1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple typo question: Radial & circumferential components of velocity

  1. Sep 25, 2013 #1

    s3a

    User Avatar

    1. The problem statement, all variables and given/known data
    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.

    2. Relevant equations
    Derivatives, chain rule and trigonometry.

    3. 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!
     

    Attached Files:

  2. jcsd
  3. Sep 25, 2013 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You need to develop some confidence in your own understanding. If you think it should read as 'radians', just go ahead and work the problem that way and see what happens! You can compare your own solution with the one supplied; of course, there is always the possibility that the supplied solution is incorrect. Then, if your answer differs from the one supplied, you can then come to us and ask about the difference.
     
  4. Sep 25, 2013 #3

    s3a

    User Avatar

    Trying out what you said, 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?
     
  5. Sep 25, 2013 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    I have already suggested that you try it out for yourself. Then--after solving the problem--if your solution differs from the one supplied, come back here with questions. As I said before: try to develop some confidence in your own understanding. That is by far the best way to learn.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Simple typo question: Radial & circumferential components of velocity
Loading...