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Math Help - Belt and Wheel Problem

  1. #1
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    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.

    Belt and Wheel Problem-circular-motion-picture.png

    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)
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  2. #2
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    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.
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  3. #3
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    Re: Belt and Wheel Problem

    Quote Originally Posted by skeeter View Post
    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!
    Thanks for your help!
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