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 3.2 cm and 80 slots at its edge. Measurements taken when the mirror is L = 360 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?

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 3.2 cm and 80 slots at its edge. Measurements taken when the mirror is L = 360 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

For part (a)

angle= (2Pi)/80 = .07854

t = 2*360 / 3.0*10^8 = 2.4*10^-6 s

use =angle/time =0.07854 / 2.4*10^-6 s


For part (a) I get: ? = 32725 rad/s

For part (b)

= angular speed * .032m

For part (b) I get: v = 10472 m/s

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