# Angular momentum paradox with 2 identical gears

Consider two identical gears touching each other. The system is friction less. One has a handle that you use to apply a torque on the entire system. If you turn the handle, there will be a non-zero torque on the system, but since the gears are identical and would have equal angular speeds but rotate in opposite senses their angular momenta would add to zero at any time. So how can the angular momentum of the system remain zero (i.e. never change) when there is an external torque being applied to the system?

Edit: The two gears are fixed on axles. And what if, to simplify, you are just applying a tangential force on the edge of one of the gears (no handles involved) to supply the torque?

• If the gears are fixed on axles, the torque can be transferred to the other end of the axles. You don't have a closed system, so the conservation law does not apply. It is just like when you are standing and start walking forward. Your momentum increases. Does that violate momentum conservation? No, you have transferred it to the earth, which has changed velocity and angular velocity ever so slightly. – Ross Millikan Dec 8 '15 at 6:18