Angular velocity question im stuck

- LynFran

Angular velocity question im stuck

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- LynFran

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- jtvatsim

These are some rough notes I typed up, maybe someone can expand on them. :)
"small wheel = 0.4 m
big wheel = 1 m
small wheel makes 860* in 3 seconds.
860*/3 seconds = 286.67*/sec = 5 rads/sec = 2 m/sec
2 m/sec = 2 rads/sec on the larger wheel"
You will have to note that rads are converted to meters depending on the size of the wheel.

- LynFran

im confused

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## More answers

- amistre64

how many degrees is a full rotation?

- LynFran

360

- amistre64

then we should start by finding out how many 360s are in 860
what is 860/360?

- LynFran

2.388

- amistre64

right, or if we keep it in fraction form
2 and 7/18
now each rotation is also a circumference, multipy that by the circumference of the little one and that is how far the belt travels in 3 seconds

- amistre64

\[\frac{860}{360}~2\pi~r=d\]
d is the distance covered, and the belt moves this distance so we need to determine how many of the large circumference goes into d
\[\frac d{2\pi R}=k\]
k is the number of times the large wheel has rotated in 3 seconds.

- amistre64

since one rotation is equal to 2pi
in general
\[2\pi*\frac a{360}*\frac{2\pi~r}{2\pi~R}\]
\[2\pi*\frac a{360}*\frac{r}{R}\]
and since this is in 3 seconds, we want 1/3 of it
\[\frac23\pi*\frac a{360}*\frac{r}{R}\]

- LynFran

Whats R for? its that the large wheel radius

- amistre64

yes :) large R for the larger Radius

- amistre64

strategy
determine the number of rotations made: 860/360
that tells us how many circumferences have been made, multiply it by 2pi r
to determine the number of Larger circumferences it takes to travel the same distance, divide by 2 pi R
this tells us the number of times the larger wheel has turned, and each turn is equal to 2pi radians
adjust it, since this is the speed for a 3 sec interval ... divide it by 3 to get a 1 sec interval

- LynFran

o whats the a/360 for? what a?

- amistre64

what did we divide by 360 to start with?

- amistre64

in order to determine the number of times the small wheel has turned; we take its overall degree, and divide it by 360.

- LynFran

ok so a=860

- amistre64

correct

- LynFran

is the answer 2.0013?

- amistre64

do you need an exact result? or an decimal approximation?

- LynFran

it just say determine the angular velocity in radians per second, of large wheel

- amistre64

\[\frac{86}{135}\pi\approx 2.0013\]

- amistre64

unless it asks you to approximate it, id leave it as an exact value ... but thats just me

- LynFran

ok quick question if your ask to find the linear velocity is there like a pattern/structure that you can follow like what you give me for the angular velocity?

- amistre64

linear velocity is simply how fast the belt is moving
determine how many rotations we make, and that determines how many circumferences we can stretch out.
|dw:1433642163240:dw|

- amistre64

if you know how many circumference you can travel in a time frame, you have a linear speed

- amistre64

\[\frac a{360}*2\pi~r\]

- LynFran

and what if the angular velocity was per hour instead of per second would that change anything?

- amistre64

just the time frame.

- amistre64

if you know how far you go in 1 hour, you can determine how far you go in a day, or a second, or a week ... its all relative

- LynFran

how? would you have to divide by anything to find the other?

- amistre64

lets say you are going 6 miles an hour, what would you do to determine the speed per minute?

- amistre64

1 hour = 60 minutes sooo
6 miles per 60 minutes ... we only want 1 minutes, and we have 60 of them, we are 60 times to great, so yeah we divide for this
6/60 miles per 1 minute

- amistre64

how fast are we moving per day?
6 miles per hour, 24 hours in a day so
24*6 per 24 hours is our daily speed

- LynFran

ok i get it now thanks

- amistre64

youre welcome

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