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 a slot at the outside edge of the wheel, as in the figure, 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 5.0 cm and 600 slots at its edge. Measurements taken when the mirror was L = 480 m from the wheel indicated a speed of light of 3.00×108m/s. What was the (constant) angular speed of the wheel?
B)))What was the linear speed of a point on the edge of the wheel?

Explanation / Answer

a)

here

delta t = 2*L /c = 2 * 480 / (3.8 * 10^8) = 2.5 * 10^-6 sec

then

600 slots = 2 * pie

1 slot = 1.0467 * 10^-2 rad

w = delta displacement / delta t = 1.0467 * 10^-2 / (2.5 * 10^-6)

w = 4.18 * 10^3 rad/sec

b)

v = w * r = 4.18 * 10^3 * 0.05 = 209 m/s

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