Let imagine that we put wind indicator on rotating merry-go-around. Will wind indicator stay prepedicular to the radius of circle,showing tangetinal airflow velocity?
(Wind indicator has equal mass and distance from pivot point so moment about pivot point is zero.It desing like this to stop centrifugal force to move one end out of turn..)
I think wind indicator will be prependicular to radius of rotation.. (I ask this because of glider yaw string...)
Let imagine that we put wind indicator on rotating merry-go-around. Will wind indicator stay perpendicular to the radius of circle,showing tangential airflow velocity?
Assuming that the indicator has a mass distribution such that the apparent "centrifugal force" from the rotation has no effect on it, and also assuming that the physical length of the wind indicator is trivially small compared to the radius of the circle, then yes, the wind indicator will remain perpendicular to the radius of the circle at the point where it is located, showing that the "relative wind" is tangent to the circle.
A very lightweight piece of yarn would do essentially the same thing, though there would be a very slight tendency for the apparent "centrifugal force" to displace the free end of the yarn toward the outside of the circle.
However the problem gets more tricky if the length of the wind indicator is not trivially small compared to the radius of the circle. If the length of the wind indicator is not trivial, this means that the "vane" or fin is located well aft of the weathervane's pivot point. The relative wind at every point along the circumference of the circle is aligned with the line that is tangent to the circle at that point. So when the vane streamlines itself to to the relative wind which is tangent to the circle at a point well behind the pivot point of the weathervane, this means that the weathervane is not parallel to a line drawn tangent to the circle at the pivot point of the weathervane. Rather, the weathervane is skewed with its nose outboard, and its tail inboard, of the line drawn tangent to the circle at the pivot point of the weathervane.
This is a large part of the reason why we tend to see some sideslip in circling flight, especially in slow-flying aircraft whose linear dimensions are not trivial compared to the radius of turn. The vertical fin tends to streamline itself to the relative wind, which means that the fuselage tends to be parallel to a line drawn tangent to the circular flight path at a point well aft of the CG.
This effect is illustrated in section 8.10 of the "See How It Flies" website.
In short, in turning flight, the "relative wind" is curved, rather than linear. It curves to follow the curvature of the flight path.
Your question specifically referenced a "glider yaw string" (which would be better termed a "slip string".) Note that if we wanted the relative wind to be exactly tangent to the fuselage near the C.G. of the glider, then we should allow a yaw string at the nose (forward of the C.G.) to stream slightly outboard. In gliders with slender, streamlined fuselages, an argument can be made that it is a better to align the vertical fin with airflow, or at least to adopt a yaw/slip attitude intermediate between the two cases of streamlining the fin and streamlining the portion of the fuselage near the C.G.. This is an argument for allowing the yaw string near the nose to stream significantly outboard. These ideas were explored in an article by Richard H. Johnson in "Soaring" magazine titled "Circling the Holighaus Way".1
Note also that in the sailplane case, minimizing the combined drag from the fuselage, fin, and rudder is not the only consideration-- the drag resulting from any aileron deflection that may be needed to neutralize the net roll torque on the aircraft is also a consideration in selecting the optimum yaw/slip attitude for circling in thermal, as detailed in Johnson's article.
Related ASE answer: Does slipping in turns allow higher climb rates?
Footnotes:
https://www.scribd.com/document/269098126/Holighaus-Thermalling-Efficiency# -- subscription required
http://www.oocities.org/volaosoppo/yawstring.pdf -- highly related article by same author published in "Gliding Kiwi" entitled "Do you really want to keep the yaw string centered"
https://wingsandwheels.com/blog/post/thermalling-in-a-slight-slip -- highly related article published in "Wings and Wheels" entitled "Thermalling in a Slight Slip" -- includes navigation to original article (SSA membership required)
(Unfortunately I cannot locate a current URL to the original article that is not behind a paywall.)
If the vertical surface at the nose and at the tail of the wind indicator (usually called a weather vane) are both flat plates, have the same surface area and are equi-distant from the pivot point then the wind indicator will remain perpendicular to the radius because the force generated by the nose and tail will be equal. If, however, it is designed like a normal weather vane and has a larger surface area at the tail then the nose will point slightly away from the merry-go-round, in your diagram above it would rotate slightly clockwise.
If there is no moment around the pivot point, then you do not have a wind indicator at all. One prominent writer here spoke of "curved airflow" in a turn, and this is a good example of it.
In order to be a "wind indicator" one must have greater Area aft of the pivot point. Because it is fixed, mass distribution is not a factor in indication of airflow direction, but may affect rapidity of response to changing relative wind.
The solution to understanding is to exaggerate the point of contact between the circle and the pivot. One will see that the back end has air flow from the outside and the front end from the inside. Because the back end has more area, the front end will point out of the circle.
It really depends how large a circle you are working with. For an aircraft with a turn radius of 1000 meters, the "weather vane" works fine.
But now comes an interesting twist. Because the weathervane is accelerating in a circular motion, center of mass must be at the pivot point, or error with be introduced to the direction of "point". Interestingly, for a known radius and rpm, placing the CG slightly behind of the pivot point will make the arrow point tangent to the circle!
Circular physics can be a bit different.
