Two discs of moments of inertia `I_(1) and I_(2)` about their respective axes (normal to the disc and passing through the centre) and rotating with angular speeds `omega_(1) and omega_(2)` are brought into contact face to face with their axes of rotation coincident. (a) Does the law of conservation of angular momentum apply to the situation ? Why ? (b) Find the angular speed of the two-disc system. (c ) Calculate the loss in kinetic energy of the system in the process. (d) Account for this loss.

Two discs of moments of inertia `I_(1) and I_(2)` about their respecti

1.	Two discs of moments of inertia `I_(1) and I_(2)` about their respective axes (normal to the disc and passing through the centre) and rotating with angular speeds `omega_(1) and omega_(2)` are brought into contact face to face with their axes of rotation coincident. (a) Does the law of conservation of angular momentum apply to the situation ? Why ? (b) Find the angular speed of the two-disc system. (c ) Calculate the loss in kinetic energy of the system in the process. (d) Account for this loss.
Answer» (a) By the conservation of angular momentum `I_(1)omega_(1)+I_(2)omega_(2)=(I_(1)+I_(2))omega` `omega=(I_(1)omega_(1)+I_(2)omega_(2))/(I_(1)+I_(2))`, where `omega` is the final angular speed (b) Initial `K.E., K_(i)=(1)/(2)I_(1)omega_(1)^(2)+(1)/(2)I_(2)omega_(2)^(2)` Final `K.E., K_(f)=(1)/(2)(I_(1)+I_(2))omega^(2)` `=(1)/(2)(I_(1)+I_(2))((I_(1)omega_(1)+I_(2)omega_(2))/(I_(1)+I_(2)))^(2)` `K_(i)=K_(f)=(1)/(2)(I_(1)I_(2))/(I_(1)+I_(2))(omega_(1)-omega_(2))^(2)=+ve, K_(i)gtK_(f)` `K_(i)-K_(f)=DeltaK:` loss in kinetic energy

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