Question

Angular velocity question im stuck

Answer 1

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.

Answer 2

im confused

Answer 3

how many degrees is a full rotation?

Answer 4

360

Answer 5

then we should start by finding out how many 360s are in 860

what is 860/360?

Answer 6

2.388

Answer 7

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

Answer 8

\[\frac{860}{360}~2\pi~r=d\]
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.

Answer 9

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
\[\frac23\pi*\frac a{360}*\frac{r}{R}\]

Answer 10

Whats R for? its that the large wheel radius

Answer 11

yes :) large R for the larger Radius

Answer 12

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

Answer 13

o whats the a/360 for? what a?

Answer 14

what did we divide by 360 to start with?

Answer 15

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

Answer 16

ok so a=860

Answer 17

correct

Answer 18

is the answer 2.0013?

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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?

Answer 24

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.

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

just the time frame.

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

ok i get it now thanks

Answer 35

youre welcome