Conceptual Rotational Motion and angular velocity

[JPhillips]

Homework Statement

A rigid body is rotating about a fixed axis through the origin. The angular velocity is $$\omega$$$$\hat{k}$$ where $$\omega$$ 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?

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 $$\hat{j}$$

 

[horatio89]

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?

 

[JPhillips]

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?

Ah, I was just getting confused by what that really meant, but now (after some sleep, and your question) it seems a lot clearer. I for some reason believed that the magnitude of rotation was transposed onto every plane.

 

[JPhillips]

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.

 

[horatio89]

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.

 

[JPhillips]

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.

 

[horatio89]

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?

 

[JPhillips]

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.

 

[horatio89]

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.

 

[JPhillips]

Thank you very much for your help horatio