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 $ω_{1}$ and $ω_{2}$ . They are brought into contact
face to face coinciding the axis of rotation. The expression for loss of energy during this process is
[NEET 2017]

Question

Infinity Learn · Accepted Answer

When no external torque acts on system, then angularmomentum of system remains constant.Angular momentum before $$contact=I$$ω$$1+I2$$ω$$2=I$$ω$$1+I$$ω$$2=I$$ω$$1+$$ω$$2Angular$$ momentum after the discs brought into $$contact=Inet$$ ω$$=I1+I2$$ω$$=2I$$ωFrom law of conservation of angular momentum,Iω$$1+$$ω$$2=2I$$ω⇒ω$$=$$ω$$1+$$ω$$22Now$$, to calculate loss of energy, we subfract initial and final energies of system.Loss of $$energy=12I$$ω$$12+12I$$ω$$22$$−$$12(2I)$$ω$$2=14I$$ω$$1$$−ω$$22$$

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