# Thread: Belt and Wheel Problem

1. ## Belt and Wheel Problem

The treadmill at Robert's gym is run by a belt and wheel system.
A motor spins wheel A which is attached by a belt to wheel B.
Wheel B is fixed by an axle to wheel C which spins the conveyor that Robert runs on.
The machine is set to run the conveyor at a pace of 1 mile every 8 minutes.

The figure is not to scale.

The radius of wheel A is 0.9 inches, the radius of wheel B is 0.75 inches, and the radius of wheel C is 3 inches.

At what angular speed is the motor rotating wheel A? Give your final answer in revolutios per minute.
This is what I know:
The equations:
s=rΘ
Θ=wt
v=wr (This is the one I will use)
1) I know that it's a pace of 1 mile every 8 minutes, so 1/8 = 0.125
2) Thus, vC=0.125mi/min, now find wA
3) vC=wCrC -> 0.125mi/min=wc(3)
4) 7920in/min (converted miles to inches)
5) wC=2640(1rev/2pi)-420.169 = wB

Though I'm not really sure where the -420.169 came from, I had my teacher help me but I didn't quite understand, can someone explain it to me and what I should do next after this?

Thanks!

Answer is supposed to be 350.1409 rpm (from what my teacher said)

2. ## Re: Belt and Wheel Problem

note that $v_C = \frac{1 \, mile}{8 \, min}$ needs to be converted to inches/min ...

here are the equations necessary to find the angular speed of wheel A , $\omega_A$ in radians per minute

$\omega_C = \frac{v_C}{r_C}$

$\omega_C = \omega_B$

$r_A \cdot \omega_A = r_B \cdot \omega_B$

when you get done, you'll need to convert $\omega_A$ from radians/min to revolutions/min

... I agree with your teacher's final solution.

3. ## Re: Belt and Wheel Problem

Originally Posted by skeeter
note that $v_C = \frac{1 \, mile}{8 \, min}$ needs to be converted to inches/min ...

here are the equations necessary to find the angular speed of wheel A , $\omega_A$ in radians per minute

$\omega_C = \frac{v_C}{r_C}$

$\omega_C = \omega_B$

$r_A \cdot \omega_A = r_B \cdot \omega_B$

when you get done, you'll need to convert $\omega_A$ from radians/min to revolutions/min

... I agree with your teacher's final solution.
Well I converted it in step 4 (if that works)
So I know vc=is 7920
rc=3
After that I get wc=2640 then
Since you say wc=wb
Then if that's true
wb=2640 then

rawa=rbwb
0.9wa=0.75(2640)
0.9wa=1980
wa=2200

Then 2200(1rev/2pi)=350.1409!

OH WOW! I actually did it!
Thanks!!!

Belt and Wheel Problems aren't really my greatest strengths, since there many variables (that have subscripts), but now I think I'm starting to get it!