What is your point? The spool requires traction just as the bb does.
Last word on the reel.
Traction is
another problem, but as I have said, the rolling friction works against a car's wheel, just as it does for the reel, but on a car, the torque from the axle
drives the wheel in the direction of rotation, whereas in the case of the "under" reel, the thread produces a torque in the
direction opposite to rotation. That
appears to be paradoxical, because the reel turns CW and to the right.
A reel on a spindle held in the hand will turn CCW, because of the torque produced by pulling the thread, but when on the ground, it turns CW and moves to the right. That is not something that can be seen by observation, nor drawn with simple diagrams because it is not static. But math gives the answer. "Thought experiments" have their limits too.
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Much can be found here, and through links from there.
http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html
This link shows that wheels have linear and angular components.
http://hyperphysics.phy-astr.gsu.edu/hbase/rotwe.html#ro
It's algebra and a basic Newton. I have added some explanation to the original post and diagrams.
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A reel can be rolled towards the hand applying F, but may also turn counter-clockwise (CCW), and roll away from the hand.
Assuming that the force is applied parallel to the floor ( no lifting of the reel), which way will it go?
a = inner radius
b = outer radius
Fd = Friction
F = Applied force
m= reel mass
I = reel moment of inertia
v= linear velocity
w = angular velocity (radians/sec)
This is the significant bit;
1) Linear component:
Net force to the right = F - Fd ( applied force less the drag force)
Acceleration dv/dt = F - Fd/m ( simple application of f=ma)
If the hook is employed, the reel will move at the speed of the hook on that linear force alone, and will roll CW. ( It can slide too, but we will ignore that case)
But, when the thread is used, it generates a CCW torque. It's important to see that the thread produces
both linear force (like the hook) and angular force CCW.
2) Angular Component:
Net clockwise (CW) moment = b*Fd - a*F ( net force, geared by the ratio)
Angular Acceleration dw/dt = (b*Fd - a*F/)I ( F=ma for rotating objects)
When a wheel rolls without sliding ( pure rolling) the axle of the reel moves a distance equal to the circumference. So, the linear velocity (the speed the axle moves) and the angular velocity ( the speed it turns) are related by;
3) v = b*w
( That is the no-slip case. Velocity = large radius*rpm w=radians/sec)
The linear and angular accelerations are related as:
dv/dt = b*dw/dt
( relates the linear acceleration (1), to the angular acceleration (2)
The rest is equating forces, which always come in opposing pairs. Perhaps if worked with a= b, it may be clearer.
From a = f/m
(F - Fd)/m = b(b*Fd - a*F)/I
Rearranging to relate Fd in terms of F
Fd( I + mb^2) = F( I + mab)
Fd = F(I + mab)/(I + mb^2)
If the reel moves to the right, then both the linear and angular forces will be positive (to the right). That depends on the friction to the surface and how the force is applied. If pulled slowly, the reel will tend to roll with the hand, but a jerk
may send it away.
It's a balance of the inertia of rotation and the friction to the surface, where the angular component is either positive or negative.
There is a third case, where there reel does not roll, but slides, so the angular component is zero. That may happen when the friction is very low. Wheels cannot roll without adequate friction.
The under reel is the worst choice, because it basically opposes itself.