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Russian ice skater, Alina Zagitova, spins her way to projected Gold in the 2018 Olympics.
During one particular spin, she moves from a camel spin that rotates at about 95. RPM to a tight spin. If her rotational inertia changes from 129kgm² to 32kgm², what is the final spin rate of Miss Zagitova in rad/s and RPM

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IsrarAwan

Given data:
Initial Rotational Inertia = 129[tex] kgm^{2} [/tex].
Final Rotational Inertia = 32[tex] kgm^{2} [/tex].
Initial RPM = N[RPM] = 95
Initial Angular velocity = ω = [tex](2 \pi /60).N[RPM][/tex] = 9.95
Final Angular Velocity = ω = ?

This question is perfect for applying the law of conservation of angular momentum because there is no net external torque acting on the system.

As angular momentum = (rotational inertia) * (angular velocity)

Initial Angular momentum = Initial Rotational Inertia * Angular Velocity
[tex]L_{i} [/tex]=129 * 9.95 = 1283.55;


And Law of Conservation of momentum is:
Initial Angular momentum = Final Angular momentum
1283.55= 32 * ω
Ans-1(in rad/s): ω= 40.1 rad/s

The conversion formula for [rad/s] to [RPM] = [tex](60/2 \pi ).[/tex]ω   
Put the value of ω in the above equation.
Ans-2(in RPM): = 382.9 RPM


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