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Homework Help: 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).
     
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