Question

A dancer spins about himself with an angular speed w. With his arms extended. When he draws his hands in, his moment of inertia
reduces by 40%. Then his new angular velocity would be​

Answer 1

Given : A dancer spins about himself with an angular speed w. With his arms extended. When he draws his hands in, his moment of inertia

reduces by 40%.

To find : initial angular speed = ω

Let I is the moment of inertia of dancer.

a/c to question,

moment of inertia of dancer reduces by 40% .

so, new moment of inertia, I' = I - 40% of I

= I - 40/100 × I

= I - 0.4I

= 0.6I

from law of conservation of angular momentum,

ω₁I₁ = ω₂I₂

⇒ω × I = ω₂ × 0.6 I

⇒ω₂ = ω/0.6 = 5ω/3

Therefore new angular velocity is 5ω/3

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