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 9.5 cm and 140 slots at its edge. Measurements taken when the mirror is L- 1100 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? Light beam Light source Mirror perpendicular to light bean Rotating slotted wheel

Explanation / Answer

Angular separation between two slots, theta = 2*pi/140

= 0.04488 rad

time taken for the ray to reach back, t = 2*L/c

= 2*1100/(3*10^8)

= 7.3333*10^-6 s

a) angular speed of the wheel, w = angular dispalcement/time taken

= 0.04488/(7.33333*10^-6)

= 6120 rad/s or 58441 rev/min

b) use, v = r*w

= 0.095*6120

= 581 m/s

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