First time asking question here.

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.


Gear Example:

enter image description here

  • $\begingroup$ Thats kind of the definition of torque on rigid bodies. $\endgroup$ – 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. $

So regrdless of the diameter of the gears the torque on them is equal.


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