Two discs of same moment of inertia rotating about their respective geometrical 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

Question

Two discs of same moment of inertia rotating about their  respective geometrical 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

Infinity Learn · Accepted Answer

Common angular veocity ω is given , Iω$$1$$ $$+$$ Iω$$2$$ $$=$$ $$2I$$ω   ⇒  ω $$=$$ ω$$1+$$ω$$22(K$$.E.$$)i$$ $$=$$ $$12I$$ω$$12+12I$$ω$$22(K$$.E.$$)f$$ $$=$$ $$12$$×(2I)ω$$2$$ $$=$$ $$I($$ω$$1+$$ω$$22)2Loss$$ in K.E. $$=$$ $$(K$$.E.$$)i-(K$$.E.$$)f$$ $$=$$ $$I4($$ω$$1-$$ω$$2)2$$

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material