In an experiment to measure the speed of light using the apparatus of Fizeau (see Fig. 35.2) , t

step 1 So we have Phizzo's wheel and it's rotating. So let me draw that for you guys. We have Fizzle's

In an experiment to measure the speed of light using the...

Key Concepts

Angular Speed and Angular Displacement

Angular speed is the rate at which an object rotates, measured in radians per second or revolutions per minute. Angular displacement refers to the angle through which a point or line has been rotated in a specified sense about a specified axis. In the context of the experiment, the relationship between the angular displacement (i.e., the rotational gap between consecutive notches) and the time interval determined by the light’s round-trip travel is used to calculate the minimum angular speed of the rotating device.

Speed of Light Measurement Using Rotating Shutter Techniques

This concept involves measuring the speed of light by modulating the light beam with a rotating device such as a toothed wheel or shutter. In this technique, light is allowed to pass through a gap in the rotating device, travels to a distant mirror, and returns. The timing and synchronization between the rotating gaps and the returning light determine the speed of light. This method was historically significant and underpins the experimental design described.

Time-of-Flight Measurement

Time-of-flight measurement is the technique of determining the time taken for a wave or particle, such as a photon, to travel from one point to another. In these experiments, the known distance between the light source and the reflector, alongside the measured time delay (or the time it takes for the light to traverse this distance and return), is critical for accurate computation of the speed of light.

Unit Conversion in Rotational Motion

Unit conversion in rotational motion concerns translating between different measurement units such as converting angular speed from radians per second to revolutions per minute. This conversion is essential in experiments where laboratory instruments and reporting standards may require different units, ensuring that the computed angular speeds are expressed in a convenient and understandable form for practical applications and comparisons.

Transcript

00:01 So we have phizzo's wheel and it's rotating.

00:10 So let me draw that for you guys.

00:12 We have fizzle's wheel and it's rotating.

00:18 So there's a beam of light that is passing through here.

00:25 And the distance that's been given to us that is traveling between here and the mirror, which we're going to draw in blue, i guess, is going to be d.

00:42 So this d is 11 .45 kilometers, which is the same thing as 11 ,450 kilometers, or just meters.

01:04 Next we have the number of keith on this wheel, so that is n, which is 720 .20.

01:17 And we have an experimentally determined c of 2 .998 times 10 to the 8 meters per second.

01:29 So we want to know what speed is this wheel spinning at? what speed is it spinning at? so the first thing we're going to do is we're going to say that c is equal to 2d over the change in t because that is the amount of distance that this is traveling is traveling from the wheel to the mirror and back right so that's that accounts for a 2d and the t is what we're trying to find out so we want to know this time interval so our change in t is going to be equal to 2d over c that's going to be equal to two times 11 ,450 over 2 .998 times 10 to the 8th.

02:26 So this gives us a change in time of 7 .64 times 10 to the negative 5th seconds.

03:03 So now that we know that, we can use that to solve for our omega.

03:13 So our omega is going to be found using the following equation.

03:18 So the change in time is going to be equal to the change in angle over the angular speed, right? that's just the definition of what this is.

03:27 So the change in angle that we're looking for, because it's going to be in between this guy going from point a, which is here, this tooth going to point b.

03:39 So it's in the amount of time that takes together from here to there, it's traveling some change in theta.

03:44 And since we know that the number of teeth is 720, we're going to call this...

Please give Ace some feedback