# Ax and Ay As a linear combination of Atan and Arad

• spirof
In summary, the problem involves a rod set in a pendulum motion with a high enough angle that simple harmonic motion does not apply. The aim is to find the x and y acceleration about the center of mass, which requires using the angle between arad and ax as a reference. After receiving a hint, the individual was able to find all necessary angles, but was unsure how to proceed. Eventually, the solution was found by expressing the x and y acceleration as a linear combination of arad and atan using the angle between them.
spirof

## Homework Statement

The problem is about a rod that is set in a pendulum way but that has an angle high enough so the SHM doesn't apply to it. It starts at Pi/2 until it reachs 0. I was able to find the tangential and radial acceleration about the center of mass but now I need to know the x and y acceleration about the center of mass.

## Homework Equations

It says that I should be using the angle between Atan and Ax as a reference

## The Attempt at a Solution

Completly stuck!

#### Attachments

• prblm.png
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welcome to pf!

hi spirof! welcome to pf!
spirof said:
I was able to find the tangential and radial acceleration about the center of mass but now I need to know the x and y acceleration about the center of mass.

the only difficulty is working out the angle between tan (or rad) and x (or y) …

the hint is simply telling you to write those angles as either ±θ or ±(90° - θ) …

go for it!

tiny-tim said:
hi spirof! welcome to pf!

the only difficulty is working out the angle between tan (or rad) and x (or y) …

the hint is simply telling you to write those angles as either ±θ or ±(90° - θ) …

go for it!

Thanks u did put me on the track, I do possesses all the θ already for a definite period of time. Actually, correct if I am wrong, if I have and angle of 1.40 rad, then if if i do pi/2 - 1.4, which will give me something around 0.17 rad.

From there, i know that the angle between arad and ax is 0.17 rad, the same angle betweenay and atan. I would then be tempted to simply do ax = ar cos 0.17. However, I cannot assume that they form a right angle triangle. Anymore inputs?

hi spirof!
spirof said:
From there, i know that the angle between arad and ax is 0.17 rad, the same angle betweenay and atan. I would then be tempted to simply do ax = ar cos 0.17. However, I cannot assume that they form a right angle triangle. Anymore inputs?

i'm confused … there's right-angles everywhere …

which angle isn't a right- angle?

tiny-tim said:
hi spirof!

i'm confused … there's right-angles everywhere …

which angle isn't a right- angle?

Well between Ar and Ax, If u look at my attached image, you will see that I cannot assume that they are parts of a right angle triangle. Ax seems to long to be the hypothenus of Ar, doesn't it?

the length doesn't matter

all you need is the angle between ar and ax

tiny-tim said:
the length doesn't matter

all you need is the angle between ar and ax

Thanks, I went over the internet and I have found the solution. I have to express as linear combination of the Ar and Atan.

It sums up to Ax = Ar cos (90-θ) + Atan sin (90-θ)
Ay = -Ar sin (90-θ) + Atan cos (90-θ)

## 1. What is a linear combination?

A linear combination is a mathematical operation in which two or more quantities are multiplied by constants and then added together. It is often used in physics and engineering to describe the relationship between different variables.

## 2. How can Ax and Ay be expressed as a linear combination of Atan and Arad?

Ax and Ay can be expressed as a linear combination of Atan and Arad by using trigonometric identities and equations. For example, Ax = Atan * sin(theta) and Ay = Atan * cos(theta), where theta is the angle between the x-axis and the vector Atan.

## 3. What is the significance of expressing Ax and Ay as a linear combination of Atan and Arad?

Expressing Ax and Ay as a linear combination of Atan and Arad allows us to understand the relationship between these variables and how they contribute to the overall vector Atan. It also helps us to simplify calculations and make predictions about the behavior of the system.

## 4. Can Ax and Ay be expressed as a linear combination of other variables besides Atan and Arad?

Yes, Ax and Ay can be expressed as a linear combination of any two variables, as long as they have a linear relationship. However, using Atan and Arad is often the most convenient and meaningful choice in the context of trigonometry and vector analysis.

## 5. How is a linear combination different from a dot product?

A linear combination involves multiplying two or more quantities by constants and adding them together, while a dot product involves multiplying two vectors and then taking the sum of their products. In other words, a dot product is a specific type of linear combination that only involves two vectors.

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