# Thread: [SOLVED] linear/angular speed (another question)

1. ## [SOLVED] linear/angular speed (another question)

"suppose that a belt drives two wheels of radii R (bigger wheel) and r"

there is a figure and it's like a big wheel and a small wheel with a belt around them.....so they have the same linear speed i think...

R=8 ft
r=3 ft

a) the angular speed of the larger wheel in radians/minute - i know this is 400pi radians/min

b) the linear speed of a point on the circumference of the larger wheel (also a point on the belt) - 3200pi ft/min

i know those answers are right because we did the problems in class and i understand how to get them.... i just dont understand this last part:

c) the angular speed of the smaller wheel in revolutions/minute........ok i dont understand this at all.

i think the answer was 533 revolutions/minute but i'm not sure if i copied that down correctly (we did it in class )

i thought i'm supposed to use the formula v=rw since i already have v=400pi radians/minute and r=3 ft

so i got 1200pi radians but i think the teacher divided this by 3 (i have no idea why) and got that answer 533 revolutions/minute

thankss

2. ## Linear/angular speed

Hello desperate_on_sunday_night
Originally Posted by desperate_on_sunday_night
"suppose that a belt drives two wheels of radii R (bigger wheel) and r"

there is a figure and it's like a big wheel and a small wheel with a belt around them.....so they have the same linear speed i think...

R=8 ft
r=3 ft

a) the angular speed of the larger wheel in radians/minute - i know this is 400pi radians/min

b) the linear speed of a point on the circumference of the larger wheel (also a point on the belt) - 3200pi ft/min

i know those answers are right because we did the problems in class and i understand how to get them.... i just dont understand this last part:

c) the angular speed of the smaller wheel in revolutions/minute........ok i dont understand this at all.

i think the answer was 533 revolutions/minute but i'm not sure if i copied that down correctly (we did it in class )

i thought i'm supposed to use the formula v=rw since i already have v=400pi radians/minute and r=3 ft

so i got 1200pi radians but i think the teacher divided this by 3 (i have no idea why) and got that answer 533 revolutions/minute

thankss
You have correctly said that $\displaystyle r = 3$ ft, and that the linear speed, $\displaystyle v$, is $\displaystyle 3200\pi$ ft/min. So plug these values into your formula $\displaystyle v = r\omega$, and you get:

$\displaystyle 3200\pi = 3\omega$, where $\displaystyle \omega$ is measured in radians per minute

$\displaystyle \Rightarrow \omega = \frac{3200\pi}{3}$

and $\displaystyle 1$ revolution = $\displaystyle 2\pi$ radians. So the number of revolutions per minute = $\displaystyle \frac{\omega}{2\pi} = \frac{3200\pi}{3\times 2\pi}$

$\displaystyle = \frac{3200}{6} = 533$ revolutions per minute.