LynFran
  • LynFran
Angular velocity question im stuck
Trigonometry
schrodinger
  • schrodinger
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LynFran
  • LynFran
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jtvatsim
  • 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
  • LynFran
im confused

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amistre64
  • amistre64
how many degrees is a full rotation?
LynFran
  • LynFran
360
amistre64
  • amistre64
then we should start by finding out how many 360s are in 860 what is 860/360?
LynFran
  • LynFran
2.388
amistre64
  • 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
  • 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
  • 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
  • LynFran
Whats R for? its that the large wheel radius
amistre64
  • amistre64
yes :) large R for the larger Radius
amistre64
  • 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
  • LynFran
o whats the a/360 for? what a?
amistre64
  • amistre64
what did we divide by 360 to start with?
amistre64
  • 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
  • LynFran
ok so a=860
amistre64
  • amistre64
correct
LynFran
  • LynFran
is the answer 2.0013?
amistre64
  • amistre64
do you need an exact result? or an decimal approximation?
LynFran
  • LynFran
it just say determine the angular velocity in radians per second, of large wheel
amistre64
  • amistre64
\[\frac{86}{135}\pi\approx 2.0013\]
amistre64
  • amistre64
unless it asks you to approximate it, id leave it as an exact value ... but thats just me
LynFran
  • 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
  • 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
  • amistre64
if you know how many circumference you can travel in a time frame, you have a linear speed
amistre64
  • amistre64
\[\frac a{360}*2\pi~r\]
LynFran
  • LynFran
and what if the angular velocity was per hour instead of per second would that change anything?
amistre64
  • amistre64
just the time frame.
amistre64
  • 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
  • LynFran
how? would you have to divide by anything to find the other?
amistre64
  • amistre64
lets say you are going 6 miles an hour, what would you do to determine the speed per minute?
amistre64
  • 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
  • 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
  • LynFran
ok i get it now thanks
amistre64
  • amistre64
youre welcome

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