Let's consider a hypothetical situation where a communications satellite is launched into orbit. However, no launch is perfect so after burnout the satellite has picked up some roll. In order to correct this roll, the reaction wheels that the satellite is equipped with are used to apply the appropriate torque necessary to negate the rotation of the spacecraft. This is done by rotating the reaction wheels in the opposite direction to the rotation of the spacecraft, until enough angular momentum is applied that the spacecraft's rotation is nullified.
However, in this situation the reaction wheel would still be spinning even when the angular velocity of the craft is corrected. There are a couple problems here...
If we assume friction is negligible...
If we assume friction is negligible or non-existent, then the reaction wheel which is now spinning will continue to spin until the reaction wheel is powered up again (as per Newton's first law of motion). Now lets say that due to external factors the spacecraft picks up more rotation in the same direction as before, and the reaction wheel must be sped up further in order to counter this. Eventually, this cumulative application of angular force to the reaction wheel will speed up the reaction wheel so fast that it goes beyond its limits of structural integrity - which is bad.
If we consider friction...
If we consider friction to be a factor in the aforementioned hypothetical situation, then the reaction wheel will begin to slow down as the force of friction is applied on it. However, this force of friction would not only be applied to the wheel, it's equal and opposite reaction would also apply a rotation to the spacecraft and destabilize it, making it necessary to use the reaction wheels even more...
Is it true that reaction wheels are not, on their own, capable of stabilizing a spacecraft? If not, why not?