# Finding the position vector for translated frame of reference

• simphys
In summary, the conversation discusses the derivation of the position vector ##\vec r## in the x'y' frame, given its initial position and velocity in the xy frame. The conversation also touches on the concept of relative frames of reference and the relationship between the vectors ##\vec R##, ##\vec r##, and ##\vec r\:'##.
simphys
Homework Statement
Please refer to the picture, I don't really have a question problem.
I was posed the question on how I would model what the position would be when the frame of reference is translated as shown on the picture.
Relevant Equations
##\vec r = 8t \hat i + 6t \hat j## for the y-x reference framse.
what would be the y'-x' ##\vec r## vector be?

I think it is
##\vec r = (8t - 1) \hat i + (6t - 2) \hat j## (not sure whether it is correct or not.)
I thought about it as at t = 0 the position needs to be -1i -2j so that is why I took the signs in the y'-x' frame position vector as a - instead of + signs for 1 and 2.

Is it ok to reason like this or do I need to derive it from somewhere else? I am not very acquianted with translation of the axes that's why I am asking.

Delta2
What is the origin of x' y' system as measured in the x y system?

simphys
drmalawi said:
What is the origin of x' y' system as measured in the x y system?
in points (1,2) = (x,y)

can you find a relation for the vectors ## \vec R##, ##\vec r## and ##\vec r\:'##?

Delta2 and simphys
drmalawi said:
What is the origin of x' y' system as measured in the x y system?
oh wait, isn't this actually the 'relative frames of references' that are used to describe relative motion?
than it becomes r_x/p = r_x'/x + r_p/x' (where the condition was that it should be an inertial frame aka cst velocity or at rest for it to be valid)

malawi_glenn
drmalawi said:
View attachment 304325
can you find a relation for the vectors ## \vec R##, ##\vec r## and ##\vec r\:'##?
yep exactly my post #5 no?

simphys said:
aka cst
?

simphys
drmalawi said:
?
constant, apologies.

simphys said:
constant, apologies.
np glhf

simphys and Delta2

## 1. What is a translated frame of reference?

A translated frame of reference is a coordinate system that is shifted or moved from its original position. This is often used in physics and mathematics to describe the position of an object relative to a different point of reference.

## 2. How do you find the position vector for a translated frame of reference?

To find the position vector for a translated frame of reference, you need to know the coordinates of the original frame of reference and the distance and direction of the translation. You can then use vector addition to calculate the new position vector.

## 3. Why is it important to find the position vector for a translated frame of reference?

Finding the position vector for a translated frame of reference is important because it allows us to accurately describe the position of an object relative to a different point of reference. This is crucial in many fields, such as physics, engineering, and navigation.

## 4. Can you give an example of finding the position vector for a translated frame of reference?

Yes, for example, if a car is initially located at position (2,3) on a coordinate plane and then moves 5 units to the right and 2 units up, the position vector for the translated frame of reference would be (7,5). This means the car is now located at position (7,5) relative to its original position.

## 5. What is the difference between a translated frame of reference and a rotated frame of reference?

A translated frame of reference involves shifting the entire coordinate system to a different position, while a rotated frame of reference involves rotating the coordinate system around a fixed point. Both methods are used to describe the position of an object relative to a different point of reference, but they involve different types of transformations.

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