I want to roll the function f(x)=sqrt(x), x∈[0,1] along the y-axis.

I know how to rotate the graph around a point, but I'm not sure how to rotate along an axis in 2D.

Rotating around a point e.g. (0,0) would look like this:

Manipulate[ParametricPlot[{{t, t^(1/2)}, RotationTransform[k, {0, 0}][{t, t^(1/2)}]}, {t, 0, 1}, PlotRange -> {{-2, 2}, {-2, 2}}], {k, 0, 2 \[Pi]}]

Thank you in advance!