Rigid Bodies Relative Motion Analysis: Velocity Dynamics (Learn to solve any question step by step)

[@French408]

Dude. No lie, I had literally no idea what was going on in class and I had an exam the next day. Like, I didn't know how to even start the HW, didn't understand lectures, etc. I didn't even know how much I didn't know. So the day before the exam, I watched your videos and took really good notes. After the exam, the grade comes out and I got a 98% after the curve, the second highest score for that exam. You are a literal lifesaver.

[@QuestionSolutions]

Wow, that's actually pretty crazy. I am really happy (not at the fact that you didn't do your HW), but at the fact that you were able to take notes from these videos and get a 98%. That's amazing! Keep up the great work and I wish you the best with your studies.

[@Uziiiiiiiiiiiiiiiiiiiiii]

the dynamics playlist single handedly thought me in one all nighter before my exam than the lectures of this semester have in total.

[@QuestionSolutions]

I am really glad to hear that! Keep up the great work and I hope your exam went well.

[@ghadeeralharbi2131]

You are better than all doctors who teach this subject in my uni (combined).

[@QuestionSolutions]

Thank you very much. Best of luck with your studies! :)

[@mrmagoo-i2l]

@@QuestionSolutions Could you still do the slider problem using k if it wasn’t a 45 degree angle?

[@QuestionSolutions]

@@mrmagoo-i2l Can you give me a timestamp? I'll take a look and let you know 👍

[@QuestionSolutions]

@@mrmagoo-i2l What do you mean by k? Please elaborate.

[@Aegis4521]

probably because doctors don't know too much about engineering

[@abhineetnirmal]

The question looks so complex in the beginning but when you really focus I see how easy you have made this. Thanks dude, saving lives out here.

[@QuestionSolutions]

You're very welcome! Glad you could follow along, hopefully it helps you out :)

[@enes577]

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[@QuestionSolutions]

Thank you very much for your kind comment. I really appreciate it! I also wish you the best of success with everything you do.

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[@QuestionSolutions]

You're very welcome. I hope you did amazingly on your exam :)

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[@QuestionSolutions]

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[@QuestionSolutions]

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[@donnymcjonny6531]

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[@Western_Hemlock]

This video was truly revolutionary for me, I understand this section so much better now. Thank you

[@QuestionSolutions]

I'm so glad! Keep up the great work and best wishes with your studies.

[@bradleyxavier-sm8qn]

Your animations make the problems more intuitive where the book and Mastering cannot/will not. Thank you. I wish I had found these sooner, might have less desk imprints in my face.

[@QuestionSolutions]

You're very welcome! I am glad to hear the animations help :)

[@psedach]

Best explanations of dynamics I've seen so far - even better than Jeff Hanson.

[@QuestionSolutions]

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[@jtcarney8214]

Seeing the problems animated helped so much when it came to solving.

[@QuestionSolutions]

Glad to hear that! :)

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[@QuestionSolutions]

Thank you very much! Best wishes with your studies.

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[@QuestionSolutions]

I am really glad to hear that :) I hope you did amazingly on your exams.

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[@QuestionSolutions]

Thank you so much :)

[@sugumarprabhakaran]

Great job. Really nice clean animations that help with visualizing the problems.

[@QuestionSolutions]

Thank you very much! Best wishes with your studies.

[@ibrahimhassan2949]

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[@QuestionSolutions]

I'm happy to hear KZbin has been helping you. Could you elaborate on what you mean by "chapters in sections?" I like feedback so if it's something I can keep in mind for the future, I'll incorporate it.

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we need more video. this are really getting me through dynamic

[@QuestionSolutions]

Glad to hear they are helping! If possible, please share these videos with friends/classmates who may also find them helpful. That will help this channel and help them as well, win win 👍

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[@QuestionSolutions]

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[@robbieenglish4439]

Thank you thank you so much for this video. You earned yourself a subscriber 1 minute in. I will be watching many more of these for my upcoming exam. Thanks you thank you!!

[@QuestionSolutions]

You are very welcome and thank you for the sub. Keep up the great work and I hope all the videos help you out with your upcoming exam!

[@SirGabeII]

I just wanna let u know my professor with "A Ph.D." can't do half as good of a job as you. Thank You Truly!

[@QuestionSolutions]

I'm glad to hear these videos help :) You're very welcome and I wish you the best with your studies. Keep up the good work!

[@olamide1480]

such a legend you'll be remembered forever mate.

[@QuestionSolutions]

Thank you very much!

[@kanhchanaly6445]

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[@QuestionSolutions]

You're very welcome! Best of luck with your studies.

[@김대현-h5z5q]

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[@QuestionSolutions]

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[@CollinXanderr]

This was extremely helpful, thank you

[@QuestionSolutions]

You're very welcome! Best wishes with your studies.

[@abdulrahmanabdeh4083]

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[@QuestionSolutions]

You are very welcome! I wish you the best with your studies.

[@Maisara7]

The Videos is very helpful and the explanation is very good you are better than all doctors I've seen in this subject 💙💙

[@QuestionSolutions]

Wow, thank you! I am glad it was helpful to you. Keep up the great work and best wishes with your studies. ❤

[@jadkhalil9263]

Thanks dude I have midterm in 2 days and I'm going to ace it all thanks to you :D

[@QuestionSolutions]

Glad to hear! I wish you the best with your midterms. :D

[@bradleyeidex7777]

How did the midterms go

[@5leafclover_]

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[@QuestionSolutions]

Nicely done! Keep up the awesome work and I wish you the best in your other courses.

[@priyajit3285]

Your Videos with helpfull Concepts are GOAT(Greatest of all time)🙏

[@QuestionSolutions]

Thank you very much, glad to hear it was helpful!

[@chadbullard979]

3:24 I-components: 0=8sin45-2wbc, answer you have wab = 2.282rad/s cw, J-components: -2wab = -8cos45, answer you have is wbc = 2.828 rad/s ccw. I think subscript is switched. I-component is wbc=2.828 rad/s cw, and J-component is wab = 2.828rad/s ccw.

[@QuestionSolutions]

No, what's shown is correct. So imagine this to be a fully moving system. Imagine the block at C actually sliding down. When it's sliding, is it possible for rod AB to rotate counter-clockwise? No, right? Now look at rod BC, and imagine it rotating about point B while block C is sliding down. Can it rotate clockwise? No. So it must be counter-clockwise. You can actually see the angular velocity arrows drawn in black shown on the diagram. Once we find the angular velocity, the i, j, k components are irrelevant to us since we get a scalar answer.

[@ryanbragg4334]

At 2:25, why is the angular velocity defined to be in the -k direction? If it's moving clockwise, shouldn't it be moving in the -j direction because it is moving towards -y axis?

[@QuestionSolutions]

Good question, one where a lot of people can get confused. The vector for the angular velocity must be found using the right hand thumb rule. So you have to curl your fingers in the direction of rotation, and point your thumb out. The direction of the thumb shows the angular velocity vector. This image shows it well: scripts.mit.edu/~srayyan/PERwiki/index.php?title=File:AngularKinematics02.png

[@ryanbragg4334]

@@QuestionSolutions Thank you sir. I realised my understanding of these problems was completely off. Thanks for taking the time to help!

[@QuestionSolutions]

@@ryanbragg4334 You're very welcome! You can sort of think of angular velocity as how fast something rotates about an axis, but just keep in mind that the vector for it has to be found using the right hand rule. And most problems, we see it in 2D, but it's really a 3D problem, so you sort of have to imagine the pin where something rotates around is actually a 3D pin, and it'll become easier to visualize in your mind. Anyways, best of luck with your studies!

[@ryanbragg4334]

@@QuestionSolutions That's exactly why I was confused haha. I was thinking in 2D. Thanks again!

[@QuestionSolutions]

@@ryanbragg4334 No worries!

[@MuhammadAbdullah-cj6nx]

what a saviour! man you are amazing!

[@QuestionSolutions]

Thank you very much!

[@MrMakeItRain.]

Very good video! May I please ask how do u know where to start please? For example, U start with Velocity of B in the first example, but in the last one, u start with velocity of e. Thanks in advance!

[@QuestionSolutions]

Thank you. To answer your question, I think it comes from intuition. Just a hunch that going this way will work our better and give an answer faster. Sometimes, it's wrong but usually, it's right. As you do more questions, your intuition becomes better and you can just visualize the flow of the question and answer. :)

[@M-ks4vo]

Thank you for your videos, they're immensely helpful.

[@QuestionSolutions]

You are very welcome!

[@zentuckyfriedckn2587]

Concise, easy to follow channels like yours make me wonder why I am paying $20k/yr for college 🙃

[@QuestionSolutions]

Glad to hear you found it concise and easy to follow! Keep up the good work and best wishes with your studies :)

[@cornerbloke8861]

Thank you so much for this video mate, great explanation and great video quality too. Btw at my university our prof. talked about something called "Stübler Theorem" or Stübler's Theorem" when she was explaining relative acceleration on rigit bodies. I couldn't find anything about it online, have you ever heard of such a thorem?

[@QuestionSolutions]

Thanks! Hmm, I don't think I heard of Stübler Theorem. If you do ask your professor again on what it is, please share with me also, I am curious to know what it is. I searched for it but couldn't get any hits.

[@Saadvlogs123]

Well Explained

[@QuestionSolutions]

Thank you very much!

[@tanejaparvesh]

You saved me from failing. I have an exam tomorrow morning. Thank You my unknown friend 🙂

[@QuestionSolutions]

You're very welcome! I hope your exam went okay. Best wishes with your studies :)

[@johntello8904]

wish i had these videos when i was taking dynamics in university

[@QuestionSolutions]

I hope they are helpful to new students :)

[@gm__1234]

thank you so much you're videos are really helpful for my mechanics exam

[@QuestionSolutions]

Glad to hear. I wish you the best on your exam!

[@TimGieselaar]

Thanks for the great video bro

[@QuestionSolutions]

You're welcome and thanks for the comment!

[@lumbalumba2436]

could you please explain where you get vc = 8 sin theta - 8 cos theta? Appreciated your video so much

[@QuestionSolutions]

Please see 2:46. We are breaking the velocity into x and y components using the 45 degree angle given to us. So the x-component can be found using sine and y-component using cosine. Y-component is negative because we chose up to be positive, but the component is downwards. I hope that helps!

[@lumbalumba2436]

@@QuestionSolutions Thank you!

[@truewassabian2491]

Thanks for the videos they are very helpful. One mistake you have is you have labelled the angular velocities in rad/s but your values have been calculated in degree mode. This means some of your values have come out incorrect w.r.t the units you have used

[@QuestionSolutions]

You are incorrect. The answers shown are correct. So I can see where the confusion comes from, but the degrees were used to break velocity into components. What you end up as units is still m/s. So the components of 8m/s can be 8sin45 degrees, but the answer that comes out is 5.66 m/s. So there is no correlation between the degrees and rads for the final answer. The units shown are correct :)

[@truewassabian2491]

@@QuestionSolutions hm interesting. I never knew you could use rads and metres interchangeably. I was always taught to convert the units, when I presented this problem to others they also said the units were mixed up. Maybe this is a difference in method of teaching

[@QuestionSolutions]

@@truewassabian2491 Here is a solved example directly from a textbook. Please see: bit.ly/3y7xE0o

[@EngineersAcademy2020]

Nice work! How you do this animation.

[@QuestionSolutions]

Thank you. I use illustrator for the diagrams and after effects for animations.

[@umiturgutaswwsa]

ı owe you a comment because of your great content

[@QuestionSolutions]

Thank you very much :)

[@battery8943]

Really helpful video thank you. How do you know whether a rotation is positive or negative?

[@QuestionSolutions]

Thanks! Can you give me a timestamp where you're confused about which direction is positive or negative?

[@texastoast4120]

Love the animations!

[@QuestionSolutions]

Thank you very much!

[@nickungefug364]

Thank you these are awesome!!!!

[@QuestionSolutions]

You're very welcome!

[@maumaura6482]

All of ur videos are very useful & very easy to understand...☺️🥰 Thanks a lot 🌝

[@QuestionSolutions]

You are very welcome! :)

[@ahn4814]

For the example at 4:20, why do you use the cross product to solve for Vb and why not just Vb=wr, whereas at 6:20 you just used Ve=wr?

[@QuestionSolutions]

You can solve these questions in many different ways. I showcased relative motion analysis, but it's up to you what method to use.

[@johnnybrown1148]

Hi, how do u determine the direction of velocity? like for the very first example, we know Vb from w but how do we know Va from Vb?

[@QuestionSolutions]

You can usually make an educated guess as to the the direction of velocity, you just have to imagine the system moving in your mind. If not, that's alright, in the end, if you end up with a negative value, that means the assumption you made for the direction of velocity is incorrect, in other words, it's opposite to your assumption.

[@omerfarukakkuzu5584]

you are perfect man, thanks a lot

[@QuestionSolutions]

Thank you for the kind comment :)

[@trevboy98]

Bravo sir. This was very helpful, thank you

[@QuestionSolutions]

Glad it was helpful and you're very welcome!

[@HariSenthuran-ws6ns]

These are great videos, thank you so much! at 2:24 how did you determine that the angular velocity was in the k direction?

[@QuestionSolutions]

So the vector would point into the screen. Curl your right hand fingers in the direction of the rotation and look to see where your thumb points. Since it points into the screen, that's the negative k-direction, or negative z-axis.

[@aitanuja9362]

Thank you 🙏🙏🙏

[@QuestionSolutions]

You're very welcome!

[@MegaNone1235]

Great video, really appreciate it!

[@QuestionSolutions]

I am glad to hear that! Best of luck with your studies.

[@chadbullard979]

In first example, you have angular velocity of i component as wab and j component as wbc? Should it be wbci and wabj?

[@QuestionSolutions]

Could you provide me with the timestamps you're referring to? I am having a hard time understanding your question. I'll try my best to help. Also, the steps shown are correct, there are no mistakes in the solution.

[@zanelholwill8860]

Hii there love your videos, I just want to clear up some of my confusion, at the third example (6:19) how do we know that we should calculate the VE and VC, like what would be the reasoning ? I understand what you are doing I just struggle to understand how to know in an exam that, that is what i should be doing. I hope this makes sense 🙈

[@QuestionSolutions]

I am not too sure how to answer that question. :( It should sort of "appear" in your head what steps to take next. If it doesn't happen, that's okay, but it just means you need to solve more problems and visualize the method to solve that problem in your head. Everyone does it at a different pace, but the more questions you solve, the easier it is to know how to tackle that problem.

[@mohammedzohair4035]

Very helpful! Thnx a lot!

[@QuestionSolutions]

You're very welcome!

[@userqskmldfjazekjmr]

In the first exercise (with the slider block C at 8m/s); when filling in the general equation of relative velocity it is confusing to have 8sin45.i . Shouldn't the i component be 8COS45 i and the j - 8 sin45° ? For this exercise it doesn't matter because cos and sin of 45° is the same, but I think the sin and cos should we switched, unless I'm wrong ofc.

[@QuestionSolutions]

So here, I can't give you a definite answer because I don't know whether you took the top angle or the bottom angle and both will be 45 degrees. If you took the top angle, then opposite to the angle give you the y-component, and adjacent gives you the x-component. If you took the bottom angle, opposite gives you the x-component and adjacent gives you the y-component. If you, for whatever reason have an idea that says x-components are always cosine and y-components are sine, you need to get rid of that before you fall into a lot of pitfalls and lose marks on your exams. Here is a video < 60 seconds that will really help you understand how it works: kzbin.infovynnKlJD_Jo?feature=share

[@epik_robie1709]

Im confused, if the problem is in 2D why are we using K if that's technically in the Z direction? Wouldn't we only need I and J?

[@QuestionSolutions]

For the future, please kindly use timestamps so I know where you are referring to. I assume you're asking about the k component of the angular velocity? If so, the vector actually points into the screen. You have to use the right hand rule and see where the thumb points. So here (2:24), the angular velocity is clockwise, so if you curl your fingers so that they are clockwise, the thumb will point into the screen, which is the negative k direction. Here is a diagram illustrating the vector directions. scripts.mit.edu/~srayyan/PERwiki/index.php?title=File%3AAngularKinematics02.png

[@epik_robie1709]

@@QuestionSolutions Thank you that explained it!

[@hassankhalil9184]

Great video as always, but why did we not find VB in the second problem the way we found VE in the 3rd problem which all we did was multiply the angular velocity by the radius? Thank you

[@QuestionSolutions]

We can't do that because there is a gear rack on the bottom that's affecting the speed of the wheel. It's not an independent object, it's connected to something else. In the case of VE, you can see that it rotates about a fixed axis, in this case, point B, and point B doesn't move. In the VB question, the center moves along the x-axis. 👍

[@hassankhalil9184]

@@QuestionSolutions Thank you

[@erickcastellanos6814]

at 5:02, why do we write the relative velocity as Va=Vb + (Vab) and not Vb= Va+ (Vab)?

[@QuestionSolutions]

So you're trying to solve for va, which is why it's isolated on the left side. You can do it the other way, make sure your position coordinates and values are properly set.

[@AnhTran-ze8qb]

Thank you so much for these videos!

[@QuestionSolutions]

You're very welcome!

[@chadthundercock1793]

during the first example when you got the cross product for -WabK x 2i i think you made a mistake because kxi equals -j and the correct answer should have been 2WabJ right ?

[@QuestionSolutions]

No errors; k cross i, is a positive j, not negative.

[@reetambaidya6914]

At the end of solution of question 1, why are the rotation directions opposite ? both the values of omega are taken to be positive and must be anticlockwise according to the convention

[@QuestionSolutions]

They are positive, meaning the directions we assumed were correct. Notice how we assumed a clockwise rotation for AB and a counter-clockwise rotation for BC. Getting positive values indicates that those assumptions were correct. But regardless of sign conventions, with these problems, it's easy to figure out directions just by imagining how these contraptions would move. Here, block C moves down, and there is no way for that to happen if link BC was going clockwise with AB also going clockwise. The same is true for the opposite, if link AB was going counter-clockwise, then block C can't move down, it has to move up.

[@h.muralikrishnan368]

the formula is only applicable for rigid bodies right?

[@QuestionSolutions]

Yes, for relative velocity of particles, see: kzbin.info/www/bejne/paG5fIF5msmeiNE

[@daemon7013]

Got my 2nd test tomorrow, wish me luck guys!

[@QuestionSolutions]

Best of luck with your test!

[@floof505]

At 4:30 why does the wheel spinning clockwise dictate that the value should be negative?

[@QuestionSolutions]

So clockwise means that if you use the right hand rule, where you curl your fingers to match the direction of rotation, you will see that your thumb points away from you. If it's away from you, it's in the negative z direction so it's a negative k component. Keep in mind that while the rotation is clockwise/counter-clockwise, the vector for angular velocity is found using the right hand rule. See: hyperphysics.phy-astr.gsu.edu/hbase/rotv.html

[@floof505]

@@QuestionSolutions Wow... I don't know how to thank you enough. I appreciate you and your content so much 🙏🙏

[@QuestionSolutions]

You're very welcome! Best wishes with your studies :)

[@EngineersAcademy2020]

Which software you use for this animation???

[@QuestionSolutions]

I use after effects to animate.

[@ShangWeiorNoWay]

for the second question wouldnt the j component of r_a/b be negative and the i component be positive?

[@ShangWeiorNoWay]

nvm numbers work out to be the same

[@QuestionSolutions]

@@ShangWeiorNoWay 👍

[@mallbyahmed1285]

Amazing thanks alot

[@QuestionSolutions]

You're very welcome!

[@sinahafezi425]

I have a question at 5:18 why is it -0.5cos60? and not +0.5cos60?

[@QuestionSolutions]

So the position vector goes from B to A. In other words, to the left and up. We chose up and to the right to be positive. Since the x-component goes to the left, it's negative.

[@sinahafezi425]

Ahhhh make sense, you are a legend subscribed.

[@QuestionSolutions]

@@sinahafezi425 Thank you! :)

[@sunnytalukder7393]

What does rb/c mean?? do we take components of r from b to c or from c to b??

[@QuestionSolutions]

it's c to b.

[@chesquick]

why do you use the 30rad/s for Ve and 15 rad/s for Vc @6:26 ?

[@QuestionSolutions]

So Ve is found by multiplying the angular velocity of gear A by the radius, where as Vc is found by multiplying the angular velocity of the rod BC by the length. So each have their own corresponding angular velocities.

[@dariosakaj8305]

can someone please tell me why at min 2:30 is in the negative k direction ? i dont get it that part

[@QuestionSolutions]

The vector for the angular velocity must be found using the right hand thumb rule. So you have to curl your fingers in the direction of rotation, and point your thumb out. The direction of the thumb shows the angular velocity vector. This image shows it well: scripts.mit.edu/~srayyan/PERwiki/index.php?title=File:AngularKinematics02.png

[@inky-pinky-punky]

This might be dumb question but how do you know that counter clockwise rotation is positive? is counterclockwise always postive?

[@QuestionSolutions]

You have to use the right hand rule. Did you watch the video on moments? It's really important to know the fundamentals, it'll make your life much easier. So in 3D space, if it's going counter-clockwise, you curl your right hand fingers and see which way the thumb points. You will notice it comes towards you, so along the positive z-axis. For 2D problems, you can pick your own positive direction and adjust your answer accordingly. Please see: kzbin.info/www/bejne/h3-xn4OQa52Giqs

[@artbybigvee]

God bless you...

[@QuestionSolutions]

Thanks!

[@My_Friends_Call_Me_Zee]

(02:50) Shouldn't Vc = 8cos(45)i + 8sin(45)j ?

[@My_Friends_Call_Me_Zee]

Instead of Vc = 8sin(45)i + 8cos(45)j

[@QuestionSolutions]

No, the opposite side to the angle gives us the x-component, so sine, and the adjacent side gives us the y-component, so cosine.

[@programmingprograms726]

I wish you did more questions for this subtopic

[@QuestionSolutions]

I will create more in the future :)

[@programmingprograms726]

@@QuestionSolutions Thank you.

[@masondebeer5580]

well-done, this is great

[@QuestionSolutions]

Many thanks :)

[@howis-goin]

at 5:18, can i ask why is "-0.5cos60i", but not "0.5cos60i" ?

[@QuestionSolutions]

So the position vector goes from B to A. In other words, to the left and up. We chose up and to the right to be positive. Since the x-component goes to the left, it's negative.

[@howis-goin]

@@QuestionSolutions ohhh, thank you so much sir :>>

[@e-zgo8435]

hello, could you explain why does Vb including K direction. it should be j right bcause it is going down y axis?

[@QuestionSolutions]

Please see: hyperphysics.phy-astr.gsu.edu/hbase/rotv.html In simple terms, you need to use the right hand rule to figure out the direction of the vector. So if it's going clockwise, then you curl your right hand fingers to match that direction. Then you will notice that your thumb points into the screen. That would be the negative k direction, in other words, the negative z-axis. Let me know if you need further clarifications. Thank you!

[@edwardmouawad9443]

when we say relative motion for the second point on the rod how can we assume if it is only on x axis or both for example and when to do this assumption

[@QuestionSolutions]

Sorry, but I don't understand your question. Where are you referring to? Is there a specific part on the video? Let me know and I will try to help you out. Thanks!

[@ابراهيمبنعبداللهالسيف]

You are the best thank you

[@QuestionSolutions]

You're very welcome 🙂

[@AAA-bb8bf]

How did we know the angular velocity of (AB) is in K and not i or j direction? And the same for angular velocity of (BC). I get the point of why it’s positive or negative but the direction is a little confusing.

[@QuestionSolutions]

You have to use the right hand rule. The vector actually comes out of the screen or goes into the screen depending on the direction (+k/-k). Please take a look at this: scripts.mit.edu/~srayyan/PERwiki/index.php?title=File%3AAngularKinematics02.png Let me know if you still want to talk it through, but I think the diagram helps a lot :)

[@user-si1sh2lr8r]

my fav video

[@QuestionSolutions]

:) Thanks!

[@tuandanish3764]

At 5:12, why the angular velocity is in k ?

[@QuestionSolutions]

So it's rotating clockwise, right? When we look for the vector, we have to use the right hand rule. So you curl your right hand fingers in the clockwise direction and see where your thumb points. It points towards you, in other words, out of the screen, so that's the z-axis, (k component).

[@eretiamwaene2661]

2:54 can u pls explain how do u get the Vc?

[@QuestionSolutions]

Vc in the question is given to us as 8m/s. All we did there was just break that into components. Since the 8m/s is at an angle of 45°, we can use cosine and sine to break the velocity into x and y components.

[@jenniferwilson8783]

Hi! firstly, i love your videos! they are so helpful :D I do have a question, do you have any videos explaining the vector analysis in relation to this topic? I was following along great until vectors came along :(

[@QuestionSolutions]

Thank you very much! :D So generally, dynamics is covered after statics, and in statics, vectors are covered. Vector analysis isn't really a specific subject, but rather, it's slowly built up one by one. So here is the video talking about vectors and forces (pretty much the same thing here): kzbin.info/www/bejne/f6nZYoSPiqaAjc0 and this one might be more helpful: kzbin.info/www/bejne/eXTIiKxnoNKrg9U It talks about position vectors, i, j, k components, etc. I am also going to link the statics playlist so you can take a look at them. kzbin.info/aero/PLXePpKFSUW2ZxGn6VdAPY9d7l7HowWVYL Also, if you look through the dynamics playlist (kzbin.info/aero/PLXePpKFSUW2ZXw_D5h0TTyac-KGlFRxnS), it covers a lot of questions with vectors before we get to rigid bodies, especially during relative motion analysis, so maybe that will help you out as well. If you need to review something specific, let me know, I can point out to a video if I made it.

[@jenniferwilson8783]

@@QuestionSolutions Thankyou for replying so quickly! I love your dedication!!! I feel like what i specifically struggle with is assigning the coordinate vectors (i,j,k) to the values in equations such as vB= vA + w * rB/A

[@QuestionSolutions]

@@jenniferwilson8783 Can you give me a timestamp so I can maybe go over where you struggled? It's easier with an example :)

[@jenniferwilson8783]

@@QuestionSolutions I would say 2:24 and 4:15

[@QuestionSolutions]

@@jenniferwilson8783 Okay at 2:19, we have a position vector from A to B. That's the dark blue line. It goes from left to right, so in the positive x-direction. You can see the coordinate system with the up and right arrows in purple just below the diagram. So since it's going in the positive x-direction, it will have a positive "i" component. The value would be 2, since it's 2 m in length. So r_AB=2i. Now when the member AB turns, it's turning clockwise, so if you use your right hand and curl your fingers to match the clockwise movement, you will see that your thumb will point towards the screen, in other words, away from you. That's the negative z-direction. If the thumb was pointing at you, that's positive z. Since it's pointing in the negative z-direction, the angular velocity vector is -k. Remember, i for x, j for y, and k for z. At 4:16, let's look at VC first. That's the velocity vector at the very bottom, applied to the rack. Notice that it faces to the left, meaning negative x-axis. The magnitude of that vector is given to us as 5m/s, so our vector is -5i. The next term is the angular velocity of the gear wheel. We are told that it turns clockwise, with an angular velocity of 10 rad/s. So again, using your right hand, the thumb points to the screen when we curl our fingers to be clockwise. So that's -10k. (we curl our fingers whenever we need to find the angular velocity vector). The last term is rBC. That's the perpendicular distance from the rack to the wheel, and it's length is 0.075m and notice I drew it in red at 4:36. It's a straight upward line, so that's in the positive y-direction. That means that position vector is 0.075j. I hope that helps, let me know if you have any other questions.

[@noalily6922]

Hi there :) in the example at 3:24 , from the equations of the i and j components, don't Wab and Wbc have the same sign and therefore direction of rotation?

[@QuestionSolutions]

Yes, there is a typo there :)

[@noalily6922]

@@QuestionSolutions okay, thank you very much for the prompt reply. I really appreciate your videos! Many thanks.

[@QuestionSolutions]

@@noalily6922 You're very welcome!

[@radiatedbug]

Greatly explained as usual! I've got a question though, a simple one rather. At 6:51 , for the relative velocity equation. What if we wrote it for C with respect to E, so Vc/e instad. So [ Vc=Ve+Vc/e] I've done that and my answer came out to be negative (-105), what is this supposed to mean? Becaus clearly it cant go the other direction. The gear does infact rotate and has to rotate in a clockwise manner I believe haha for the system to work in the first place, atleast in this question per se.

[@QuestionSolutions]

Most likely a positive/negative error. For your r_C/E, was it -0.05? Because you switched it around, so it'll now be negative. If you get 105, but the sign is wrong, it's almost always just a positive/negative error, maybe when you did the cross multiplication, you forgot a positive or negative, etc. It's hard to say 😅

[@radiatedbug]

@@QuestionSolutions Ah yes, it was a simple sign error haha. To my luck, my errors are mostly always related to the signs. It was the R_c/e as u said. Thank u once again!! Have a graat day

[@JulianJArens]

Amazing!!!

[@QuestionSolutions]

Thank you!

[@bonkgaming3646]

How is W(ab) in the -k direction when it's moving in j direction, please explain 🙏

[@QuestionSolutions]

Please see: hyperphysics.phy-astr.gsu.edu/hbase/rotv.html In simple terms, you need to use the right hand rule to figure out the direction of the vector. So if it's going clockwise, then you curl your right hand fingers to match that direction. Then you will notice that your thumb points into the screen. That would be the negative k direction, in other words, the negative z-axis. Let me know if you need further clarifications. Thank you!

[@huzaifaali3317]

Sir why we take k component in Wab k and wbc k... here only 2 axis x and y

[@QuestionSolutions]

So while the problem is 2D, the vector is not. When we have a clockwise angular velocity, the vector direction has to be found using the right hand rule. So you curl your fingers in the direction of the angular velocity, and see where your thumb points. Here, Wab is going clockwise, so curl your right and fingers clockwise and see where your thumb points. See: encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcSm-tkiGmpmb7tqpXQqyy7rSqTwTRWL8HjjKg&s

[@uchiha_kakashi6716]

can we solve all those problem above using instantaneous center of zero velocity and if not how can we tell the difference to use that instead

[@QuestionSolutions]

You can use it all the time, but you might not be given enough information to use it. For instantaneous center of zero velocity, you need to be given angles that change with respect to movement, if you don't have that, you will need to figure it out.

[@uchiha_kakashi6716]

@@QuestionSolutions thank you,for the reply. Wish me luck for the exam tomorrow.

[@QuestionSolutions]

You're very welcome and best of luck on your exam tomorrow!@@uchiha_kakashi6716

[@flyhighlow3]

Do you have a video that can help/refresh me with the geometry in these problems? Love the videos, keep up the good work!

[@QuestionSolutions]

Geometry as in breaking velocity into components? If so, this one goes through breaking forces into components (same thing for velocity) kzbin.info/www/bejne/hKOvZpdjZ6iUmLM For position vectors, please see this video: kzbin.info/www/bejne/eXTIiKxnoNKrg9U

[@aashishkumarjha3993]

For a given instant ICR has zero velocity and for the problem at 3:29 ICR is the point of contact between the surface i.e. poin C If this statement is true why have you used V,C as 5i during calculation of V,B at 4:17

[@QuestionSolutions]

The gear rack has a velocity of 5 m/s, this is a given in the problem. So all we are doing, in the simplest sense, is actually just comparing the velocity of one point to the velocity of another. We use -5i because that is the velocity of the rack. If it's zero, then the gear above will go on top, carrying the whole system with it. I think for these problems, you really have to use your imagination to see how this device would move in real life. What you're thinking of is a system that's making contact with a surface that's not moving, but here, that is not the case. I hope that helps!

[@aashishkumarjha3993]

Thank you! :)

[@EngSereneJibreen]

u r the best

[@QuestionSolutions]

Many thanks!

[@ayhamaljbour9182]

thanks so much bro

[@QuestionSolutions]

You're welcome!