Why does a constant force result in 0 torque in Barlow's wheel experiment?

[NooDota]

Homework Statement

In the Barlow's wheel experiment, let's say I want to find the torque of the forces that affect it. (Friction is ignored)

I have W (weight) has no torque
R (reaction) also has no torque
F (the force that moves the wheel) does have torque

I can calculate F's torque individually.Now my question is, if I use ΣΓ = I*α, I'll get 0, because the angular acceleration is 0 since the angular velocity is constant.Why do I get 0 when I do have torque?
Thanks

Homework Equations

ΣΓ = I*α

The Attempt at a Solution

 

[mfb]

Without friction, the wheel is constantly accelerating (unless your current breaks down at some unrealistic speed).

 

[NooDota]

But alpha in this case is 0 because the velocity is constant, no?

 

[mfb]

Why do you expect the velocity to be constant in the absence of friction?

 

[NooDota]

Because the force that's causing the velocity is constant? Neither the current, the radius or the magnetic field are changing.

 

[mfb]

Which force?
Without friction, you have an accelerating force (more precise: torque), so the wheel keeps accelerating.

 

[NooDota]

I don't know what you call it in English. The F = I*L∧B force.

It's what's moving the wheel, and it's constant, and so the angular velocity is constant and the acceleration is 0, since the velocity isn't changing.

 

[mfb]

It's what's moving the wheel, and it's constant, and so the angular velocity is constant and the acceleration is 0, since the velocity isn't changing.

No, a constant force leads to a constant acceleration.

What you actually need is the integral $\int_0^L I B r dr$ for the torque, but that follows the same rules.