Friday, February 21, 2014

What does a tornado and an Olympic medalist have in common?

No, this isn't a joke. Here's a hint: every tornado needs it and every Olympic medalists control it. The answer: conservation of angular momentum.
The United States won Bronze during the team skate competition in the 2014 winter games.

In physics, angular momentum (L) is a measure of rotation. It is equal to the product of an objects mass (m), velocity (v), and radius of rotation (r).

L = mvr

Angular momentum is a conserved property meaning it doesn't change (as long as no external forces are applied to the system). Thus, if we change any variable in the equation, the other variables will change to a degree in which the angular momentum remains unchanged. Thus, we may write a change in angular momentum as follows where the "i" indicates a variable at an initial time and "f" indicates the variable at a final time. (We assume the mass does not change, but this doesn't have to be true in every case.)

m * v_i * r_i = m * v_f * r_f

A figure skater or freestyle skier can change their radius by hold out their arms or bringing their arms close to their body. When an Olympian holds his or her arms out, they increase their radius of rotation and their spinning velocity decrease. Conversely, when they bring their arms close to their body, their radius decreases and their rotation velocity must increase.

Tornadoes are subject to the same law. When a column of air is stretched, the radius of rotation is reduced causing the velocity to increase. Lots of stretching means strong winds. The figure below illustrates the conservation of angular momentum in large convective storms.

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