Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities \(\omega_1\) and \(\omega_2\). They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is : 

\(\frac{I}{4} (\omega_1 - \omega_2)^2\)

According to the law of conservation of angular momentum, the angular moment of the system remains conserved.

Iω₁ + Iω₂ = 2Iω_o

ω_o = \(\frac{ω_1 + ω2}{2}\)

K_initial = \(\frac{1}{2}\)I(ω₁² + ω₂²)

K_final = \(\frac{1}{2}\)(2I)(ω₁ + ω₂)²

Change in kinetic energy will be = K_final - K_initial 

ΔKE = I[\(\frac{ω_1^2}{4}\) + \(\frac{ω_2^2}{4}\) - \(\frac{2ω_1ω_2}{4}\)]

ΔKE = \(\frac{I}{4} (\omega_1 - \omega_2)^2\)