Torque between concentric gears

I'm not a mechanical engineer!

I have a simple question that I can't explain the answer to it. I have a double gear (2 concentric gears with different radius) and I don't understand why the torque is the same for both. I found in the internet that the torque should be the same because they are cocentric, but don't understand why.

Thanks!

Gear Example:

• Thats kind of the definition of torque on rigid bodies. – joojaa Jan 21 '20 at 5:54

Consider, for example, the shaft passing through the two gears has a torque of 10Nm and the diameter of the larger gear is twice as the diameter of small gear, $$R_{large}= 2*r_{small}$$.
The tangential force on the circumference of the large gear is then $$\frac{10Nm}{R}=\frac{10Nm}{2r}\quad$$ but the tangential force on the small gear is twice as much$$=\frac{10Nm}{r}$$
Therefore the torque produced by the small gear is $$=\frac{10Nm}{r}*r=10Nm.$$
And the torque produced by the big gear is $$=\frac{10Nm}{2r}{2r}=10Nm.$$