Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 34, Problem 1P

In an experiment to measure the speed of light using the apparatus of Armand H. L. Fizeau (see Fig. 34.2), the distance between light source and mirror was 11.45 km and the wheel had 720 notches. The experimentally determined value of c was 2.998 × 108 m/s when the outgoing light passed through one notch and then returned through the next notch. Calculate the minimum angular speed of the wheel for this experiment.

Expert Solution & Answer
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To determine

The minimum angular speed of the wheel for this experiment.

Answer to Problem 1P

The minimum angular speed of the wheel is 114rad/s .

Explanation of Solution

Given info: The distance between the light source and the mirror was 11.45km , no of notches in the wheel is 720 notches, experimentally determined value of c was 2.998×108m/s .

The formula to calculate the angular speed of the wheel is,

ω=dθdt (1)

Here,

ω is the angular speed of the wheel.

dθ is the degree movement of the wheel in consecutive notches.

dt is the time for the light to travel to the stationary mirror and back.

The formula to calculate dθ is,

dθ=2πnumber of notches

Here,

dθ is the degree movement of the wheel in consecutive notches.

Substitute 720 for the number of notches.

dθ=2π720 (2)

The formula to calculate dt is,

dt=2dc (3)

Here,

d is the number of notches in the wheel.

c is the experimentally determined value of speed of light.

Substitute 2π720 for dθ and 2dc for dt in equation (1).

ω=(2π720)(2dc) (4)

Substitute 11.45km for d and 2.998×108m/sec for c in equation (4).

=2π/720rad2×(11.45km×103m1km)2.998×108m/sec=114rad/sec .

Conclusion:

Therefore, the minimum angular speed of the wheel is 114rad/sec .

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