The graphical relationships and the relationship between the linear and angular variables allows finding the results for the movement of the vortex are:
- In the attachments we have a diagram of the clockwise and counterclockwise linear speed.
- The relationship between speed and distance is: v = w r
A vortex is a circular motion where the angular speed of the particles is constant.
They indicate the function of the linear velocity of the vortex is:
[tex]v= w ( - y \hat i + x \hat j[/tex]
Where v is the linear speed, w the angular velocity and (y, x) the position of the particle.
a) In the attachments we can see the linear velocity for the cases:
- w = 1. In this case we have a counterclockwise turn.
[tex]v = 1 ( -y \hat i + x \hat j\\v = -y \hat i + x \hat j[/tex]
- w = -1. In this case the turn is clockwise turn.
[tex]v = -1 ( -y \hat i + x \hat j) \\v= y \hst i + - x \hat j[/tex]
b) The linear and rotational variables are related.
v = w r
We can find the distance with the Pythagorean theorem.
r = [tex]\sqrt{x^2 + y^2}[/tex]
Let's substitute.
[tex]v= w \ \sqrt{x^2 + y^2 } \\v= w r[/tex]
In conclusion using the graphical relationships and the relationship between the linear and angular variables we can find the results for the movement of the vortex are:
- In the attachments we have a diagram of the clockwise and counterclockwise linear speed.
- The relationship between speed and distance is: v = w r
Learn more about vortex here: brainly.com/question/1305555
