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Math Help - [SOLVED] linear/angular speed (another question)

  1. #1
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    [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
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  2. #2
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    Linear/angular speed

    Hello desperate_on_sunday_night
    Quote Originally Posted by desperate_on_sunday_night View Post
    "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 r = 3 ft, and that the linear speed, v, is 3200\pi ft/min. So plug these values into your formula v = r\omega, and you get:

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

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

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

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

    Grandad
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