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Conceptual Rotational Motion and angular velocity

  1. Nov 30, 2008 #1
    1. The problem statement, all variables and given/known data

    A rigid body is rotating about a fixed axis through the origin. The angular velocity is [tex]\omega[/tex][tex]\hat{k}[/tex] where [tex]\omega[/tex] is positive. What is the unit vector in the direction of the velocity of a point on the body located on the positive y axis?





    3. The attempt at a solution


    Well, I'm pretty confused about what this is actually asking me [could be the time of night.] All I can think of that's applicable is the fact that angular velocity is the same for all points of a rigid body, so perhaps the answer is just [tex]\hat{j}[/tex]
     
  2. jcsd
  3. Dec 1, 2008 #2
    You are right about angular velocity being constant for all points in the same rotating body. So, why choose a unit vector for velocity of a point on the body that differs from the unit vector of velocity for the whole body?
     
  4. Dec 1, 2008 #3
    Ah, I was just getting confused by what that really meant, but now (after some sleep, and your question) it seems alot clearer. I for some reason believed that the magnitude of rotation was transposed onto every plane.
     
  5. Dec 1, 2008 #4
    Oh, actually this question is multiple choice and I cannot give K hat as an answer. hmm...there is always the E.) there is not enough information given to determine the answer option, but physics books hate resorting to that.
     
  6. Dec 1, 2008 #5
    Upon rereading, I think the question is asking for VELOCITY... in that case, we are looking for the linear velocity of a point on the positive y-axis.
     
  7. Dec 1, 2008 #6
    The question is specifically asking for the unit vector, or bearing of the velocity in positive Y direction, which is exactly where I'm confused. Is it really just testing whether or not I know that the positive Y direction is the j hat unit vector? That seems a little too easy for this level physics class.
     
  8. Dec 1, 2008 #7
    The unit vector for angular velocity of a rotating object in the counterclockwise direction on the x-y plane is k hat, which is what the question gives you. The linear velocity vector for a point on the body is on the x-y plane. I made a mistake earlier because I was assuming the question was asking for the unit vector of the angular velocity of a point on the positive y-axis, which would still be K hat.

    One question remains now. Specifically, for a point on the y-axis what is its LINEAR velocity unit vector?
     
  9. Dec 1, 2008 #8
    After re-reading, I realize I may have to make a few assumptions. One being the positive direction of angular motion, if we take it to be counterclockwise, then I believe that the answer would be -i hat.
     
  10. Dec 1, 2008 #9
    Yes, I agree fully. The best reply I can give you is that you should follow the convention your text has set for you. But, I am of the opinion generally counterclockwise is accepted as the positive convention.

    Based on this premise, then -i hat should be the right answer.
     
  11. Dec 1, 2008 #10
    Thank you very much for your help horatio
     
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