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 150 slots at its edge. Measurements taken when the mirror is L = 850 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

o=theta

angular position

o=2pi/X =2pi/150 =0.04189 rad

time taken

t=2*L/c =2*850/(3*108)=5.67*10-6 s

angular velocity

W=o/t =0.04189/5.67*10-6

W=7392.35 rad/s

b)

V=r*W=0.095*7392.35

V=702.3 m/s

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