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 700 slots at its edge. Measurements taken when the mirror was L = 470 m from the wheel indicated a speed of light of 3.00×108 m/s. What was the (constant) angular speed of the wheel?


What was the linear speed of a point on the edge of the wheel?

Explanation / Answer

For the angular speed of the wheel, we need to know twothings: the distance in radians between slots and the time ittakes the light to make the round trip. To find the distance: we know that there are 2p radians in one full circle. There are 700 slots in this circle so we have: 2p / 700 = arclength of one slot = 8.9759 x 10^-3rads To find the time: We know the distance from wheel to mirror is 470m. Multiplying by two for the round trip we have 940m. Knowingthat the speed of light was given as 3.0x108 m/s wedo: t = d / v = (940m) / (3.0x108 m/s) = 3.13µs Now we can find the angular velocity by dividing the arclength bythe time: ? = (8.9759x10^-3rads) / 3.13µs = 2867.72 rad/s To convert this to a linear speed we simply multiplythe angular velocity by the radius: 2867.72 rad/s * 5cm = 14338.62462 cm/s or143.38m/s

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