Parallel Forces: Painter on scaffold x meters from 1 end.

[Ocata]

Hi,

My book says that although there is a natural point of rotation, we can however choose any point as a center of rotation. But without explaining further, it goes directly to an example where the endpoint is the center of rotation.

I would like to know what the book means by being able to choose any point as a center of rotation.

For example,
A painter weighing 150lbs is standing on a 6ft scaffold at a distance of 2 ft from one end. How much weight must each end of the scaffold hold?

F1 + F2 = 150lbs

Torque = Torque
Fs = Fs
150lbs(2ft) = F2(6ft)
F2 = 50lbs

So F1 + F2 = 150lbs
F1 + 50lbs = 150lbs
F1 = 100lbs

Here, F1 was the point of rotation. But how can this problem be approached if a different point of rotation is considered? And is there an infinite number of choices for points of rotation? Or is there a finite number of possible points/centers of rotation?

 

[RUber]

Let's say you chose a point of rotation on the scaffold, 0<x<6.
Then if F1 is placed at 0 and F2 placed at 6, you still have to balance the forces.

 

[Ocata]

Thank you RUber.