An early method of measuring the speed of light makes use of a rotating slotted

Question

An early method of measuring the speed of light makes use of a rotating slotted wheel. A beam of light passes through one of the slots 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 12.0 cm and 900 slots at its edge. Measurements taken when the mirror was l = 500 m from the wheel indicated a speed of light of 3.0 multiplied by 105 km/s.What was the (constant) angular speed of the wheel?

Explanation / Answer

if the light passed through the very next slot, the change in angle that occured is
2/900 radians

distance travelled by the light in that time = 500+500m= 1km

at a speed of = 3*105=415 km/s

therefore the time taken was= T=D/s= 1/415 seconds

therefore the angular speed of the wheel= angle changed/time
= (2/900)/(1/415)= 2.897 rad/s

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