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 ω₁ and ω₂. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is

Concept:

The moment of inertia is the angular mass or rotational inertia. It is defined as a quantity that decides the amount of torque required for angular acceleration.  

The formula of Moment of Inertia is expressed as I = mr2 where m and r is mass and distance from the axis of rotation of the body. 

The SI unit of moment of inertia is kg m2.

The kinetic energy of a body in rotational motion is calculated using the formula:

\(k=\frac{{\rm Iw}^2\ }{2} \)

where I is a moment of inertia and w is the angular velocity of the body in rotational motion.

Calculation:

Change in Kinetic energy = Δ KE = \(\frac{1}{2}\frac{l_1l_2}{l_1+l_2}\)\((ω_1-ω_2)^2\)

=\(\frac{1}{2}\frac{l^2}{(2l)}\)(ω₁ - ω₂)²

\(=\frac{1}{4}l(\omega_1 - \omega_2)^2\)