An early method of measuring the speed of light makes use of a rotating slotted 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 8.8 cm and 100 slots at its edge. Measurements taken when the mirror is L = 1100 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?

Expert Solution

a) Here, t = 2L/c

= 2 * 1100/(3 * 10⁸)

= 7.33 * 10^-6 s

theta = (2pi)/100

= 0.0628 rad

Thus, the (constant) angular speed of the wheel = theta/t

= 0.0628/(7.33 * 10^-6)

= 8567.53 rad/s

b) the linear speed of a point = r * w

= 0.088 * 8567.53

= 753.94 m/s

genius_generous answered 2 years ago

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