Does hair rotate while growing?

If you take a very fine pencil and daily make a mark on a growing hair, at it’s base, always on the same side of the follicle, would you have drawn a spiral after some time?
The hair-pushing cells can’t be exactly at 90 degrees. If they are more slant at one side of the hair, the hair will change orientation while growing, wouldn’t it?
Are there lefties and righties?
How many RPMs (revolutions per month)?

More than you really wanted to know about how hairs grow.

http://alopecia.mcg.edu/html/alopecia/documents/HairGrowthLoss/Growth&LossOfHair.html#HairGL-1-1

It doesn’t look to me like hairs grow in a spiral pattern. There are concentric rings of hair-growing cells that surround the central shaft, and they all reproduce straight up and out, more or less.

http://alopecia.mcg.edu/html/alopecia/documents/HairGrowthLoss/figure4.JPG

At an estimated 1:300 scale of your linked image on my monitor, the hair could easily reach 50 meters!
At a length some thousand times greater than diameter, ‘more or less straight’ at the base may sum up to a good deal of twisting at the top:

A line drawn on a cylinder spirals around it once every height of h=c/tan(a),
with c=circumference of cylinder, a=angle of the line to the vertical.

If all cells uniformly get pushed out, say, clockwise at an angle of a mere 1 degrees,
a hair of diameter=0.075mm will turn around once every 13mm of growth.
At 0.4mm per day, this would be one revolution per month. I’m dizzy!

I remember this NewSci Last Word article
(It’s no shame reading it, hey, they only know because Cecil told them.)
saying most trees are ‘screwed up’!

Now, not all cells can grow in exactly the same straight direction / at the same angle,
there should be a net torque. But big enough to notice?
Do I have to spend one lonely month in front of a mirror?