Two discs of moments of inertia $$I1$$ and $$I2$$ about their respective axes, rotating with angular frequencies ω$$1and$$ ω$$2$$ respectively, are brought into contact face to face with their axes of rotation coincident. The angular frequency of the composite disc will be

Question

Two discs of moments of inertia $$I1$$ and $$I2$$ about their respective axes, rotating with angular frequencies ω$$1and$$ ω$$2$$  respectively, are brought into contact face to face with their axes of rotation coincident. The angular frequency of the composite disc will be

Infinity Learn · Accepted Answer

The initial angular momentum of the two $$discsL1=I1$$ω$$1+I2$$ω$$2The$$ moment of inertia IC. of the composite system will $$beIC=I1+I2If$$ ωCto" be the angular frequency of the composite system, then the final angular momentum $$L2$$, is given $$byL2=Ic$$ω$$c=I1+I2$$ωcApplying the law of conservation of angular momentum, we $$haveI1+I2$$ω$$C=IC$$ω$$1+I2$$ω$$2or$$ ω$$C=I1$$ω$$1+I2$$ω$$2I1+I2$$

Two discs of moments of inertia I₁ and I₂ about their respective axes, rotating with angular frequencies $ω_{1}$ and $ω_{2}$ respectively, are brought into contact face to face with their axes of rotation coincident. The angular frequency of the composite disc will be

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Two discs of moments of inertia I1 and I2 about their respective axes, rotating with angular frequencies ω1and ω2 respectively, are brought into contact face to face with their axes of rotation coincident. The angular frequency of the composite disc will be

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Two discs of moments of inertia I₁ and I₂ about their respective axes, rotating with angular frequencies $ω_{1}$ and $ω_{2}$ respectively, are brought into contact face to face with their axes of rotation coincident. The angular frequency of the composite disc will be