RADIUS 6400 kilometers (1) The radius of the Earth is...

RADIUS 6400 kilometers (1) The radius of the Earth is approximately 6400 kilometers. How far would you travel, in kilometers, in going around the equator? (2) What is the speed of a point on the equator in kilometers per hour as the Earth rotates on its axis? (3) (Extra Credit) If the radius of the Earth's orbit around the Sun is 150 million kilometers, what is the speed of the Earth in its orbit in kilometers per hour? Part (2) Angles An angle is formed between two straight lines that meet at a point called the vertex of the angle. The size of an angle is determined by the difference in direction of the two sides and is a fraction of a full circle. The ancient Babylonian astronomers divided a circle into 360 parts or degrees. (Apparently this was based on the fact that there are approximately 365 days in the year. Exercise (2A) 1. Using your protractor, measure the value in degrees for angles A, B, C, and D on your Data Page. Record the value of the angle beside the vertex. Exercise (2B) 1. Using you protractor, measure and record each of the three angles in each triangle in the figure on your Data Page. 2. What do you conclude about the sum of the angles in any triangle? Exercise (2C) Using your protractor, construct the following angles on your Data Page: 25", 130", and 315".

Transcript

00:02 All right, so your question is about how do we find the rotational speed of a person standing on the equator and then the revolution speed of the planet as it travels around the sun each year.

00:18 So both questions are all about the speed equation.

00:24 So speed is equal to the distance, divide by the time.

00:29 And we also know one thing about the distance around a circle.

00:33 Is the circumference, which is 2 pi r.

00:37 So we can make that substitution here that on these equations, since these are circular pathways, that the speed is going to be 2 pi r divided by time.

00:51 So let's do that.

00:52 So on this first one here, we're going to have s is equal to 2 pi times 4 ,000.

01:02 They want our answer in miles per hour, we don't have to do any conversions here.

01:07 One day is 24 hours in length, or in time.

01:13 I shouldn't say length.

01:17 So 8 ,000 pi times 24 hours.

01:27 Oops, not times 24 hours.

01:30 Divide by 24 hours.

01:33 So they're going, on the equator, they're going 1 ,047 miles per hour, depending on our significant figures.

01:46 Your instructor rounded 4 ,000 miles, that's kind of just one significant figure, so i'm going to round mine to, i shouldn't say meters per second either.

01:59 I'm used to meters per second physics, but miles per hour.

02:04 So a thousand miles per hour is approximately speed that a person that's standing on the equator has to be traveling in order to get around the planet in one day.

02:18 The unusual thing about this is that if you were standing on, say, one meter away from the north pole, you would barely be moving per mile per hour because you only have to go around a circle that's one meter in radius in one day.

02:37 So it seems strange that the person standing near the north pole has a tangential speed that's a lot different than a person sitting on the north pole has a tangential speed that's a lot different than a person sitting on the, the equator.

02:49 But that is what happens.

02:51 We call that the coriolis effect.

02:53 It's actually one of the reasons we have, say, the jet stream and the westerlies and easterly winds and such is the coriolis effect.

03:05 Now the revolution speed, we got some really good numbers here.

03:09 We want this in miles per hour as well.

03:13 So let's see what we have to do to convert.

03:16 This one has to convert some stuff from days into hours.

03:22 So it won't take much, though.

03:24 S equals 2 pi again.

03:29 This time the r is a really large number, 92 ,956 ,000 miles.

03:36 So the sun is about eight light minutes away from us.

03:42 It takes eight minutes for the light from the sun to get here.

03:45 So the scary thing is, is if the sun blew up, we wouldn't know for eight minutes.

03:49 But that's for a different question.

03:53 This one we're looking at how much time it takes to get around the sun in one year, or how fast you have to be going to do that.

04:02 So here we've got the days, but we need this in hours because we want our final answer to be miles per hour.

04:09 So what we're going to do is multiply this by 24 hours because there is in one day there's 24 hours so we can make that multiplication on that denominator there so two times high times 92 million 956 thousand divided by 365 .24 and then divide that again by 24 we get 66 we get even faster now we're going at 67 ,000 miles per hour.

04:56 I guess we have pretty well, pretty accurate or precise values here.

05:03 So let's go all the way to what.

05:05 We got five digits of significant figures here that we can go with.

05:08 So let me let me erase that.

05:10 I was going to go with one digit again like i did in the last one.

05:14 But because we have much more precise measurements here, we can do that.

05:18 So we've got 66 ,600 ,600 .6 ,000.

05:27 29 miles per hour.

05:34 66 ,629 miles per hour.

05:36 That's how fast the earth has to be going to get around the sun in one year from the orbit that we have.

05:46 So pretty fast.

05:48 Fall of a sudden the earth came to a stop.

05:51 We'd all be going and flying off the surface at at least 75 ,000 miles per hour.

05:58 So that's pretty crazy...

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