) A vortex that rotates at constant angular velocity w about the z-axis has velocity vector field v⃗ =w(−yi⃗ +xj⃗ ). (a) Sketch, on a separate sheet of paper, the vector field with w=1 and the vector field with w=−1. Then determine the speed ∥v⃗ ∥ of the vortex as a function of the distance from its center, r. speed

Explanation:

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The graphical relationships and the relationship between the linear and angular variables allows finding the results for the movement of the vortex are:

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:    

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:

b)   The linear and rotational variables are related.      

               v = w r

We can find the distance with the Pythagorean theorem.  

             r =

Let's substitute.

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:

Learn more about vortex here:  link

answer: strength i guess

explanation:

muscle endurance

explanation:

i can do 50 in a row ( but i get so tired after that)