?
Not usually. It is the distance at which the whole mass would need to be placed to give the same moment of inertia.
Related topics in Rotational Motion
Moment of inertia of a hollow sphere · Parallel axis theorem · Perpendicular axis theorem · Newton's second law for rotation · Rotational kinetic energy · Rolling without slipping