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Another angular velocity problem

  1. May 27, 2009 #1
    A Ferris wheel makes two rotations per minute. The radius of the Ferris wheel is 25 m.

    a) Determine the angular velocity in rad/s
    b) A ride lasts 4 min. How far will a rider travel in 4 min?

    My Work:

    a) C = 2Pi(25 m) = 50Pi m
    50Pi m / 25 m = 2Pi rad

    2 rotations/min x 2Pi = 4Pi rad/min

    Therefore the angular velocity is Pi / 15 rad/s

    b) 4 x 4Pi = 16Pi
    16Pi = a / 25 m
    a = 25(16Pi)
    a = 400Pi
    a = 1256.6 m

    I believe I am correct but I am hoping someone could check over my approach to the problem as my text was not very clear at all and I have tried to figure this out mainly on my own.
     
  2. jcsd
  3. May 28, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Why did you calculate this? Surely you knew from the start that there are [itex]2\pi[/itex] radians in any circle!

    Yes, although I think I would have said "one rotation in 30 seconds is [itex]2\pi/30= \pi/15[/itex] radians per second", this is fine.

    You had already calcuated in (a) (where it wasn't necessary!) that the circumference of the wheel is [itex]50\pi[/itex] meters. Now you calculate it again! In 4 minutes you will have made 8 rotations: [itex]8(50\pi)= 400\pi[/itex] m just as you say. I think I would leave it as [itex]400\pi m[/itex] and not change to an approximate answer.

    You've done some unnecessary work but you have the correct answers.
     
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