Rotational Speed with the Speed of Light

[BlasterV]

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)

[Gamma]

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? 2\pi / 800.

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

Tangantial speed is simply radius * angular speed.