Understanding Rotating Coordinate Systems: A Visual Approach

In summary, the conversation discusses a question about a rotating coordinate system and the equations involved. The question involves understanding how u can be expressed in terms of x and y. Through manipulation of the equations, u is found to be equal to sin(theta)y + xcos(theta), as shown in equation (2). The individual asking the question struggles to understand this concept visually and seeks further explanation.
  • #1
xzibition8612
142
0

Homework Statement



http://www.brookscole.com/math_d/sp...athematica_labs/14-multipleintegrals/p05a.pdf



Homework Equations





The Attempt at a Solution



My question concerns the (1) and (2) next to the figure of the rotating coordinate system.

x=ucos(theta)-vsin(theta)
y=ucos(theta)...
...

So my problem is I can't visualize it. I can visualize that u = ucos(theta) + usin(theta), but I don't get how u = xcos(theta) + ysin(theta).
If anyone can explain or try to visually show it to me would be great. Thanks.
 
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  • #2
Hi,xzibition8612.

Multiply both side of equatlity (1) x=ucos(theta)-vsin(theta) with cos(theta) and both of equality y=ucos(theta)...with sin(theta) you will see some terms will vanish.And you will get your answer...
 
  • #3
ok i did as you said and got u = sin(theta)y + xcos(theta) which is (2). I still don't get how come u is this quantity. I mean in a visual manner. I'm not so smart to understand it abstractly. Sorry for my poor intelligence.
 

1. What is a rotating coordinate system?

A rotating coordinate system is a mathematical tool used to describe the positions and movements of objects in space. It involves defining a set of axes that rotate along with the object, allowing for a more accurate representation of its motion.

2. Why is a rotating coordinate system important in science?

A rotating coordinate system is important in science because it allows for a more accurate analysis of the motion of objects. It can be particularly useful in fields such as physics and astronomy, where objects may have complex or changing movements.

3. How is a rotating coordinate system different from a fixed coordinate system?

A rotating coordinate system differs from a fixed coordinate system in that the axes of the rotating system are constantly changing, while the axes of a fixed system remain in the same position. This allows for a more dynamic representation of an object's motion in a rotating system.

4. Can a rotating coordinate system be used in all situations?

No, a rotating coordinate system may not be appropriate or necessary in all situations. It is most commonly used when analyzing the motion of objects with complex or changing movements. In simpler cases, a fixed coordinate system may be sufficient.

5. How is a rotating coordinate system represented mathematically?

A rotating coordinate system is represented mathematically using equations that describe the rotation and transformation of the axes. These equations can vary depending on the specific situation and the type of rotation being used.

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