LynFran one year ago Angular velocity question im stuck

1. LynFran

2. 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.

3. LynFran

im confused

4. amistre64

how many degrees is a full rotation?

5. LynFran

360

6. amistre64

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

7. LynFran

2.388

8. 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

9. 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.

10. 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 $\frac23\pi*\frac a{360}*\frac{r}{R}$

11. LynFran

Whats R for? its that the large wheel radius

12. amistre64

yes :) large R for the larger Radius

13. 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

14. LynFran

o whats the a/360 for? what a?

15. amistre64

16. amistre64

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

17. LynFran

ok so a=860

18. amistre64

correct

19. LynFran

20. amistre64

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

21. LynFran

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

22. amistre64

$\frac{86}{135}\pi\approx 2.0013$

23. amistre64

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

24. 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?

25. 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|

26. amistre64

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

27. amistre64

$\frac a{360}*2\pi~r$

28. LynFran

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

29. amistre64

just the time frame.

30. 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

31. LynFran

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

32. amistre64

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

33. 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

34. 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

35. LynFran

ok i get it now thanks

36. amistre64

youre welcome