ORIGINAL: Anthoop
The smaller spur gear is second gear, it will only engage to drive the wheels when the shaft is turning fast enough for the second gear clutch to operate. So, yes it is normal that it rotates freely.
If it is not shifting to second gear then it could be adjustment or something physically wrong with it. Note also that if the engine is not turning the gears fast enough for whatever reason this will also prevent it from shifting.
Many thanks for your help.