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 5.3 cm and 240 slots at its edge. Measurements taken when the mirror is L = 760 m from the wheel indicate a speed of light of 3.0 x 105 km/s. (a) What is the (constant) angular speed of the wheel? (b) What is the linear speed of a point on the edge of the wheel?

Explanation / Answer

r = 5.3cm = 0.053m
c = 3.8*10^5 km/s = 3.8*10^8m/s
L = 760m

a) w = /t
t = 2L/C = 2(760)/3.8*10^8 = 4*10^-6 s

= 1 slot
500 slot = 2pi rad = 1 slot = 2pi rad/240 =2.61*10^-2 rad
=2.61*10^-2 rad

w = /t = 6525rad/s

b) v = wr = (6525)*(0.053) = 345.82m/s

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