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 3.4 cm and 240 slots at its edge. Measurements taken when the mirror is L = 290 m from the wheel indicate a speed of light of 3.0 x 105km/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?

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 3.4 cm and 240 slots at its edge. Measurements taken when the mirror is L = 290 m from the wheel indicate a speed of light of 3.0 x 105km/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

For part (a)

angular speed of the wheel = angle/time

angle = (2Pi)/240 = .0261799

t = 2*290 / 3.0*10^8 = 1.93*10^-6 s

angular speed of the wheel = .0261799 /1.93*10^-6 = 13564.74 rad/s

angular speed of the wheel = 13564.74 rad/s

For part (b)

linear speed = wr

v = wr = (13564.74)(0.034m) = 461.2 m/s

v = 461.2 m/s

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