Conservation of Angular Momentum is Great OR I Miss Physics Class

In other words, I've been listening to music spinning in my chair. Wheee.

I've done some super specific tests (watching a clock and counting rotations) to figure out my angular velocity ω. With my arms held inward, I make five rotations in seven seconds, resulting in an average angular velocity ω1 of 4.488 rad/second. With arms outstretched, I make five rotations in twelve seconds, resulting in an average angular velocity ω2 of approximately 0.417 rotations/second, or 2.618 rad/second.

Now, in both situations, my momentum should be approximately the same - L = Iω, where I is my moment of inertia and L is my angular momentum. To figure out my moment of inertia in the first case, I have to cheat a little and assume I'm a uniformly distributed cylinder. I'll assume the chair I'm using weighs about forty pounds, since it's a computer chair with plenty of steel on it, and seems to weigh about 3-4 times what my ten pound weight weighs. Added with me, that's about 92 kilograms. The me plus chair system has a varying radius, but I'll assume it averages at about fourteen inches, or 0.3556 meters. Thus, the moment of inertia is:

I1 = (mr^2)/2 = (92 kg)(0.3556 m)^2 / 2 = 5.816 kg-m^2

My angular momentum in the first case is therefore:

L = (5.816 kg-m^2)(4.488 rad/s) = 26.106 kg-m^2/s

And I can find out my moment of inertia in the second case by using the same equation:

26.106 kg-m^2/s = I2*(2.618 rad/s)
I2 = (26.106 kg-m^2/s)/(2.618 rad/s)
I2 = 9.97 kg-m^2

The only thing different between the two situations in a practical sense is the radius of my arms; we can find how much I "spread out" my weight with:

9.97 kg-m^2 = (92 kg)(r^2)/2
r^2 = 0.216 m^2
r = 0.466 m

Essentially, it's like my weight was "spread out" by a factor of 1.31 in the second scenario. This seems pretty realistic. Though my arms are a small part of my weight, my "wingspan" is fairly significant and the weight of my outstretched arms can add a lot to the moment of inertia. Think of it like a see-saw, where the further you are from the middle, the more upward force you exert on your partner's side.

Error could be introduced by my shoddy timekeeping, pushing with more or less force in either scenario, and the friction and air resistance differences in the two situations. When my arms are outstretched, air resistance can play a big part. Friction will also obviously have more effect on the second scenario, since I'm spinning for longer. Also I'm not a cylinder. Oh well though, it was just for fun. Need to do some good math here and there, even if it's just a little algebra.