Here is the part of the problem that I am referring to (that is also fully portrayed in a more aesthetically-pleasing manner in the TheProblem.jpeg attachment).:
Consider a particle moving on the curve whose equation in polar coordinates is r = 1 + cos(θ). The rate of change of θ is given as 2 radius per second (which is exactly what it written). The solution to part (a) is also attached as TheSolution.jpeg, should it prove useful.
Determine for the point with rectangular coordinates [˝ + 1/√(2), ˝ + 1/√(2)] the
(a) radial and circumferential components of the velocity.
Basically, in the problem, it says that the rate of change of θ is given as 2 RADIUS … I just wanted to ask/confirm if the author intends to say 2 RADIANS or 2 RADII. I think the author meant RADIANS because, it seems more likely that the θ (angle) variable uses an angular unit. So, what would be the value of ##ν_r## when the units are included? Would the (final) value be –√(2) radians/second or radii/second? My confusion arises from the fact that I am searching for the velocity along the radius but, I think the rate of change of θ as time passes is in radians.
It seems that, if I use the word “radii” (instead of “radians”) for where it says “radius” in the question, differentiation of r = 1 + cos(θ) would yield dr/dt = dr/dθ dθ/dt = -sin(θ) (2r) = dr/dt = -2rsin(θ) which is a differential equation so, since this is not a question intended for the study of differential equations, it must be “radians” (instead of “radii”) for where it says “radius” in the question, right?
Despite this being just a small typo, I would still VERY much appreciate any confirmation/contradiction!