Need some clarification with torque or force and gear ratio

Hi guys, I have a question about gear ratio, sprocket or wheel ratio.

So lets say I have a motor with connect to a small output sprocket, and I want to use this motor to pull some load, so in order to do this I need to connect the chain with a larger sprocket, lets say 2 time bigger than the other. So this increase my torque by 2x while the RPM is 2x less.

Ok, now I want to generate more torque (not sure if I should say force), I dont know how to say this, but I want to stick a cylindrical object, concentric with the larger sprocket, but this cylinder will have a smaller radius (lets say 2x smaller), and a string that will connect this cylinder to the load (like an inner pulley). Would this increase the pulling force 2x as much as just using the larger sprocket?

Thanks and sorry for my lack of terminology.
This is why I can't find the thing I need by searching google =(

CWatters
Homework Helper
Gold Member
I want to stick a cylindrical object, concentric with the larger sprocket, but this cylinder will have a smaller radius (lets say 2x smaller), and a string that will connect this cylinder to the load (like an inner pulley). Would this increase the pulling force 2x as much as just using the larger sprocket?

Yes. Consider a winch.... The smaller the radius of the drum the greater the pulling force but the slower the wire is wound in.

Yes. Consider a winch.... The smaller the radius of the drum the greater the pulling force but the slower the wire is wound in.

Thanks, and the reason that I get a greater force is because they spin together with the same ω the torque is also the same on both, but the radius is difference right?

and for chain and sprocket, what do they both have? The tangential force is the same right? but the larger sprocket have a bigger radius so it give more torque and slower rpm?

CWatters
Homework Helper
Gold Member
Yes. The basic equation is..

torque = force * distance (eg radius)

Gears on a common axle have same torque so treat that as a constant and you can rearrange it to give..

force = torque/distance

Change the distance (radius of the winch drum) and the force changes.

For sprockets connected by a chain...The chain tension (force) is the same so treat that as a constant..

torque = force * distance

As you change distance (radius of the sprocket) the torque changes.