Trigonometry help for Angular and Linear Speeds.

Discussion in 'General Math' started by John K. Chunn, Jr., Sep 25, 2004.

  1. I need some help with 2 problems for Trigonometry.. Radian Measure and Circular Functions: Linear and Angular Speed. ...

    #1 The tires of a bicycle have radius 13in. and are turning at the rate of 200 revolutions per minute. How fast is the bicycle traveling in miles per hour? (Hint: 5280 ft= 1 mi)

    #2 Two pulleys have radii of 15cm and 8cm, respectively. The larger pulley rotates 26 times in 36 seconds. Find the angular speed of each pulley in radians per second.

    All I know is that the answer to #1 is 15.5, but do not know how to arrive at that answer. Thanks for any help.

    John Chunn
    John K. Chunn, Jr., Sep 25, 2004
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  2. John K. Chunn, Jr.

    Tim Brauch Guest

    If at all possible, don't post in HTML.
    You know the radius, you know the RPM's. That is all you need to know.
    Let's think this one through. The bicycle is moving along the ground.
    What part of the bicycle is actually touch the ground? How far does the
    bicycle move in one revolution? How many revolutions does it make in a
    minute? How far does it travel in one minute? Do some unit conversions.
    First thing, change to standard units. How many revolutions would the
    first pulley make in one minute (RPM)? Second part, you have the radius
    and the RPM of the first pulley. How much rope passes through the pulley
    in one revolution? How much rope passes through in one minute? How much
    rope passes through the second pulley in one minute? How many revolutions
    does the second pulley have to make to pass that much rope?
    Those questions are probably too leading of questions. But if you can
    answer them, then you should find the answers you need.

    - Tim

    Timothy M. Brauch
    NSF Fellow
    Department of Mathematics
    University of Louisville

    email is:
    news (dot) post (at) tbrauch (dot) com
    Tim Brauch, Sep 25, 2004
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  3. What is the circumference of the tires? How many circumferences does
    the tire move per unit of time? Convert linear and time units to
    miles and hours.
    For the larger pulley: How many radians in one rotation? How many
    rotations per second?

    For the smaller pulley: What is the circumference of both pulleys?
    How far does the rope travel on the first pulley in one second? How
    far on the second pulley? How many rotations must the second pulley
    perform to achieve this "length"?

    <<Remove the del for email>>
    Barry Schwarz, Sep 25, 2004
  4. John K. Chunn, Jr.

    Adam Guest

    Since you already know the answer, I don't see any problem with
    explicitly working out the solution for this one... but for the next
    one you're on your own.

    As the wheel turns through one revolution, the bike moves forward by
    2*Pi*r inches. So as the wheel turns through 200 revolutions, the bike
    moves forward


    Since this takes one (1) minute, the velocity of the bike is

    (200*2*Pi*13)/1 inches per minute

    Then use conversion factors to put this into miles per hour

    200*2*Pi*13 (inches/min)*(1ft/12inches)(1mile/5280ft)(60min/1hr)

    = 200*2*Pi*13*(60/(12*5280))

    =15.47 miles/hour

    That's not so hard, now is it? Good luck on number 2.
    Adam, Oct 2, 2004
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