The kinetic energy of the whole body is equal to the sum of the kinetic energy of all the particles present in the body. A rotating rigid body has kinetic energy because all atoms in the object are in motion.

The formula for kinetic energy of a rotating rigid body is given as,
Kinetic Energy (K.E.) = 1 /2 ( Moment of inertia (I) × (angular velocity)²)

where  ω = angular velocity

Radius of gyration is the distance between the given axis and the centre of mass of the body. The centre of mass of a body is point where the entire mass of the body is supposed to be concentrated. It is denoted by ‘K ’.

If M is mass of the body, the moment of inertia is given as,
Moment of inertia (I) = mass of the body (M) × (radius of gyration)²

So, the formula for radius of gyration (K) is given as,

where K = radius of gyration, I = Moment of inertia and M = mass of the body.

Inertia of a body is its inability to change by itself its state of rest or of uniform motion in a straight line. Similarly Moment of inertia of a body is its inability to change by itself its state of rest or of uniform rotatory motion about an axis.
The formula for Moment of Inertia of a rigid body is given as,
The moment of inertia of the rigid body (l) = Sum of moments of inertia of
all the particles present in the body.
Let us consider,

m₁, m₂, m₃ = masses of large particles in a rigid body

r₁, r₂, r₃ = distance of the masses from the axis
The formula for Moment of Inertia of a rigid body will be,

 l= m₁r₁² + m₂r₂² + m₃r₃² + …

The above formula can also be expressed as,

m_i = mass of i^th particle

r_i = distance between i^th particle and axis o rotation

Moment of inertia of a particle about an axis is equal to the product of the mass of the particle and square of its distance from the axis.

The formula for Moment of Inertia of a particle is given as,
Moment of inertia of the particle about the axis = mass of the particle (m) × distance of particle (r)
from the fixed axis

Formula for Moment of inertia of the particle about the axis =  mr²
The S.I. unit for moment of inertia is kg m²