Question

Each roller under a conveyor belt has a radius of 0.5 meters. The rollers turn at a rate of 30 revolutions per minute. What is the linear velocity of the conveyor belt?

Please no direct answers :)

Answer 1

how about a formula
v=\(r\omega\)

Answer 2

Where w is the angular velocity..

Answer 3

So it would be 0.5 times 30rev/min? We'd need to convert...

Answer 4

yes exactly,
so the trick is to convert 30 rev/ min to radians/second

Answer 5

Times 2pi

Answer 6

Like radius times 2pi right?

Answer 7

wait

Answer 8

the formula
v=rw

requires r to be in meters
and w to be in radians/second

Answer 9

\[\frac{8rev}{sec}\times\frac{2\pi0.5m}{rev}\]

Answer 10

This is using the conversion method I learned from a friend...

Answer 11

25.1m/s right?

Answer 12

umm...sorry i dont follow that conversion at all....

Answer 13

Oh...

Answer 14

radius is 0.5 meter, its alerady meters, no conversions required

Answer 15

but w is in rev/min
we need it to be in radian/second

Answer 16

yeah...

Answer 17

so lets focus on w now

Answer 18

30 revolution every minute
=30 revolutions in 60 seconds

Answer 19

can you calculate how many revolutions every second?

Answer 20

0.5?

Answer 21

yes,
now we have w in revolutions/ second

now we know that \(360^0 =2\pi\) radians
and one complete revolution is 360 degrees

Answer 22

LOL isn't one rev always 2pi?

Answer 23

yes that is exactly what i've said^

Answer 24

I've known that x'D

Answer 25

one rev = 2pi =360 degrees

Answer 26

so we have w= 0.5 rev every second

how many radians every second is that?

Answer 27

2pi(0.5)/sec...

Answer 28

yes exactly, how how much does that become when you simplify

Answer 29

3.141592654....aka pi xD

Answer 30

haha, thats right

Answer 31

so all thats left is
v=rw

Answer 32

1.57?

Answer 33

yep

Answer 34

any doubts?

Answer 35

Naw, thanks mate

Answer 36

sure :)