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 7.0 cm and 400 slots at its edge. Measurements taken when the mirror was 500 m from the wheel indicated a speed of light of 3.0 x 105 km/s. Light beam Light source Mirror to light beam Rotating slotted wheel (a) What was the (constant) angular speed of the wheel? 6.5 rad/s (b) What was the linear speed of a point on the edge of the wheel? m/s

Explanation / Answer

(a) Indicated speed of light is 3.0 x 10^5 km/s

And the light travels 1 km (2 times 500 m) while the wheel advances one slot, then we can calculate that it takes 1/3 x 10^-5 s (= 1 km / (3 x 10^5 km/s)) for the wheel to rotate a distance of one slot, which is 1/500 of a revolution.

To calculate revolutions per second, we have:
(1/500) revolution / (1/3 x 10^-5 ) = 600 revs/s

Convert this in rad/s:
= 600 revs/s x 2 pi radians per revolution = 3769 rad/s

(b) Radius of the wheel = 7.0 cm = 0.07 m,

So, we have:
3769 rad/s x 0.07 meters per radian = 263.8 m/s

So, linear speed of a point at the edge of the wheel = 263.8 m/s

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