A uniform brass disc of radius and mass m is set into spinning with angular speed ω$$0$$, about are axis passing through centre of disc and perpendicular to the plane of disc. If its temperature increases from θ$$1$$∘C to θ$$2$$∘C without disturbing the disc, what will be its new angular speed ? (the$$ coefficient of linear expansion of brass is α$$)

Question

A uniform brass disc of radius and mass m is set into spinning with angular speed ω$$0$$, about are axis passing through centre of disc and perpendicular to the plane of disc. If its temperature increases from θ$$1$$∘C to θ$$2$$∘C without disturbing the disc, what will be its new angular speed ? (the$$ coefficient of linear expansion of brass is α$$)

Infinity Learn · Accepted Answer

Using the principle of conservation of angular momentum, we have $$Li=Lf$$  or  $$I0$$ω$$0=I$$ω∴ ω$$=I0$$ω$$0IHere$$ $$I=I01+2$$αθ$$2$$−θ$$1$$∴ ω$$=I0$$ω$$0I01+2$$αθ$$2$$−θ$$1=$$ω$$01+2$$αθ$$2$$−θ$$1$$

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