# (just joined) I with my pre ap precal; angular and linear velocity)

• Amaroq Zev
In summary, the conversation is about a pulley problem in which a small pulley is connected to a larger pulley by a belt. The small pulley is turning at 120 rpm and the conversation is focused on finding the angular and linear velocities of both pulleys. The participants also discuss the relationship between angular and linear velocities and how to find them using different equations. They also mention difficulties in understanding the problem and ask for help and resources.
Amaroq Zev
1.(okay just to let anyone know, I have a lot of this left to do, and I don't understand much of it, like when to use certain equations and such.) pulley problem: A small pulley 6 cm in diameter is connected by a belt to a larger pulley 15cm in diameter, the small pulley is turning at 120 rpm.(from a friend I got the first two answers but I still don't understand really how to find it.)
A.) find the angular velocity of the small pulley in radians per second.= 12.566 rad/s or 4(pie) rad/s
b)find the linear velocity of the rim of the small pulley.=37.699 rad/s
c)What is the linear velocity of the rim of the large pulley? explain
d)Find the angular velocity of the large pulley in radians per second.
e)how many rpm is the large pulley turning?

2. I know that to find linear it's L=w(omega) * radius but other then that I am lost.

3. I have no real clue, at first I thought I was getting everything quite well, but I have failed miserably at it, someone aid me please.

(I have a lot of other problems, any help for anything...anyone...would help me so much, this is all due tomorrow...26 problems of stuff that I don't understand. Makes me feel so...icky if you will.

does anyone know any other online tutors or websites that help with this kind of stuff? Like pre-ap pre-calculus help?

(I am going to search around, see if anyone else in on right now, I am really desperate on help here...)

(help on the site or anything? Is anyone there? I don't know if these messages would be considered flooding but I do need help...)

okay, someone answer this, is the angular velocity the same when the two circles are atop of each other or when there is two separate gears connected by a belt?

the pulley looks like this
_______
(o_____O) like...one large circle connected to the little one by a belt..I don't know if that helps at all...I really need help.)

Your equation L=wR -- Do you know what omega is?

Angular velocity once found

(still there? sorry I was looking around, trying to learn the site...also helping another person, hopefully your there...)

for A all you do is take 120 rpm and convert it to rads/sec

120 rev/min * 1min/60sec * 2(pie)/1 rev= 4 pie rad/sec

(Yeah I got that far, I just get confused, my teacher isn't the best descriptive teacher...um, angular velocity is to always have what unit and what does Linear supposed to have?
And how do you find the larger circle's linear and angular? Is the linear velocity the same as the smaller one?

(I'm not sure but I think the angular velocity is the same when the two circles are atop of one another and the linear the same when they are seperate, but again I am not completely sure, I second guess things to much. I think..)

Anyone there? I just have a lot of questions, I know the basics, but I get it all out of order, I don't remember what belongs where and such.

angular velocity would be in terms of radians/seconds while linear is in meters/second. The velocities of the larger pulley would be the same.

Sorry i can't be more descriptive I'm still trying to picture the problem so far i think that to find the angular velocity of the larger pulley you need to find its circumference. you know that the smaller pulley goes around around twice in 1 second so now you just have to find how that relates to the larger pulley.

(okay, this is what I know for fact, 1 revolution equals 2 (pie) radians. angular velocity is zero in the very very center of the circle, angular velocity is always in radians(I think) and linear is distance(cm,in,miles,meters) per time. I know how to do the work and such, but my answers are never right, I think my problem is that I don't gather the information out of the given info correctly, and I still don't know if the angular velocity is the same when the two circles are on top of each other or seperate, same as linear...that would clear up a lot of my problems. plus I don't know how to find rpm...revolutions per minute...

the picture looks like that of a bicycle
_____
(o___0) that's the best I can make the picture

The rim velocities will be the same for each pulley because they are directly connected with a belt. Their angular velocities will be different, since they are different sizes.

EAch 2 pi radians is 1 revolution.

(I am confused when you said that the velocities of the larger circle are the same...that would be impossible I thought. for the two circles to turn they would have to be going the same speed...so that would make the linear velocity of the two the same right? so to find the angular velocity...um...I don't know how to find the angular velocity if you only know the linear, but I know how to find the linear with angular...do you know the equation for that? to find the angular with the linear known?

Alright, so given rev's over the given time times 2(pie) over revolution(mark out what cancels) an dyour done unless you have to change it into a certain time right?

Amaroq Zev said:
(I am confused when you said that the velocities of the larger circle are the same...that would be impossible I thought. for the two circles to turn they would have to be going the same speed...so that would make the linear velocity of the two the same right? so to find the angular velocity...um...I don't know how to find the angular velocity if you only know the linear, but I know how to find the linear with angular...do you know the equation for that? to find the angular with the linear known?

wait wait wait, Amaroq Zev. I just sent the message about 2 minutes ago and you responded less than one minute later. Go back,read again and think through carefully. You are in too much a rush. Think first, and then maybe try panicing; you might see part a more clearly.

so how do you find the angular velocity if you only know the linear?

(I was typing that before you ever sent that one, sorry, and I think that was to another person... I am not entirely sure though. I am in a bit of a rush, I am understanding this better on here, it is odd, maybe I can't remember anything in the class room because of stress...that women is very rude...she has gotten into my face and yelled at me for not understanding something...)

angular velocity would be in terms of radians/seconds while linear is in meters/second. The velocities of the larger pulley would be the same.
This was from glasshut and the person that I was previously responding to. Just to clear things up, sorry if I offended you previously but let it be known that the post was not sent to you, sorry for the misunderstanding, I guess I will put a short version of your names so that you know which message was to be sent to whichever person, now back to the previous question, is there an equation to find angular when you only know the linear?)

hello?

to find the rpm you'd divide the linear velocity by 7.5(the radius of the big circle) multiply it by 60(since the answer is in seconds) and...uh..hold on

gah! I don't know..I need equations...

Amaroq Zev,
You are most probably frustrated by now. You have sent in many more reports of your having difficulty and no one yet gave more informative responses. Then, I found I was not getting logged in when I tried. Now the forum is letting me log in again.

What course exactly are you studying? It seems to be the initial topic of Trigonometry in which you are first dealing with angle measures and reference to the circle. Some of the equations that you want are derived there. If you are in "PreCalculus", then I suggest you check an actual TRIGONOMETRY textbook, since it develops some topics in more detail than you'll find in an PreCalculus book.

Be sure not to confuse angular velocity with linear velocity. Angular velocity relates to rate of rotation; while linear velocity relates to LENGTH on the rim, as if the arc were stretched straight.

Check back a few messages; I gave you a start for part (a).

## 1. What is the difference between angular and linear velocity?

Angular velocity is the measure of the rate of change of angular displacement over time, while linear velocity is the measure of the rate of change of linear displacement over time. Angular velocity is typically measured in radians per second, while linear velocity is measured in meters per second.

## 2. How are angular and linear velocity related?

Angular and linear velocity are related through the radius of the circle or arc being traveled. The linear velocity is equal to the angular velocity multiplied by the radius. This relationship is described by the formula v = ωr, where v is linear velocity, ω is angular velocity, and r is the radius.

## 3. How are angular and linear velocity used in real-world applications?

Angular and linear velocity are used in a variety of real-world applications, such as in the design of mechanical systems, robotics, and transportation. For example, understanding the relationship between the two can help engineers design gears and pulleys for efficient motion.

## 4. Can angular and linear velocity be negative?

Yes, both angular and linear velocity can be negative. This indicates a change in direction, such as when an object is moving in a counterclockwise direction with a negative angular velocity. However, the magnitude of the velocity is still a positive value.

## 5. How does precalculus help in understanding angular and linear velocity?

Precalculus provides the necessary mathematical concepts and tools to understand and calculate angular and linear velocity. This includes understanding trigonometry, radians, and the use of derivatives and integrals to calculate rates of change. Without a strong foundation in precalculus, it can be difficult to fully grasp the concepts of angular and linear velocity.

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