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math: radians problem, need answer really fast!!!





alalex
Arrow If you want to find the angular space, (w) you use the formula w = v/r where v = linear speed and r = the radious. And that is m/s over m. So the meters would cancel out, leaving only seconds. But the answer is radians/seconds!! Where do the radians come from!!
please answer really fast! Very Happy
NewGuyinTown
alalex wrote:
Arrow If you want to find the angular space, (w) you use the formula w = v/r where v = linear speed and r = the radious. And that is m/s over m. So the meters would cancel out, leaving only seconds. But the answer is radians/seconds!! Where do the radians come from!!
please answer really fast! Very Happy


Radian is arc length / radius, where arc length and radius is usually measured in meters. Their units may cancel out, but it's not really "unitless" (can't think of the right word).
alalex
ook... and do you know if there is any way to prove why the answer is in radians??? like a math prove or something....?? It would just be so helpful for me Exclamation
Bondings
First of all the angular space is usually represented by the Greek omega (big o) "ω" and not "w", unlike a lot of students (and teachers) think. But that completely aside.

Radian is not a unit like meters or seconds. It's a way to denote that the result is a sort of normalized answer for the angle that is being passed per second.

It means that it is the distance that is being passed per second if it would be on a circle with a radius of 1 meter. The whole circle is 2Pi in that case.

You could also use percentages (divide by 2PI and multiply by 100%) or degrees (divide by 2Pi and multiply by 360). But those are rarely used.
saskshadowplayers
Weird... I just finished this chapter in math. Anyways radians are usually meased in comparison to Pi... 2pi = 360 degrees... ok well I cant really explain it without really knowing the question.
alalex
ok, thanks to all. I also got this same answer in other forums. thanks a lot!!

About this:
Quote:
First of all the angular space is usually represented by the Greek omega (big o) "ω" and not "w", unlike a lot of students (and teachers) think. But that completely aside.

I knew it was ω, but i didnt have time to find out how to insert it... Sad
Well, thanks! Very Happy
Scoria
aew, dont remind me about that stuff.
Math is just terrible, good luck anyways Smile
Nyizsa
First of all, we are talking about rotation now. ω is measured in rad/s. And if you need the angle of the rotation, it's ω*t, as the movement happened during t time with ω speed. The unit nicely evaluates to radian.
To get the length of the movement at a given radius, use radius by angle. You get meters because:
Code:

circumference: 2π r (m)
               -------- * Δω (rad)  :angle of movement
full rotation: 2π (rad)

You can simplify with 2π but keep in mind that the upper one is a number and the lower one is an angle!
alalex
cool! i guess then that radiands dont have any kind of prove, apart from their definition... Very Happy
thanks to all of you!! Smile

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Kaisonic
I remember my Calculus professor actually explained the other day why Pi is equal to 180 degrees. It was very interesting, yet utterly useless, hence the reason I forgot it mere minutes later.
[FuN]goku
Kaisonic wrote:
I remember my Calculus professor actually explained the other day why Pi is equal to 180 degrees. It was very interesting, yet utterly useless, hence the reason I forgot it mere minutes later.
yeah my grade 9 math teacher told us too... was wierd..
jveezy
NewGuyinTown wrote:
Radian is arc length / radius, where arc length and radius is usually measured in meters. Their units may cancel out, but it's not really "unitless" (can't think of the right word).


The term I've always heard from teachers is "dimensionless unit". I don't know if that's what you're thinking of but that's pretty much the way I've always heard it.
allanxiao
"w" is angular velocity in physics, w=v/r = (distance travelled around the circle)/(time)/(radius of the cirtle) =(distance travelled around the circle)/(radius of the cirtle)/(time), since (distance around the circle)/(radius of the circle) is the definition for "radian", so the unit for "w" is just "radian/second".

But we often omit the unit "radian".
alalex
ok cool! Very Happy
i also heard a lot of ansers like "radians are just radians by definition. no prove"
i just wanted to see other opinions.!.
Nyizsa
alalex wrote:
i also heard a lot of ansers like "radians are just radians by definition. no prove"

Radian is defined as the angle corresponding to an arc whose length equals to the radius of the circle. (~57.295779515 degrees.) So yes, it is radian by definition, no prove.
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