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.

 

[thepatientmental]

The rotational speed of the wheel can be calculated by dividing the circumference of the wheel (2πr) by the time it takes for one rotation, which is equal to the time it takes for the light to travel to the mirror and back (2L/c). So the rotational speed would be (2πr)/(2L/c) = (πrL)/L = πr. In this case, the rotational speed would be approximately 0.35 radians per second.

The translational speed of a point on the edge of the wheel can be calculated by multiplying the rotational speed by the radius of the wheel. So the translational speed would be 0.35 radians per second multiplied by 0.11 meters, which equals approximately 0.0385 meters per second.