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 :
Answer & explanation
Correct answer: option 3
According to the law of conservation of angular momentum, the angular moment of the system remains conserved.
Iω1 + Iω2 = 2Iωo
ωo = \(\frac{ω_1 + ω2}{2}\)
Kinitial = \(\frac{1}{2}\)I(ω12 + ω22)
Kfinal = \(\frac{1}{2}\)(2I)(ω1 + ω2)2
Change in kinetic energy will be = Kfinal - Kinitial
ΔKE = I[\(\frac{ω_1^2}{4}\) + \(\frac{ω_2^2}{4}\) - \(\frac{2ω_1ω_2}{4}\)]
ΔKE = \(\frac{I}{4} (\omega_1 - \omega_2)^2\)