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Trig Problem: Angular Velocity.

  1. Oct 18, 2009 #1
    1. The problem statement, all variables and given/known data

    A Ferris Wheel with a radius of 25.3m makes two rotations per minute.

    A) Find the average angular speed of the Ferris wheel in radians per second.

    B) How far does a rider travel if the ride lasts 5 minutes?

    3. The attempt at a solution

    A) I got this question after a little bit of trial and error. i stated one rotation was 360 degrees which is equivalent to [tex]2\pi[/tex] Radians. It rotated twice per minute, so i stated that it rotated [tex]4\pi[/tex] radians per minute, my final equation to solve for the angular velocity was:

    [tex] \frac{4\pi}{60} \cong 0.21 radians[/tex]

    B) I can't seem to get this answer. My answer is 794.82, if i multiply it by 2 i get the correct answer so i don't understand where im missing the 2. the correct answer is 1590 m.

    i started with this equation

    [tex] \frac{10\pi}{2\pi} = \frac{d}{2\pi r} [/tex]

    after some mismatching i cancelled out the common term of 2 pi on both sides and got:

    [tex] d = 10\pi r [/tex] which yields the aforementioned answer. Does anyone know what I'm missing?

    Thanks,

    Senjai
     
  2. jcsd
  3. Oct 19, 2009 #2

    danago

    User Avatar
    Gold Member

    One full rotation would cover a distance of [tex]2\pi r[/tex] meters.

    With a rate of two rotations per minute, a total of 10 rotations is made in 5 minutes.

    Hence, the total distance travelled is [tex]2\pi r * 10[/tex] which yields the required answer.


    Im not 100% sure where that equation you wrote came from ( [tex]
    \frac{10\pi}{2\pi} = \frac{d}{2\pi r}
    [/tex]), but i suspect that the [tex]10\pi[/tex] should be [tex]20\pi[/tex], the total angle covered?
     
  4. Oct 19, 2009 #3
    I got that equation from the fact the sector angle is proportional to an increase in sector or arc. But i understand where your coming from. Thanks for all your help!
     
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