Shadowing Practice: Orbital Mechanics - Newton's Laws - Learn English Speaking with Video
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1
All right, so welcome back.
Muy bien, bienvenidos de nuevo.
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So today's lecture is going to be very short because all we need to cover to finish chapter one are Newton's laws.
Así que la clase de hoy va a ser muy corta porque lo único que necesitamos cubrir para terminar el capítulo uno son las leyes de Newton.
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And the reason why we need to review Newton's laws of motion as well as Newton's gravitational law is
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because in the previous lecture we looked at kinematics where we saw techniques
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and methods to study the motion in a force-free environment.
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But when you think about a spacecraft orbiting a planet, there are obviously external forces being applied to our spacecraft and precisely gravitational forces.
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So in order to be able to solve the motion, we need to invoke dynamics.
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And again, the basis to start with dynamics is to review Newton's laws.
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So first up, we have in 1.5.1, we have Newton's laws. of motion.
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So there are three laws of motions derived by Newton.
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The first one is known as the law of inertia.
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That law says that unless being acted by an external force, a particle in motion will remain in uh in set motion
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without the mean deviation will remain in a recti linear motion
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okay uh let me just write it down for you for completeness
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so this law states that unless acted upon by force
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A particle will
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remain in its
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state of rest or will remain
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in a straight line, motion with constant
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inertial velocity.
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Okay?
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So all this to say that unless you perturb or push or pull on particle, well that particle will just continue its motion.
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Okay, that's obvious.
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And this is the law we observe in my laboratory where we have the granite table upon
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which are floated spacecraft platform and because of
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that they aren't experiencing any frictional effects and as such
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if you were to push a platform in my lab the
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platform will continue traveling with constant velocity in its initial direction
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without any deviation thanks to the law of inertia as stated by Newton.
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Okay so that was the first law of motion discovered by Newton.
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The second one which is probably his most famous law is is f equal ma
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okay so in a vector form you just say
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that the net force being applied to the particle is equal
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to the mass of the particle times its acceleration in a vector form
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you could also reformulate that to solve for the acceleration
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that the particle will experience given the net force being applied
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to it all right pretty self-explanatory one thing to realize here is
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that this acceleration you see on the left hand side of that equation acceleration is always the inertial acceleration.
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Alright, so again, the acceleration in Newton's second law, F equal to mA, is always the inertial acceleration,
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always, always, always, such that you could say
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that this is the velocity vector inertial derivative or equivalently double inertial derivative of the position vector r
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and this is why we studied previously how to relate the inertial acceleration to the non-inertial acceleration
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because it was such a big deal to obtain the inertial acceleration right by virtue of newton's second line
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that we're going to reuse ultimately in chapter two to come up with the spacecraft orbital dynamical equation okay
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so second law of motion by newton finally we're down to the last one so this is the law of action
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reaction, which says that for every applied force
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is an equal and opposite reaction force.
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Okay, so if you have a particle, say M1, and a particle M2 over there,
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if M1 exerts a force on M2, say it's pulling on m2 like
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that with f21 well then m2 will also exert the force on m1 of equal magnitude
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but in opposite direction f12 all this to say that If F21 is the action,
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you're going to get a reaction in the opposite direction,
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like that, where F21 is equal to minus F12.
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okay so same magnitude yet opposite direction what did I just say here that doesn't make any sense
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f21 is unequal to minus f21 so if if you have f21 like that you get f12 like this
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And they are in equal magnitude but opposite direction.
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And that's all I wanted to say.
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Apologies for that.
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All right, so these are the three laws, as stated by Newton.
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But perhaps the most important one in our context here is the law of gravitation.
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Newton's law of gravitation. and 1.5.2.
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So, that's considered a case again where we have two masses, M1 and M2.
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And now we're looking specifically at gravitational forces.
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So, we have M1 attracting M2 towards itself.
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with a force being denoted F21 as previously.
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So we're going to say that F21 vector
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is the force of attraction on M2 by M1.
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So M1 attracts M2 essentially.
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And then you have the opposite direction, F12,
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or F12 is the force of attraction applied on M1 exerted by M2.
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and again by virtue of Newton's third law they are equal to magnitude yet in opposite direction
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now Newton was able to quantify mathematically those gravitational forces
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or attraction forces by virtue of the fact
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that those point masses have finite mass of a kilogram
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and the way they're quantified is F21 is equal to minus capital G where this is known as the universal
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gravitational constant times m1
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times m2 times r21 where r21 is the position vector of mass 2
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with respect to mass 1 I'm just going to move my F12
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and that makes a lot of sense because if R21 is to the right
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then you get F, if R21 is to the right, F21 is to the left, like that, in opposite direction.
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And all this is divided by R21 into the position of M2 with respect to M1.
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The norm of that, cube.
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So this is quantifying the gravitational forces of M1 attracting M2 towards it.
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And similarly, you could solve for F21,
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or sorry, F12, by saying that this is now a force in the same direction as R21.
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So this time we don't have the minus in front of everything.
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So G, M1, M2, R21,
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position vector, over the distance between those two masses, Q.
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By the way, this gravitational constant, you don't have to remember
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that on top of your head in an exam I'm going to provide all constants for you
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but for completeness this constant is given by 6.6732 times
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10 to the negative 11 newton meter square over kilogram square.
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And this concludes Chapter 1.
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Alright?
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So in Chapter 2, we're going to start right away by using those gravitational forces,
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specifically in case of a planet attracting the spacecraft towards itself and thereby creating an orbit around itself.
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Okay?
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Hope you enjoyed Chapter 1.
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Congratulations, you survived.
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That wasn't an easy chapter to go through was pretty dry
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a lot of new theory new mathematical operator mathematical objects the vector c's the hollow dot all those great things
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but you made it thus far congrats and i'll see you again in chapter two soon see you
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Vocabulario y notas de pronunciación para esta lección
Esta lección de conversación de nivel C1 se basa en el vídeo “Orbital Mechanics - Newton's Laws”. Las palabras que más se repiten: force, motion, acceleration, particle, equal. Este vídeo tiene 102 frases y 1174 palabras para practicar shadowing. La parte hablada dura 13:53. El hablante habla despacio, unas 85 palabras por minuto, así que hay tiempo para imitar cada sonido. Solo el 78 % de las palabras está entre las 3.000 más comunes del inglés, por lo que el vocabulario es exigente.
Vocabulario clave de este vídeo
Las 15 palabras más avanzadas del vídeo, con su pronunciación y significado:
| Palabra | Pronunciación | Significado |
|---|---|---|
| acceleration sustantivo | /əkˌsɛl.əˈɹeɪ.ʃən/ | aceleración, aceleramiento |
| particle sustantivo | /ˈpɑɹtək(ə)l/ | partícula |
| gravitational adjetivo | /ˌɡɹævɪˈteɪʃənəl/ | gravitatorio, gravitacional |
| inertial adjetivo | /ɪˈnɜː.ʃəl/ | inercial |
| vector sustantivo | /ˈvɛktɚ/ | vector |
| newton sustantivo | /ˈn(j)uːtən/ | newton |
| spacecraft sustantivo | /ˈspeɪsˌkɹæft/ | nave espacial |
| minus | /ˈmaɪ.nəs/ | menos |
| magnitude sustantivo | /ˈmæɡnɪtjuːd/ | magnitud |
| exert verbo | /ɪɡˈzɝt/ | ejercer |
| quantify verbo | /ˈkwɑn.tɪˌfaɪ/ | cuantificar, cifrar |
| velocity sustantivo | /vəˈlɑsəti/ | velocidad |
| virtue sustantivo | /ˈvɝt͡ʃu/ | virtud |
| completeness sustantivo | completitud, completud | |
| deviation sustantivo | /ˌdiː.viˈeɪʃən/ | desviación |
Phrasal verbs que vas a escuchar
| Palabra | Significado |
|---|---|
| come up with verbo | ingeniar, ingeniarse |
| go through verbo | atravesar |
Pronunciación a tener en cuenta
El hablante usa 15 contracciones y formas reducidas, como we're, don't, I'm. Dilas en su forma corta, tal como las oyes.
- Los sonidos de “th”: mathematical /ˌmæθ(.ə)ˈmæt.ɪ.kəl/, thereby /ðɛɹˈbaɪ/
- Los sonidos de “sh” y “zh”: acceleration /əkˌsɛl.əˈɹeɪ.ʃən/, gravitational /ˌɡɹævɪˈteɪʃənəl/, inertial /ɪˈnɜː.ʃəl/, deviation /ˌdiː.viˈeɪʃən/, gravitation /ˌɡɹævɪˈteɪ̯ʃən/
- Palabras largas — cuida el acento: acceleration /əkˌsɛl.əˈɹeɪ.ʃən/, gravitational /ˌɡɹævɪˈteɪʃənəl/, velocity /vəˈlɑsəti/, deviation /ˌdiː.viˈeɪʃən/, gravitation /ˌɡɹævɪˈteɪ̯ʃən/
Sonidos difíciles para hispanohablantes:
- /v/ — no es /b/: los dientes tocan el labio inferior: gravitational /ˌɡɹævɪˈteɪʃənəl/, vector /ˈvɛktɚ/, velocity /vəˈlɑsəti/, virtue /ˈvɝt͡ʃu/, deviation /ˌdiː.viˈeɪʃən/
- /z/ — sonora, no /s/: exert /ɪɡˈzɝt/, observe /əbˈzɜːv/
Cómo practicar con este vídeo
- Escucha el vídeo entero una vez sin hablar y anota las palabras que no conoces.
- Haz shadowing frase por frase a velocidad normal, repitiendo cada una hasta que tu ritmo coincida con el del hablante.
- Grábate y compara con el original, prestando atención a palabras como acceleration, particle, gravitational.
¿Qué es la Técnica de Shadowing?
Shadowing es una técnica de aprendizaje de idiomas respaldada por la ciencia, desarrollada originalmente para la formación de intérpretes profesionales y popularizada por el políglota Dr. Alexander Arguelles. El método es simple pero poderoso: escuchas audio en inglés nativo y lo repites en voz alta de inmediato, como una sombra que sigue al hablante con solo 1-2 segundos de retraso. A diferencia de la escucha pasiva o los ejercicios de gramática, el shadowing obliga a tu cerebro y músculos de la boca a procesar y reproducir simultáneamente patrones de habla reales. Las investigaciones muestran que mejora significativamente la precisión de la pronunciación, la entonación, el ritmo, el habla conectada, la comprensión auditiva y la fluidez al hablar, convirtiéndola en una de las metodologías más efectivas para la preparación del IELTS Speaking y la comunicación en inglés en el mundo real.