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Rotational Speed with the Speed of Light

  1. Mar 16, 2005 #1
    An early method of measuring the speed of light makes use of a rotating slotted wheel. A beam of light passes through a slot at the outside edge of the wheel, travels to a distant mirror, and returns to the wheel just in time to pass through the next slot in the wheel. One such slotted wheel has a radius of 11.0 cm and 800 slots at its edge. Measurements taken when the mirror was L = 500 m from the wheel indicated a speed of light of 3.0 x10^5 km/s.

    My work:
    Conversions:
    .11m
    3.0x10^8m/s
    L = 500m

    Arclength = 2pi*.11m
    Rotational speed = (2pi*.11m)/800
    Rotational speed = ((2pi*.11m)/800) * Speed of Light
    Rotational speed = 259181.39 rads/s <- This is wrong

    I did (Arclength/Slots) * Speed of Light to calculate 1 slot's worth.

    What was the (constant) rotational speed of the wheel? (rad/s)

    What was the translational speed of a point on the edge of the wheel? (m/s)
     
  2. jcsd
  3. Mar 16, 2005 #2
    You have not even used the length L.

    Time of travell for the light to travell from the disc and back is t= 2L/v where v is the given speed of light. Now within this time how much the disc has rotated? [tex]2\pi / 800[/tex].

    Angular speed is anlgle in rad / time = 2357 rad/s

    Tangantial speed is simply radius * angular speed.
     
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