Question

A pulley of radius 15cm turns at 8 revolutions per second. What is the linear velocity of the belt driving the pulley in meters per second?

Answer 1

\[\huge v=r \omega\]

\(\omega\) is the angular velocity
v is the linear velocity
r is the radius

Answer 2

@AlexandervonHumboldt2 help me T_T or.. us lol

Answer 3

I know, I need to multiply 8rev/sec by 15cm

Answer 4

But wouldn't we need to multiply it by the circumference rather than just the radius?

Answer 5

It gave you the frequency. From there you can calculate \(\omega\) and then plug that into the first equation I put

Answer 6

Convert from rev/s to rpm (rev/min):
\[\frac{ 8 rev }{ \sec }*\frac{ 60 \sec }{ minute }=\frac{ 480 rev }{ minute }=480 rpm\]
\[60~ \text{rpm}=1~\text{Hz}\]\[480~\text{rpm} = 8~\text{Hz}\]

Then:
\[\huge \omega = 2 \pi f\]Where f = 8 Hz

Answer 7

Well, a friend of mine says to use the conversion method...\[\frac{8rev}{sec}\times\frac{2\pi 15cm}{1 rev}\times\frac{1m}{100cm}\]

Answer 8

lol oh

Answer 9

Read this to make sure you make proper conversion for frequency. In order to use that specific equation for angular velocity, it must be in Hz https://en.wikipedia.org/wiki/Revolutions_per_minute

Answer 10

:/

Answer 11

You have to look at it backwards.

It tells you that the frequency (in order to use that equation for \(\omega\)) must be in Hz. Well what is the equivalent for Hz? Well, it tell us the conversion that 60 rpm = 1 Hz. We're initially given rps, but we can easily convert the seconds to minutes in order to get rpm!

Answer 12

"When the pulley turns once, the belt moves one circumference (2 x pi x 15 cm)

x by 8 to get distance per second in cm

divide by 100 to get it into m/s "

Answer 13

wait, I got about 7.54m/s

Answer 14

(;

Answer 15

here are you're answer choices

9.95 m/s
3.93 m/s
11.16 m/s
7.54 m/s

Answer 16

Yep! I got that too using the method I described :)

Answer 17

I got that using the method I posted ;)

Answer 18

Yup! Also I realized that rev/s is already Hz. No need to convert to rpm bahaha. But yeah, use the formulas!

Answer 19

lol thank you

Answer 20

X) you're welcome