Though one may not know the technical definition of the Conservation of Angular Momentum, most people are aware of the process.  For instance one may see a yo-yo being swung in a circle.  As the string wraps around the plastic piece every revolution, the string shortens and the yo-yo will circle more quickly.  Close observation of a tornado will reveal that the narrower bottom of the cloud rotates at a greater speed than the portion closest to the storm cloud.  What can explain this phenomenon that affects so many aspects of life?

    All of the above exist due to the Conservation of Angular Momentum.  Any object executing motion around a point possesses angular momentum.  The Conservation of Angular Momentum states that the total angular momentum at one instant in time has to equal the total angular momentum at another instant in time in a system.  It is illustrated by its equation:

Ðp = mvr

m = mass of object/mass of smaller object (if two objects are used)
v = velocity of the object/velocity of smaller object (if two objects are used)
r = radius/separation of the two objects

The letter "L" is often used to replace Ðp as the symbol for angular momentum.

    The total angular momentum (Ðp) is to remain the same, even though the values of m, v, and r are subject to change.  Therefore, if the mass of the object would increase (decrease), the velocity and/or the radius must decrease (increase).  If the radius would increase (decrease), the velocity and/or the mass would have to decrease (increase).  Since it is most likely in a situation that the object, and therefore the mass, would not change, the velocity would have to be the factor to decrease (increase).  And if the velocity would increase (decrease), the mass and/or the radius would have to decrease (increase).  In this situation, it is also likely that the object/mass would not be changed, and only the radius would decrease (increase).

    How does this relate to the examples given at the beginning of the paper and why does the yo-yo spin faster as the string is shortened?  In this problem,

m = mass of the yo-yo
v = velocity at which the yo-yo is spinning
r = the length of the string from the hand of the person spinning the yo-yo and the plastic piece

    As the string is looped around the plastic piece of the yo-yo it shortens, decreasing the value of r.  Since the mass of the yo-yo would not change, velocity would increase in this example.

    The tornado works almost the same way as the yo-yo except in this problem,

m = mass of the tornado
v = velocity at which the tornado rotates
r₁ = the radius of the top of the tornado
r₂ = the radius of the bottom of the tornado

    It was stated that the top of the tornado spins more slowly than the bottom of the tornado.  This is because the radius of the top is greater than that of the bottom (if you think of a typical tornado, you will recall that it tapers as it gets closer to the ground).  The angular momentum must be conserved throughout the tornado.  In the equation Ðp = mvr₁, the radius is larger than that of the equation Ðp = mvr₂.  (Though the mass of the tornado may change as it picks up more debris or changes its intensity, this does not factor into this equation as it is examining the tornado at one fixed moment in time.)  Therefore, it is up to the velocity to change in response to the difference in the radius.  In equation 1, the radius is greater than that of equation two:  the velocity is less in equation 1 than it is in equation 2.

    Since our group's Pre-Calc exhibit was chiefly concerned with the conservation of angular momentum of a tornado, I will assign actual values to that equation to further illustrate how this scientific principle works.  (The following values are averages except for the mass.)

m = 1818kg
v₁ = 94 mph
v₂ = ?
r₁ = 150 ft
r₂ = 450 ft

Equation 1:  Ðp = 1818 (94) (150) = 25633800
Therefore,

Equation 2:  25633800 = 181 (?) (450)
? = v₂ = 315 mph

    This proves that the velocity at the bottom of the tornado must be greater than the velocity at the top because the radius at the bottom is less than that of the top.

    Also so it is shown that the Conservation of Angular Momentum does exist, proven by math and real-life examples.  The angular momentum of a system must be conserved throughout that system.

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