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 650 slots at its edge. Measurements taken when the mirror was L = 400 m from the wheel indicated a speed of light of 3.00×108 m/s.

a) What was the (constant) angular speed of the wheel?

Explanation / Answer

angle = theta = 2pi/650 = 9.67 x 10^-3 rad

t = 2l/c

t = 2 * 400 / 3 x 10^8 = 2.67 x 10^-6 s

angular velocity = theta/t = 9.67 x 10^-3 / 2.67 x 10^-6

w = 3.62 x 10^3 rad/s

part b )

v = w*r

v = 181.086 m/s

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