momentum - How to escape the center of a room without gravity?

Imagine you're an astronaut on the International Space Station and your fellow astronauts played a prank on you by taking all your clothes and putting you in the center of a module so that you cannot reach anything with either your hands or your feet.

What would be the most effective way to escape that situation if you're reluctant to start peeing?

Answer

It is worth calculating (rather than just speculating) some of the methods described.

1. Breathe in one way, and out the other. Your resting tidal volume is about 0.5 liter; take a deep breath and it can be 3-5 liters (thanks @Aaganrmu). That is about 4 gram of material. If you purse your lips to increase the velocity with which you expel the air, you can get it to around 10 m/s (I estimate this from the data in this paper which measured the velocity of air in a cough - 15 m/s - and spoken word - 4 m/s.). This gives a net momentum of 0.04 kg m/s, which means a 70 kg astronaut will get a reaction velocity of 0.05 mm/s, moving 1 cm every 20 seconds. But if you do this 10 times per minute, your acceleration will be about $10^{-4}~\rm{ m/s^2}$ and you will travel 2 m (to the nearest wall) in about 200 seconds. Feeling somewhat dizzy from the hyperventilation... Note that it's not necessary to turn your head: it's enough to breathe in slowly, and out rapidly.


2. "swim" with your arms. If you can change the area of your arms by 20 cm$^2$ between the "forward" part of the stroke, and the "back" part of the stroke, and you can move the hand with a peak velocity of about 2 m/s for 50 cm, the approximate drag force will be $F = \frac12 \rho v^2 A C_D = 0.5*1*4*0.02*1.0 = 0.04~\rm{ N}$ - four times more than breathing out. And of course you can probably move your arms a great deal faster - let's say one complete stroke (two arms) per second, for an acceleration of $6\cdot 10^{-4}~\rm{m/s^2}$ and a time across the capsule of 80 seconds.

Combining the two techniques, the exercise with the arms will allow you to breathe more rapidly (at peak exercise, an adult male can move about 100 liters of air per minute - that is 10 times higher than the value I used). This should comfortably get you to the side of the capsule in under a minute.

If you can increase the mass you accelerate, you can greatly improve on these numbers. I briefly considered that spitting might be the answer, but your mouth will run dry pretty quickly. Other bodily fluids would greatly improve on the time - but given that you still have to live in that space after the fact, I think that spending a bit more time waving your arms about, then laugh at the videos your crew mates made, is the best approach here.