Rigid Bodies Relative Motion Analysis: Velocity Dynamics (Learn to solve any question step by step)
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- čas přidán 6. 08. 2024
- Learn how to use the relative motion velocity equation with animated examples using rigid bodies. This dynamics chapter is explained step by step to help you gain a better understanding. Topics such as angular velocity, relative velocity, and cross products are discussed with rigid bodies.
🔹Rigid Bodies Rotation About a Fixed Axis - • Rigid Bodies: Rotation...
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Intro (00:00)
The slider block C moves at 8 m/s down the inclined groove. (01:30)
If the gear rotates with an angular velocity of ω = 10 rad/s and the gear rack (03:26)
If the ring gear A rotates clockwise with an angular velocity of (05:43)
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Book used: R. C. Hibbeler and K. B. Yap, Mechanics for engineers - dynamics. Singapore: Pearson Education, 2014.
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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.
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Thank you very much. Best of luck with your studies! :)
@@QuestionSolutions Could you still do the slider problem using k if it wasn’t a 45 degree angle?
@@lesserspottedmugwump.363 Can you give me a timestamp? I'll take a look and let you know 👍
@@lesserspottedmugwump.363 What do you mean by k? Please elaborate.
probably because doctors don't know too much about engineering
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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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Seeing the problems animated helped so much when it came to solving.
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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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You're very welcome! I am glad to hear the animations help :)
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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!
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How did the midterms go
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I'm happy to hear CZcams 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.
Doing a very great job yar.
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wish i had these videos when i was taking dynamics in university
I hope they are helpful to new students :)
Really helpful video thank you. How do you know whether a rotation is positive or negative?
Thanks!
Can you give me a timestamp where you're confused about which direction is positive or negative?
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?
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.
my fav video
:) Thanks!
I got 4 in dynamics course at university all thanks to you
Nicely done! Keep up the awesome work and I wish you the best in your other courses.
Great video! Just wondering if you have one when the components have weight per unit length? Cheers
Weight per unit length as in distributed loads? Not sure if that's what you meant, but if it is, there is a video on it. If that's not what you meant, maybe take a look at the statics or dynamics playlist and maybe a video there will cover the topic you're looking for. :)
God bless you...
Thanks!
güzel özetlemişsiniz hocam, teşekkürler.
Thank you! I used google translate so I have an idea of what you said :)
@@QuestionSolutions I thought you wouldn't answer :D I m from Turkey, I m glad sir
@@e-nes4042 an itu student? right?
Nice video . Please also solve problems from merriam and kraige
Thank you. I think if students understand how to apply the new equations they learn, regardless of where the questions come from, they should be solvable. But I will keep in mind the Merriam and Kraige books as well. Thanks again for your feedback, I appreciate it.
In first example, you have angular velocity of i component as wab and j component as wbc? Should it be wbci and wabj?
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.
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.
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 😅
@@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
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!
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!
Concise, easy to follow channels like yours make me wonder why I am paying $20k/yr for college 🙃
Glad to hear you found it concise and easy to follow! Keep up the good work and best wishes with your studies :)
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 🙈
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.
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
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!
Do you have a video explaining the i, j, & k components? I struggle to understand when to put i, j or k in the terms
Short version: for x components, you use i, for y components you use j, and for z components, you use k.
Here is a video explaining this: czcams.com/video/mz7gPpIL0Gk/video.html
Note that while it talks about force vectors, the principles are all the same. 👍
can someone please tell me why at min 2:30 is in the negative k direction ? i dont get it that part
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
Do you have a video that can help/refresh me with the geometry in these problems?
Love the videos, keep up the good work!
Geometry as in breaking velocity into components? If so, this one goes through breaking forces into components (same thing for velocity) czcams.com/video/NrL5d-2CabQ/video.html
For position vectors, please see this video: czcams.com/video/CCeWy1kmxMs/video.html
ı owe you a comment because of your great content
Thank you very much :)
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
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. 👍
@@QuestionSolutions Thank you
hello, could you explain why does Vb including K direction. it should be j right bcause it is going down y axis?
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!
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?
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.
Hi sir..does it matter if my answer for angular velocity in the first question has negative value but same magnitude
So it means you assumed the opposite direction to what it really happening. You can just need to write another line with a positive value and an arrow indicating the proper direction. So whenever you get the same magnitude but a negative answer, that means the magnitude is correct, just the assumed direction was wrong.
Nice work! How you do this animation.
Thank you. I use illustrator for the diagrams and after effects for animations.
Yoh, thanks man.
You're welcome!
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 :(
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): czcams.com/video/Ixv1QYUAMWk/video.html and this one might be more helpful: czcams.com/video/CCeWy1kmxMs/video.html 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. czcams.com/play/PLXePpKFSUW2ZxGn6VdAPY9d7l7HowWVYL.html
Also, if you look through the dynamics playlist (czcams.com/play/PLXePpKFSUW2ZXw_D5h0TTyac-KGlFRxnS.html), 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.
@@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
@@jenniferwilson8783 Can you give me a timestamp so I can maybe go over where you struggled? It's easier with an example :)
@@QuestionSolutions I would say 2:24 and 4:15
@@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.
I wish you did more questions for this subtopic
I will create more in the future :)
@@QuestionSolutions Thank you.
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?
Yes, there is a typo there :)
@@QuestionSolutions okay, thank you very much for the prompt reply. I really appreciate your videos! Many thanks.
@@noalily6922 You're very welcome!
How is W(ab) in the -k direction when it's moving in j direction, please explain 🙏
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!
Which software you use for this animation???
I use after effects to animate.
why do you use the 30rad/s for Ve and 15 rad/s for Vc @6:26 ?
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.
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.
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 :)
2:54 can u pls explain how do u get the Vc?
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.
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.
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.
at 5:02, why do we write the relative velocity as Va=Vb + (Vab) and not Vb= Va+ (Vab)?
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.
is there a linear velocity for link AB as a whole, or only at a point?
Linear velocity is the distance from the rotational axis to where you're calculating it, times the angular velocity. So it's based on "r" which is the distance from the rotational axis.
could you please explain where you get vc = 8 sin theta - 8 cos theta? Appreciated your video so much
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!
@@QuestionSolutions Thank you!
What does rb/c mean?? do we take components of r from b to c or from c to b??
it's c to b.
Hi Question Solutions, how to determine the omega if negative or positive?
In Cartesian form? If yes, then you have to use the right hand rule. So let's say it's spinning clockwise, curl your right hand fingers to match the clockwise direction. You will see that your thumb points away from you. If you pick away from you to be negative, then angular velocity vector is negative. Now imagine counterclockwise rotation, curl your fingers to match. You will see that your thumb points at you. I hope that helps.
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?
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
@@QuestionSolutions Thank you sir. I realised my understanding of these problems was completely off. Thanks for taking the time to help!
@@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!
@@QuestionSolutions That's exactly why I was confused haha. I was thinking in 2D. Thanks again!
@@ryanbragg4334 No worries!
when do use Vector form V=r x omega, and when do we use scalar form V=r . omega?
You use vector formation when you express your values as vectors, and you use scalar equation when everything is expressed in scalar values. So if you have ijk components, use the vector equation, otherwise, use the scalar equation.
May I know why Vb has only -j direction? Shouldn’t there be -I direction since it is moving a circular motion ?
Please kindly provide a timestamp so I know where to look. Many thanks!
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
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.
I do not understand when to use Relative Motion Analysis and when to use Absolute Motion Analysis.
How can I know from a question which of the two methods should be used?
I will try to give a relatively simple answer. So you can use relative motion if the question gives you the velocity of one point and you're trying to find the velocity of another point, without too much geometry. For example, an angle isn't given, only a length is (this length can be used to find the velocity using v=ωr). With absolute motion analysis, you will be given a lot of geometry along with angles, because you need that to relate the changing distance. In other words, you will be given a distance and an angle that changes when the objects move, or you will be given enough data to figure out a distance and an angle that changes when the object moves.
One of the best ways of knowing which method to use is to actually do a few questions from both sections. It'll give you the insight required to know which method to use. Otherwise, you can always try one method, and if there isn't enough data, switch to the other method.
I have one confusion that is the first problem looks like can be solved as the way you solve in absolute rigid body , so could you clear that is those 2 lesson are similar in some terms right ,sorry for bad english if you dont understand
You can use any method you like to solve these problems, I just show case a specific method that's related to the chapter :)
10/10
Many thanks!
How did you determine the direction of rotation of AB and AC in Q.1
You really have to use your visual skills with these problems. You know for sure block C moves down, so try to imagine how the other pieces would have to bend for that block to slide down. If you can't imagine it, the only other way is to cut out these pieces with a carboard and pin them at the locations and move the block to see how they turn. On the other hand, if you assume a different direction of rotation, then you will end up with a negative value, so you know it's opposite to your assumption.
You saved me from failing. I have an exam tomorrow morning.
Thank You my unknown friend 🙂
You're very welcome! I hope your exam went okay. Best wishes with your studies :)
Hi.
Please, what's the name of the textbook you use for this?
I'd really appreciate your reply 🙏.
Any book used is listed in the description. Please check, thanks!
Amazing content, very clear, helping me a lot for my exam! Greetings from Italy!
Thank you and I wish you the best with your upcoming exam!
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 ?
No errors; k cross i, is a positive j, not negative.
This might be dumb question but how do you know that counter clockwise rotation is positive? is counterclockwise always postive?
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: czcams.com/video/QNNnPZ68STI/video.html
i have a question, why did the i component in 3:26 changed to wab for the final solution but it uses wbc for the calculation
It's just a typo, you can see I mixed up WAB and WBC 😅
@@QuestionSolutions i see i see was figuring hard why until i looked into the next question, thanks for the video, much appreciated
@@changjunyang7471 You're welcome. I apologize for the typo.