A child stands at the centre of a turntable with arms outstretched, and the system rotates freely at 40 rpm. The child folds the arms, reducing the moment of inertia of the system to 2/5 of its initial value. Neglecting friction, the new angular speed is
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With no external torque, angular momentum is conserved: I₁ω₁ = I₂ω₂, so ω₂ = ω₁ × I₁/I₂ = 40 × 5/2 = 100 rpm. Kinetic energy of rotation is not conserved; it increases from the work the child does.
- A.
Multiplies by 2/5 instead of dividing: ω would fall, not rise.
- B.
Treats the angular speed as unchanged, ignoring the change in moment of inertia.
- C.
Conserves rotational kinetic energy (Iω² constant), giving 40 × √2.5 ≈ 63 rpm.
NCERT: Class 11 Physics, Chapter 6 (System of Particles and Rotational Motion), Conservation of angular momentum