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 7.6 cm and 200 slots at its edge. Measurements taken when the mirror is L = 890 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? Light beam Light Source Mirror perpendicular to light beam Rotating slotted wheel (a) Number Units V (b) Number Units

Answer 1

(a)

note that distance is 2 times given as waves travels back and forth

so,

t = 2L / c = 5.933e-6 sec

$\theta$ = 2$\pi$ / 200 = 0.0314 rad

so,

w = $\theta$ / t

w = 5295.116 rad/sec

___________________________

(b)

v = rw

v = 0.076 * 5295.116

v = 402.43 m/s