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(III) Suppose a 65 -kg person stands at the edge …

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Problem 18 Medium Difficulty

(III) An asteroid of mass $1.0 \times 10^{5} \mathrm{kg}$ , traveling at a speed
of 35 $\mathrm{km} / \mathrm{s}$ relative to the Earth, hits the Earth at the equator tangentially, in the direction of Earth's rotation, and is embedded there. Use angular momentum to estimate the percent change in the angular momentum to estimate the
the collision.

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Physics 101 Mechanics

Physics for Scientists and Engineers with Modern Physics

Chapter 11

Angular Momentum; General Rotation

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Video Transcript

no license in this problem. All the forces and dogs are internal to the system. Therefore the angular momentum will become solved in the old US astray system, which means that the initial angular momentum will be equal to the final angular momentum on DDE A. Here is the total angular momentum for the alternate strike system on we know that angular momentum the magnitude of angle on this can Britain as I It is the moment of inertia off the object times omega It is the angular velocity. So for initial grace me, right, I off art times will make off art less I off stride Pleso me Go fast. Right? And these are the initial angular velocities for all on and the asteroid, respectively. And for the final case, we have I off times omega, which is the final angular velocity off art times I off, eh? It's only going off again since we'll have the same Anguilla velocities. So we were using the same ah location. And this can be done as I need less time, eh? Something good? No. Assuming the now this expression is ah comes from the assumption that the asteroid becomes embedded in the art at the surface on their full board, the art and bastard will have the same angular velocity after collision. Also really mortal the our Earth as a uniformed spear on the Astro Nick as a point muss. This means bag I off earth is equal to Don't buy five moss off Earth times off Earth Square. But this is a spear. And since Australia is assumed to be a point, must Iove cake and bitterness. Maazel, Gastric dimes. Oh, I got confused with the notation, Celia myself, The last straight times Media's off that strode sweat. Now we have. So let's solve for the first equation now. So we have I I ate the only guy unless I only got a equal Do I guess I e Thanks only guys. Now, if you compare this value with this value, we can say that the moment off in Isha off the satellite Can they ignored relative to the art? Ah, so I e yes, I a can be taken nearly equal toe. I it is when we don't know she after art. So that's what I live in a duel over here. So I mean, I did nearly equaled Oh, my time's Omega f From here, we can write omega if to be equal two I see omega, eh? Less. I only got a o much I eat now for the person dis change once we need the fractional change. So for that we need omega F minus the initial velocity off, which is on the guy. Well, what? Only God said, this is the faction of change on If we substitute this value off Omega, if over here we will get this factional James to be equal to I over i e times for me that day much me got it. Therefore, this is the faction of change. Therefore, the person they exchange the the Factional attain Stein's 100. This will be quite so I'II only guy Oh, but I e only guy time Sunday. Now let's news these expressions over there I wanting to carefully take from here is over here. The radius off rotation off the asteroid is in fact, really it's off the art, since the asteroid is very close to art. So these two are nearly equal, so we can write I a to be equal to Omar's off that story times through this off or square ice Omega e a what? Dubai? Five miles off the art and radius of the art school. I'm so me got eaten. I'm lifting. Multiply this by 100 on that. Wasn't this change? No, we have. We know that this over here is Omega Ache and Britain as No Mega again, Willard, And has, uh, off art velocity off or asteroid over. Read yourself up so we can drive back. So let's use this over here. I'm doing that. The yet didn't do this on the next page. So we simply substitute this omega and get over here. Don't get the person who's turns to be equal toe loss of the asteroid. Old lodge. Well, by five mas off art our east. Glad these to do. I can say we have the gold rush, Artie. For only guy on dde one over on me. Gotti. It is that storm over here. Times 100. Now let's light the vegetables that were given so you can substitute them into this equation. So the amounts off that street Toby tend to the par five cagey velocity off the asteroid is 2.5 times 10 to the power forward meet up a second myself. Part is 5.97 times standing apart 24 Treaty. Angular velocity in initial angular velocity off art ISS The art covers ah to 60 degrees. Art makes a food drop patient in 24 hours on one day. If you can work 24 hours in tow seconds you have two multiplied by the number of minutes in one night and then the number of seconds in on one minute. And this some sort of the equal to 86,000 400 seconds. Therefore on the gravel. Because I do to buy over the time period off art, which is 8 60 Lippman's astride the question. So do the easy for you. So this is what we will be using. And the time period for art in seconds is to buy a word. 86 bulls. You don't see the seconds? No, let's lug these. I lose. Okay. One thing. I forgot to write the radius off work. It's a six point eight times. Stand to the park six meters. Now, if you can plug all these values in this a question and saw them while you're playing by hundreds on If you do the happy, we'll get the person to exchange. So the equal wasn't his engine Angular velocity after collision to me Got the 3.2 I'm standing the butt minus 16 16%. This is the person dates by which the angular velocity off art has changed after colliding with the asteroid.

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Problem

(III) Suppose a 65 -kg person stands at the edge …

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Physics for Scientists and Engineers with Modern Physics

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Watch More Solved Questions in Chapter 11

Video Transcript

Douglas C. Giancoli

Physics for Scientists and Engineers with Modern Physics

Elyse Gonzalez

Zachary Mitchell

Aspen Fenzl

Meghan Miholics

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Physics for Scientists and Engineers with Modern Physics

Elyse Gonzalez

Zachary Mitchell

Aspen Fenzl

Meghan Miholics

Douglas C. GiancoliPhysics for Scientists and Engineers with Modern Physics

Elyse Gonzalez

Zachary Mitchell

Aspen Fenzl

Meghan Miholics

Douglas C. Giancoli

Physics for Scientists and Engineers with Modern Physics