Hurricane Fluid flow, torque, cross product

[Frozen Light]

Homework Statement

In 1993 the radius of Hurricane Emily was about 350 km. The wind speed near the center ("eye") of the hurricane, whose radius was about 30 km, reached about 200 km/h. As air swirled in from the rim of the hurricane toward the eye, its angular momentum remained roughly constant.

Estimate the wind speed at the rim of the hurricane.

r1 = 30km
v1 = 200 km/h
r2 = 350km

Homework Equations

I'm not entirely sure - it's in a section where we are learning A1v1 = A2v2
Also - p1 + (rho)gy1 +1/2 rho v1^2 = p2 + rho(gy2) + 1/2(rho)v2^2

The Attempt at a Solution

I'm not entirely sure where to start - I actually have already completed this problem but am coming back to it a week later having forgotten what I learned. I just remember it was pretty simple if you took into account a relationship with the cross product.

I want to know how to understand the cross product to solving problems in general - I only kindof understand how to use the cross product, yet it is the basis of many things.

I know that it yields a perpendicular vector to two vectors - but for example in concepts like torque I have no freaking idea what it means to have the torque vector coming out of the page when in my mind a system will clearly be rotating clockwise or counter-clockwise on the page.

I'm stuck on the concepts of two other problems as well - https://www.physicsforums.com/showthread.php?t=726053 - I understand how the axis is being used but I don't understand why it can be used that way.

A similar sort of concept is http://answers.yahoo.com/question/index?qid=20100505142314AAkwk4g with a cow gate problem -

I can more or less follow what is being done but I want to be able to think through them without any guidance.

Essentially - Are there general strategies of thinking of torque and the cross product on 2d and 3d surfaces? Do you know of any equations or tools that will help make it more intuitive for me?

 

[tiny-tim]

Hi Frozen Light!

… the radius of Hurricane Emily was about 350 km. The wind speed near the center ("eye") of the hurricane, whose radius was about 30 km, reached about 200 km/h. As air swirled in from the rim of the hurricane toward the eye, its angular momentum remained roughly constant.
…
I'm not entirely sure where to start - I actually have already completed this problem but am coming back to it a week later having forgotten what I learned.

I just remember it was pretty simple if you took into account a relationship with the cross product.

you don't need to be so technical in this case

angular momentum for circular motion is mvr

rewriting the question, isn't it simply saying that vr is constant?

I want to know how to understand the cross product to solving problems in general - I only kindof understand how to use the cross product, yet it is the basis of many things.

I know that it yields a perpendicular vector to two vectors - but for example in concepts like torque I have no freaking idea what it means to have the torque vector coming out of the page when in my mind a system will clearly be rotating clockwise or counter-clockwise on the page.

think of a fawcet, or anything that has a screw and that you move using a wrench or screwdriver …

the torque vector tells you which way (up or down) the fawcet moves …

it's the cross product of the horizontal radial vector and the horizontal tangential force

(i'll look at your two other problems later)

 

[lightgrav]

torques tend to make something rotate, around an axis ... the torque vector points along that axis that rotation axis.
In some situations it is obvious (or even given) where the object will rotate around - for other situations you might imagine several places, depending on which support Force fails. The rotation axis will tend to be far from the Force application point, because the Force has bigger torque around distant axes (torque is r x F ).

Bottom line, though, is that Forces applied along the axis have zero lever-arm, so those Forces disappear from the torque equation ... that's a great strategy to reduce the number of unknowns - but you can't solve for a variable if it disappears from the equation.