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. The solution to part (a) is also attached as TheSolution.jpeg, should it prove useful.
Determine for the point with rectangular coordinates [½ + 1/√(2), ½ + 1/√(2)] the
(a) radial and circumferential components of the velocity.
Derivatives, chain rule and trigonometry.
The Attempt at a Solution
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 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 but, I would very much appreciate any confirmation/contradiction!