3. Motion of Center of Mass; Acceleration in Rotating Ref. Frames
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- Опубликовано: 2 сен 2013
- MIT 2.003SC Engineering Dynamics, Fall 2011
View the complete course: ocw.mit.edu/2-003SCF11
Instructor: J. Kim Vandiver
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
DR. Vandiver, thank you for a powerful and classical analysis of the Motion of the Center of Mass and the Acceleration Reference Frames in dynamics. These reference frames really increase my understanding of dynamics.
It really demonstrates the superior abilities MIT teaching staff have over other Universities/Colleges. I go to a prestigious University in Australia, but this is unparalleled in terms of ability to understand fundamental concepts instead of learning how to be a technician and plug and chug all day.
+0100011001010101CK Was thinking the exact same thing! I'm third year in Australia and my lecturers are assuming we have learnt this stuff in 2nd year in Dynamics, but our dynamics course was basically "here are the formulas and the concepts, and here is when you use them". No fundamental derivations and explanations like this guy. No comparison...
+Andries Rian Gouws
In my opinion, formulas should only be used if it's clear where they are coming from.
They should basically just be handy "shortcuts" that let you sidestep tedious derivations that you already know, they shouldn't be something that you completely rely on.
College math and physics tends to be much more demanding than that anyway, and simply memorising formulas won't lead anywhere, so one might as well go hardcore and learn the derivations.
I spent two days on trying to derive all the central-force motion formulas from scratch for myself, which was a massive pain, but it was also incredibly rewarding.
Totally agree. I'm also in the best engineering university at Chile and the derivation of these equations was done just mathematically and the physics of it was left unexplained, so then you just memorize formulas and hope you're using them well.
I don't even attend the lectures at my college; the professor just talks about formulas and number all the time while completely neglecting the bigger picture. Thankfully such things as MIT opencourseware exist.
ひ = V
amazing lectures! can't believe i'm watching this great content FOR FREE, we live in a truly blessed time.
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He is a great teacher. He has a remarkable quality for describing things in unique way.
Final boss of eng
Thanks a lots for this awesome lectures MIT
Extraordinary professor.
Great Professor!
They should make this into an edx course. It's a very fundamental topic in mech and aero engineering.
vooo vooo vooo amazingggg video thanks sir for showing the great equation
Amazing!
Hi Sir it would be interesting to elaborate on why the rotation is with respect to (o) and not to (A) since rotation vectors are free vectors???
Almost certain that this is no longer being monitored, but l have a questions:
1. Choosing a location other than the center of mass of the object - would you have to add an additional term to the derivative due to the each particle of the body- say an asteroid of unknown composition
@minute 35:09 - taking the derivative of W x R results in three terms (because dR/dt is broken down into a linear and an angular component) and in particular 2 (W x V). It would be great to see where the factor 2 comes from.
Yep! Awesome lecture by a world class engineer! The fall of Rome probably experienced people who didn’t take advantage of their resources too!
ok.. so l have another query- this one with angular velocity- dtheta/dt- so the derivation of r hat, has two terms in its tiem derivative- namely theta 2qq2/dt2.deltat.thetahat+ theta dot.thetahat.
Hi, vectors in rotating frames formula be applied to angular velocities as well.Since the angular position is not a vector by itself but angular velocity is?
vector and vector dot product can become scalar for some reason idk i no experience and dk what im talking abt
how sad only 15 people had seen this great lectures while hundreds and millions of students spending all those money to go to universities.
tHERE is somthing called DEGREE too
What is answer of part b
Awesome stuff. Why does he write his R that way though
+nura loh it's a cursive r
It's a final boss R
This thinks describes that to be educated money is not important, the important thing is eager towrd education
I don't understand why he takes a partial derivative. Also, when taking the partial derivative of the position vector with respect to time (to get velocity in that formulation), it has to be zero, doesn't it? The position vector can't go anywhere in time if it's assumed that all position coordinates are fixed.
Position vector can always change in magnitude and also orientation if the point for which the position vector is defined changes position, which is very much possible.
We take the partial derivative because if you imagine the particle in a 3D coordinate system, the motion in changing in only one direction.
@@joeyGalileoHotto no, it is not like that , i think he confused everyone ,becoz he has read from WILLIAMS BOOK AND I THINK IN BOOK IT HAS BEEN MENTIONED THAT for calculating velocity of the particle as seen from AXYZ PRIME coordinates and velocity as seen from fixed reference frame OXYZ you have to take derivative of the position vector of the particle so for AXYZ PRIME he used partial deri and for fixed refernce frame he used normal derivative other than that it has no significance ......
Just to keep track in which frame we are defining velocity he used partial and normal derivative .... partial for AXYZ PRIME and normal for OXYZ
SO THAT HE DOESNT GET CONFUSED ....
I HOPE YOU GOT MY POINT...
However on the job the computer computes the action anyway-partial derivative is fine 😊
1:09:43 why the derivative of theta hat will give me minus theta dot r hat?
If you write theta hat in cartesian coordinates using a inertial coordinate system it is: -sin(theta)(i hat)+cos(theta)(j hat). Taking the time derivative it yields: theta point [-cos(theta) i hat-sin(theta)(j hat)]. Which is the same as: -theta r hat. (Taking into account that the time derivative of the inertial frame of reference is 0).
Can you explain me ....I can't understand this area
ruclips.net/video/_BuyCwdCxAc/видео.html You can this video out. He has mentioned it in a systematic way.
And why did he use underlines as notations of vectors?
+Sihan Chen just one of the possible vector notations. You can underline, bold it, or have the arrow on top. Not sure what else.
To assert dominance
Is this course for a second year in mechanical engineering bachelor degree?
Yes, since most students need to take the physics and math requirements the year before. See the syllabus for more info at: ocw.mit.edu/2-003SCF11. Best wishes on your studies!
@1:09:54 Can someone please clarify how and why he derives the unit vectors r and theta, and not z?
I'm 7 months late but here goes:
The value of z represents the magnitude of the component of the position vector in cylindrical coordinates that is parallel to the unit vector k hat.
You use the same strategy when you decompose a vector in Cartesian coordinates, where x represents the magnitude of the vector parallel to i hat, y represents the magnitude of the vector parallel to j hat and z represents the magnitude of the vector parallel to k hat, such that the resultant (or sum of those three vectors) is the position vector that you started with.
@@JansthcirlU z is not derived because it doesnt change.
is that a master course or bachelor course?
This is an undergraduate course. See the course on MIT OpenCourseWare for more information and materials (lecture notes, exams with solutions, problem sets with solutions) at: ocw.mit.edu/2-003SCF11. Best wishes on your studies!
Where do those dislikes come from? 🤔
www.file-upload.com/users/nadercca/13885/Engineering%20books
f(x)
in india we study this topic in 11 grade
n teacher is awesome
You sure? I think you are confusing basic, classical mechanics with this which is expanded galilean and newtonian mechanics at university level.
There's a big difference and if you have no degree I understand why you don't understand that. If you still believe you studied _"this topic in 11 grade"_ please provide a link to a syllabus so I can see what unparalleled, one-of-a-kind school for the gifted you studied at.
Bollibompa yes, it is in our school syllabus NCERT. In india we have an exam called IIT JEE which is had a very detailed and has all university concepts like constrained mechanics, Taylor series, vector mechancis(university level), electrodynamics and many more.
it's a lie
+Skippy Cavanaugh why you spread a wrong information. You're trained to take I IT JEE exam but it doesn't mean you know all of them. Stop lies
between why you need to learn college stuffs during your school?
Someone call this mans wife and tell her he's ready to retire lol. Please come pick him up😂