According to Wikipedia:

Radius of gyration or gyradius of a body about an axis of rotation is defined as the radial distance of a point, from the axis of rotation at which, if whole mass of the body is assumed to be concentrated, its moment of inertia about the given axis would be the same as with its actual distribution of mass.

This to me seems very similar to the concept of the center of mass, a point in space where we can assume all the mass of the object is concentrated at, and can be treated as particle.

Is this true? Can these be thought of as similar concepts defined in rotational physics?

• The equivalent of center of mass in rotational motion would be the center of gyration. – Sam Dec 21 '19 at 14:33
• @Sam so that means my guess is right? Just making sure thanks – Xosrov Dec 21 '19 at 16:07

The wording is misleading. It should say the radius of gyration is that of a ring where if all the mass was concentrated along the ring only, it would have the same rotational inertial properties.

If the mass was concentrated at a point then the body would have a different center of mass. A ring around the center of mass is the proper analogy which keeps both the center of mass and the rotational properties the same

$$\mathcal{I} = m\, r_{\rm gyr}^2$$

• Makes sense to me, But this question arose from the fact that just like pure translations in physics can always be done in the center of mass, pure rotations can be done for this ring/point of gyration, that's all. I'm still gonna pick this as answer so nobody answers i guess – Xosrov Dec 27 '19 at 14:12

Centre of mass and radius of gyration to completely different concepts.

Suppose you have a rod of mass M and length L, which is rotating about an Axis passing through one of its end and perpendicular to the plane of rotation.

Calculate the radius of gyration of this rod then it will be equal to L/root(3), but the centre of mass of the rod will be at l/2, so according to your hypothesis the radius of gyration should have been at L/2, but in this case it will be at L/root(3), so this example shows that radius of gyration and centre of mass are not the same.

Moment of inertia depends on the distribution of mass about the axis of rotation but centre of mass depends upon the location of the mass.