Question

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

Answer 1

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

`L_(i)`=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] =
`(60/2 \pi ).`ω
Put the value of ω in the above equation.
Ans-2(in RPM): = 382.9 RPM


-i