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!

Angular velocity using Newton's law

  1. Sep 20, 2012 #1
    1. The problem statement, all variables and given/known data

    Small object of mass m is placed on the inner surface of the conical dish which can rotate with angular speed ω.

    For μ=0.3 calculate the minumum and the maximum ω such that the object is remains at rest. Solve the problem using the indicated axes x-y.

    Do the following steps:
    (a) Show all forces acting on the object and and the acceleration
    (b) Write Newton’s second law along both axes and solve.
    pHuhr.png

    2. Relevant equations
    F=ma=m*ω2*r
    3. The attempt at a solution

    je6Ro.png

    I have plugged in numbers and got answers for ωmax and ωmin but I dont get the right answer.
    I have solved it right when I choose axis the ordinary X-Y axis but I need to know how to solve with using the other axis mentioned in the problem

    The right answer is
    ωmax=7.214 rad/s and ωmin =3.405 rad/s
     
    Last edited: Sep 20, 2012
  2. jcsd
  3. Sep 20, 2012 #2
    Your equation for both the X and Y direction is wrong.
    You have taken the wrong component of mg and mω2r along the X direction. In the RHS, it won't be completely mω2r, it will be some component of this force. Make a free body diagram.
     
  4. Sep 20, 2012 #3
    hbs29.png

    In my free body diagram i have the fricton coefficent on both sides because it can go both upwards and downwards.

    I dont really get what I should do on the right hand side for mω2*r

    I have been trying for a few hours now and I am completely lost now.
     
  5. Sep 20, 2012 #4
    Correct!
    The force mω2r doesn't act in the X direction, so you will have to take its component along the X direction and solve.
    See the image below, that should help you.
    5bxqfc.png
     
  6. Sep 20, 2012 #5
    Thanks very much.

    I did not know in what direction the ω2 force was heading. Tried to read it in my physics book but english is not my first language so i didn't understand it.

    I feel like i'm getting closer but there is something wrong in my 2 equations because I cant solve them ( because there is something wrong with them)

    Can you give my a hint, Sir?
    r5m4p.png
     
  7. Sep 20, 2012 #6

    Doc Al

    User Avatar

    Staff: Mentor

    ω2r is the centripetal acceleration. Don't think of mω2r as a force, but as mass*acceleration. (View things from the usual inertial frame.)

    Why can't you solve them? Eliminate N. (I think you have one of your angles wrong.)
     
  8. Sep 20, 2012 #7
    I always got an error when i tried to solve it using wolfram alpha.

    I just probably had a silly typo because it worked when I typed it in again.

    I got it right when i changed the angle to 30° in the formula for y axis.

    But I still dont get why it is not 60° in the y axis formula.

    Anyway thank you both so much for the help. Such a lovely community.
     
  9. Sep 20, 2012 #8

    Doc Al

    User Avatar

    Staff: Mentor

    The angle between mg and your y axis is 30 degrees; the angle between mω2r and your y axis is 60 degrees. And sin(30)=cos(60) & sin(60)=cos(30).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Angular velocity using Newton's law
Loading...