Consider a Disc of mass 5 kg, radius 2m, rotating with angular velocity of 10 rad/s about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping i $s _____$ J.

Question

G1 Physics · Accepted Answer

Image Moment of inertia of one disc: I = ½MR² = ½ × 5 × 2² = 10 kg m² Initial angular momentum: Lᵢ = Iω = 10 × 10 = 100 kg m²/s Initial kinetic energy: Eᵢ = ½Iω² = ½ × 10 × 10² = 500 J After the identical disc is placed, total moment of inertia: I(final) = 2I = 20 kg m² Conservation of angular momentum: Lᵢ = L(final) 100 = 20ω(final) ω(final) = 5 rad/s Final kinetic energy: E(final) = ½I(final)ω(final)² = ½ × 20 × 5² = 250 J Energy dissipated: ΔE = Eᵢ - E(final) = 500 - 250 = 250 J