Why do skaters pull their arms inward when they spin?
Topics Covered: Angular Momentum
Do you like watching figure skating? Whether you are a big figure skating fan (like me) or not, you should notice that whenever figure skaters spin, they draw their arms inward and speed up tremendously. Have you ever wondered why? Not surprisingly, our good friend physics and the concept of angular momentum will explain this fascinating phenomenon.
From our previous post about momentum, we learned that (linear) momentum is the product of mass and (linear) velocity. Now, angular momentum is similar to linear momentum, but instead of multiplying mass and velocity, we multiply moment of inertia with angular velocity.
In other words, L = I⍵.
Here’s an important concept: both linear and angular momentum are conserved. This means, unless there is a net external force, the total momentum of the system would stay the same. If we put this in an equation, IO⍵O = If⍵f (initial angular momentum = final angular momentum).
Remember our old discussion about rotational inertia? Since I = MR2, when R (distance from the axis of rotation) increases, the rotational inertia I also increases.
Now, let’s go back to our original question. When a figure skater pulls his/her arm in, the rotational inertia would decrease because R decreases. However, since total angular momentum must be conserved, if I (moment of inertia) decreases, ⍵ (angular velocity) must increase in order to keep the angular momentum constant. That’s why the figure skaters spin faster when they pull their arms in!
On the other hand, if skaters straighten their arms, then their distance from the axis of rotation R would increase, which would then increase I, and thus decrease angular velocity ⍵ in order to conserve the angular momentum. That’s how physics works with figure skating!
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