How does dividing 1 Nm over a small wheel work?

[Eithman]

I found a servo that provides a little over 1 Nm of torque. Since a Nm = 0.74 Foot pounds, if I applied 1 Nm to a wheel that had a 10cm circumference, 100cm/10cm = 10,  And changed foot pounds to meter pounds .74 FP * .305 = .226 would each rotation of the 10cm wheel be pulling with 2.26  lbs of force? .226 * 10 = 2.26 lbs? Disregarding efficiency. Is this correct, if so could you explain where I went wrong?

[jkerns]

Torque = force * distance

Force = Torque / Distance.

The distance is the radius of the wheel, not the circumference. You use the circumference to convert revolutions to distance traveled, but think of torque as a force applied to a lever with a length that is the radius of the wheel.

[Eithman]

Ok, so if the radius of the wheel was 10 cm and everything else was the same, would the answer be the same as before?

[jkerns]

10 cm radius = .33 feet.  (20 cm diameter)

.74 ft-lb / .33 ft = 2.2 pounds of tractive force.

Same answer.

[Eithman]

Excellent! Thank you very much!