Will a gas rotate as fast as the spherical container it is contained within? Let's say I have a sealed spherical glass container 30 cm in diameter which contains plain air.
The glass container is rotated about its axis at 1 revolution per minute.
My question is, would the gas also rotate at 1 revolution per minute within this sealed glass container?
 A: Given viscous effects, that is indeed the case if:


*

*We are looking at a steady state system

*It is not a rarefied gas (i.e. at pressures much lower than atmospheric) 

*The walls of the container are rough enough such that the gas molecules don't 'slip' over the surface but can be assumed at the same angular velocity (i.e. the no-slip condition)


Point 2 is important because when rarefied, gas molecules will simply bounce around without interacting with each other which is not a very effective method of momentum transfer. 
In general, it is rarefied if the so-called Knudsen number:
$$\text{Kn}=\frac{\lambda}{L}$$
where $\lambda$ is the molecular length scale (mean free path of the molecules) and $L$ is the characteristic length scale of the system. If these are comparable (i.e. $\text{Kn}\sim1$), molecules rarely interact through collisions and we consider the gas rarefied. If the mean free path is much smaller than the system (i.e. $\text{Kn}\ll1$), then molecules often interact with each other through collisions in which they exchange momentum. In that case we can consider the continuum approximation to fluid dynamics; we can consider flow fields rather than individual molecular motion.
