Spinning nauseatingly fast

Classical Mechanics Level 3

The world record for revolutions per minute for an ice skater is 308 RPM, held by Natalia Kanounnikova. You can see a video of the spin here .

When she starts the spin and her leg is extended, she's going somewhere between 1-2 revolutions per second. Let's average this and say her initial angular velocity is 1.5 revolutions/sec. She has to do work to move her leg in and get herself to speed up. To see this, calculate the ratio of her final rotational kinetic energy to her initial rotational kinetic energy (it's >1 so she had to do some work).

Details and assumptions

Neglect any friction with the ice.

The answer is 3.42.

1 solution

David Mattingly Staff
May 13, 2014

She's isolated as there is no friction between her and the ice, so angular momentum is conserved. We therefore know that her initial moment of inertia $I_i$ and final moment of inertia $I_f$ are related by

$\frac{I_i}{I_f}=\frac{\omega_f}{\omega_i}$

where $\omega_i,\omega_f$ are her initial and final angular velocities. Since rotational kinetic energy is $K.E.=\frac{1}{2} I \omega^2$ we can calculate the ratio of her final K.E. to initial, which works out to be $\omega_f/\omega_i=308/90=3.42$ .

You are incorrect. The angular velocities should be squared. The ratio is ~11.7

A Former Brilliant Member - 3 years, 8 months ago

This is false (I believe). Shouldn't it be wf^2/wi^2, coming out to 11.71?

Ace O - 5 years, 2 months ago

The moment of inertia will change since the ice skater has to move her legs. The distribution of mass is changing

Akshat Joshi - 4 years, 8 months ago

how did u calculate final angular velocity ??

A Former Brilliant Member - 4 years, 7 months ago

wf=308rpm(2pi/60)=32.25rad/s (wf)^2/(wi)^2=462

Jason Teh - 2 years, 8 months ago

I think the solution is inaccurate. The energy of rotating particle is given as integral of the angular momentum analogous to classic particle mechanics, so the energy is related as square of the angular velocity

Arpit das - 6 months, 2 weeks ago

This is false, the answer should be about 11.71 because its velocity squared

Shaurya Agrawal - 3 months, 3 weeks ago

Spinning nauseatingly fast

The answer is 3.42.

1 solution

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