Question

An early method of measuring the speed of light makes use of a rotating slotted wheel. A beam of light passes through one of the slots at the outside edge of the wheel, 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 6.0 cm and 400 slots at its edge. Measurements taken when the mirror was L = 500 m from the wheel indicated a speed of light of 3.0 ✕ 105 km/s. (a) What was the (constant) angular speed of the wheel?

Answer 1

Answer:

4.7 x 10³ rad / s

Explanation:

During the time light goes and comes back , one slot is replaced by next slot while rotating  before the light source

Time taken by light to travel a distance of 2 x 500 m is

= (2 x 500) / 3 x 10⁸

= 3.333 x 10⁻⁶ s .

In this time period, two consecutive slots come before the source of light one after another by rotation. There are 400 slots so time taken to make one rotation

= 3.333 x 10⁻⁶ x 400

= 13.33 x 10⁻⁴ s

This is the time period so

T = 13.33 X 10⁻⁴

Angular speed

= 2π / T

= $\frac{2\times3.14}{13.33\times10^{-4}}$

4.7 x 10³ rad / s