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How fast is the edge of the yo-yo spinning in mph

  1. Apr 9, 2017 #1
    1. The problem statement, all variables and given/known data
    Hello!
    I am trying to solve the exercise, but I don't see my mistakes - I can't come up with a correct answer.
    The exercise from the begging of trigonometry, so it has to be solved using concepts of a speed and angular velocity.

    A yo-yo which is 2.25 inches in diameter spins at a rate of 4500 revolutions per minute. How

    fast is the edge of the yo-yo spinning in miles per hour? Round your answer to two decimal

    places.

    2. Relevant equations
    Here is how I am trying to solve it:
    v = r x w,
    where v is the speed, r radius, w is the average angular velocity, which equals to

    w = 2π x f, where f is the frequency of revolutions and equals to number of revolutions / time

    3. The attempt at a solution
    Putting it all together I get:

    r = 2.250 / 2 = 1.225
    number of revolutions in one hour 4500 х 60 = 270 000
    w = 2π × 270 000 = 1 695 600
    v = 1.225 x 1 695 600 = 2 077 110 inches in one hour

    Convert to miles:
    2 077 110 / 63 360 = 32.78 miles per hour

    But it should be 30.12 miles per hour.

    Please, help me to find my mistake.
    Thank you!
     
  2. jcsd
  3. Apr 9, 2017 #2

    BvU

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    Science Advisor
    Homework Helper
    Gold Member

    Hello Vital, :welcome:

    It is always a good idea to estimate answers before typing them in on a calculator
    But in this case it may have been a simple oversight ?
    No it is not.
     
  4. Apr 9, 2017 #3
    Oh! Yes. It is a typo, which has gone through all calculations. And I actually do this type of calculations manually (some in mind, and others, with bigger numbers, on paper).
    Thank you very much. Indeed an awkward situation. :)
     
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