Radius of Gyration

It is the distance from the axis of rotation at which, if the whole mass of the body were to be concentrated, the moment of inertia would be the same as that with the actual distribution of mass. It is denoted by K.

If the mass of a body is M and the radius of gyration is K, then

I = MK² ---------- (1)

Also, I = m₁r₁² + m₂r₂² + ---------- + m_nr_n²

I = m (r₁² + r₂² + r₃² + ---------- +r_n²) or

But, mn = M

Comparing (1) and (2)

Hence, the radius of gyration of a body about an axis is equal to the root mean square distance of the various particles constituting the body, from the axis of rotation.