You can check the lengths of existing paths from Document info panel. There's subdialog Objects for it:
You can make circles with a wanted path length difference by drawing equally spaced full circles. The easy way is to draw 2 circles, align them to the same centerpoint, make a blend, expand the blend and ungroup it to get separate circles.
Then draw 2 straight lines from the common centerpoint. With the rotation tool you can get the angle between the lines to be a wanted one.
Cut off the sector between the lines from every circle. That's done in the next image. You can rotate every circle around the original centerpoint (=the common point of the lines) as needed. In the next image the rotations are random with no design idea.
Let's assume there's N circles, the smallest has diameter D1 and the biggest has diameter D2. Let the removed sector be X degrees. The lengths of the remaining arcs are
Pi(1-X/360))(D1+m(D2-D1)/(N-1)) where m gets values 0, 1, 2,...(N-1).
the length difference of 2 adjacent arcs is Pi(1-X/360)(D2-D1)/(N-1).
There are a few tricks which should be known for smooth working. At first have smart guides and snap to point non, no other snaps!
With the rotate tool you can set numerically the needed rotation and make a rotated copy. Select the object to be rotated, Alt+click with the rotate tool the wanted rotation center, type the wanted angle and press Copy to get a rotated copy. The next image shows the dialog which opens when you click holding the Alt key at the same time:
Here's a short cartoon of the process after you have blended the 2 circles, expanded the blend and ungrouped.
1.-2. Draw a line from the centerpoint, make a rotated copy
Select all, split all paths in the crossings with Pathfinder panel function Outline. All strokes vanish.
Ungroup. Insert a stroke color and width. Select the wanted parts and move them apart. You will need the centerpoint, do not lose the crossing of the lines! It's your only remaining centerpoint reference.
I guess you want something like the black shape in the next image:
The innermost circle has diameter = 25 mm, the outermost has 50 mm. The removed sector is 136 degrees. The rotations are calculated to cause equal arc end shifts along the arc. In addition the outermost ring has its clockwise end towards the right from the beginning of the innermost arc. The rotation difference must decrease proportionally to outwards for the same shift. The innermost arc is not rotated after it was clipped. The outermost is rotated -136 degrees. The rest of the rotations are calculated.
Both ends will have automatically the same shifts if the arcs are made by removing the same sector angle.
All this math is elementary, but to see it one must recall the arc length = Pi * D * (X/360) where D is the diameter and X is the arc sector in degrees.