Relationship between linear velocity and angular velocity

[good jelly]

Homework Statement

Find the relationship between the linear velocity and angular velocity for mass B which is moving about mass A (mass A is stationary).

Relevant Equations

v = wr

I find the velocity vector that is perpendicular to the radius which is v*cos(theta). Once I obtained the velocity that is perpendicular to the radius I used the equation : v = wr. But my answer seems to be wrong, the actual answer to this question is v = wr*cos(theta). Why?

 

[Orodruin]

the actual answer to this question is v = wr*cos(theta)

No it isn’t and it is easy to see that it isn’t by considering the limit $\theta \to 0$.

 

[kuruman]

Why?

Only the velocity component perpendicular to the radius (i.e. tangential to the path) counts. The radial component (towards or away from the center) does not count because it does not change the angle.

 

[TSny]

@good jelly :
Welcome to PF!

Have you given the complete statement of the problem "word-for-word"?
Based on your diagram, your equation $v_B \cos \theta = \omega R$ looks correct.

 

[Orodruin]

Only the velocity component perpendicular to the radius (i.e. tangential to the path) counts. The radial component (towards or away from the center) does not count because it does not change the angle.

That wasn’t the question. That was exactly what OP did. The question was why the wrong answer provided by [unknown, probably teacher] is correct. It isn’t.

 

[kuruman]

That wasn’t the question. That was exactly what OP did. The question was why the wrong answer provided by [unknown, probably teacher] is correct. It isn’t.

You are right, that was not the question. One can only provide reassurance that OP's answer is correct without attempting to divine like a haruspex why the other answer is incorrect.

 

[haruspex]

No it isn’t and it is easy to see that it isn’t by considering the limit $\theta \to 0$.

Isn't that limit the one case in which the two formulae both yield $v=\omega r$?
Maybe you meant $\theta\rightarrow \pi/2$.

 

[Orodruin]

Isn't that limit the one case in which the two formulae both yield $v=\omega r$?
Maybe you meant $\theta\rightarrow \pi/2$.

Yes, definitely. Good catch.