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

## 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

Completly stuck!

## The Attempt at a Solution

#### Attachments

tiny-tim
Homework Helper
welcome to pf!

hi spirof! welcome to pf! 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! 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 possess 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?

tiny-tim
Homework Helper
hi spirof! 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? 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?

tiny-tim
Homework Helper
the length doesn't matter

all you need is the angle between ar and ax

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)