Rigid Bodies Absolute Motion Analysis Dynamics (Learn to solve any question)

Learn how to solve rigid body problems that involve absolute motion analysis with animated examples, step by step. We go through angular velocity, angular acceleration, time derivatives and more.
Introduction (00:00)
At the instant θ = 50° the slotted guide is moving upward with an acceleration (01:48)
At the instant shown, θ = 60°, and rod AB is subjected to a deceleration (04:27)
The bridge girder G of a bascule bridge is raised and lowered using the drive mechanism shown (05:54)
🔹Learn to use the chain rule: • How to Solve Time Deri...
🔹Rigid Bodies Rotation About a Fixed Axis: • Rigid Bodies: Rotation...
Find more at www.questionsolutions.com
Book used: R. C. Hibbeler and K. B. Yap, Mechanics for engineers - dynamics. Singapore: Pearson Education, 2014.

[@daxthedestroyer7]

I'm in dynamics right now and these videos are awesome! You explain what my teacher took 2-3 hours explaining, and did it in 8 minutes... thanks!

[@QuestionSolutions]

You're welcome! Thanks for your kind comment. Best of luck with your studies.

[@initiald975]

and that is the power of power points and animation. One of a few essential teaching skills that some college professors still don't put into practice. Often because they are stubborn in their ways.

[@DiZBrad11]

Definitely better than my Dynamics professor could EVER explain!

[@QuestionSolutions]

Many thanks! Best of luck with your studies.

[@atakanerdemli407]

You are the best ! I am an aerospace student and so far I found everything I needed for my lectures. Keep it up. Good job, thanks!

[@QuestionSolutions]

Glad to hear! I wish you the best with your degree :)

[@tarifulislam7934]

Loved every bit of these tutorials.

[@QuestionSolutions]

Thank you very much!

[@Maybe.019]

Wow , You will never know how much i needed this Thank You so much

[@QuestionSolutions]

You're very welcome!

[@programmingprograms726]

Good job!! Proud to have an educator like you :)

[@QuestionSolutions]

Thank you very much :)

[@jovanmagtoto1682]

thank you for this sir, very easy to understand. Explanation and visual aids are excellent.

[@QuestionSolutions]

Glad to hear! Many thanks.

[@rhamby3470]

These videos are so helpful. It's funny how you teach better than the professors that I'm paying thousands of dollars for. definitely subscribed!

[@QuestionSolutions]

Really glad to hear these are helpful and thank you so much for subscribing! I wish you the best.

[@tiangong6616]

Unbelievable, you explained way better than my dynamics professor, now I fully understand this concept

[@QuestionSolutions]

Really glad to hear that :) Keep up the great work!

[@DietCokeIsGoodForYou]

I like barely pay attention in class now and jus watch your videos lol so much easier to understand and follow

[@QuestionSolutions]

I am really glad to hear these videos are helpful. Usually though, lectures cover a lot of theory and derivations of the equations we use, so it might also be helpful to pay a bit of attention here and there 😅

[@sanskaradhikari8827]

you are literally saving degrees xthank you is an understatement but truly thanks

[@QuestionSolutions]

You're very welcome! I am glad these videos are helpful. :)

[@zainrezaei4860]

Great job man. Your videos are super.. keep it up!!

[@QuestionSolutions]

Many thanks!

[@ALIMOHAMED-lz3fx]

you making my life easier. amazing.

[@QuestionSolutions]

Really glad to hear that!

[@supersharonnoy6551]

Thank you much for the amazing video.

[@QuestionSolutions]

You're very welcome! :)

[@willm6598]

Your videos are incredible and there is no one out there teaching as well as you are, If you have a patreon or other way to donate I am going to join

[@QuestionSolutions]

Thank you so much, I really appreciate your comment. I don't have a patreon or anything, but maybe in the future I will create one.

[@georgeselkhoury7446]

Great Job man. Absolutely Genius. You must keep up the good work always. We would appreciate if you can just upload videos fasters. Greetings.

[@QuestionSolutions]

Thank you very much! I will try my best to get videos out faster.

[@ryanmoffat4177]

Great video! The Cosine rule stated at the start is missing a two.

[@QuestionSolutions]

You're right! A typo :(

[@liuzhihao3239]

when would I use absolute motion vs relative motion? Thank you for your hard work, your videos are lifesavers.

[@QuestionSolutions]

Usually, you use absolute motion if you can relate an angle that changes along with velocity of a point and relative motion if you can find the velocity of one point and compare it to another point.

[@syabongajele6431]

wow Sir you're so incredible wow this is so amazing , you just simplified the whole topic in 8 minutes while my professor did this two hours still not vivid , sir do you have a pack of problems and exams sheets?

[@QuestionSolutions]

Thank you very much, really glad to hear these were helpful. I don't have a pack of problems or exam sheets, however, the book, mechanics for engineers - dynamics by Hibbeler is a very good book.

[@syedanasnisar846]

Thanks yar, you are doing a great job.

[@QuestionSolutions]

Thanks! Glad these help you.

[@camerongillespie870]

Many thanks, sir.

[@QuestionSolutions]

You're very welcome.

[@darrylcarter3691]

It the slot question, in the first one question, I had a feeling that angular acceleration was going to be negative because the T-shaped body attached to the slot wants to fall and the slot is pulling it up. But because the T-shaped body is falling, the slot is not going to move as fast, almost looks like it is going to slow down. An since it’s slowing down, one can assume the acceleration, whether it’s linear or angular, is negative.

[@QuestionSolutions]

👍

[@MrPJBarney]

Thank you. God bless.

[@QuestionSolutions]

You're welcome!

[@yinjunjiang4869]

Thank you for these detailed instructions! How can you create these vivid animations and perfect figures? Just in powerpoint or other software?

[@QuestionSolutions]

The diagrams are drawn on Illustrator and they are animated on after effects. 👍

[@tanejaparvesh]

Thank You so much.

[@QuestionSolutions]

You're very welcome!

[@AhmedMahmoud-gu4un]

Can you recommend any trigonometry video or chart that shows most equations?

[@QuestionSolutions]

Maybe these will help: www.mathsisfun.com/algebra/trig-cosine-law.html www.mathsisfun.com/algebra/trig-sine-law.html www.sosmath.com/trig/Trig5/trig5/pdf/pdf.html

[@desham001]

I really like your videos. I have learned a lot from them. How to solve the kinetics (i.e., force and moment equations) for these similar examples (like actuator connected with a rigid body through a link)? Any references? It would be a great help if you can suggest something. Thanks in advance.

[@QuestionSolutions]

Glad to hear they have been helpful. Are you asking for a textbook reference?

[@desham001]

@@QuestionSolutions Textbook reference will work but if you have made any videos describing this it will be a great help.

[@QuestionSolutions]

@@desham001 Other than the videos listed on the playlists, I have no other ones. For books, I always suggest Mechanics for engineers - dynamics by R. C. Hibbeler and K. B. Yap. Though any book on dynamics probably has what you are looking for.

[@desham001]

@@QuestionSolutions Thank you. I will look into it.

[@QuestionSolutions]

@@desham001 👍

[@austin8313]

I had a few questions. So on example two if link CD and BC were different lengths would their angular velocities and accelerations be different? If so, how would you relate the velocity/acceleration of x to the different links? And if not, why?

[@austin8313]

also thanks again for the videos. I'm excited for the thermodynamics ones :)

[@QuestionSolutions]

You can actually solve the question you're asking by yourself, and I really encourage you to do so, because it's an excellent question. Try setting BC and CD to different lengths, the process is exactly the same, no difference in what I show. Only difference is the triangle that's going to be formed. See what type of answer you get and let me know. :) You might even be able to guess by looking at the equations that we gain at 5:26 and how the values are related to the lengths we got from the triangle that we drew. You can think it through, what if it was 0.4cosθ instead of 0.3? Very good question, answering it yourself will give you a lot of insight as to how lengths and angles govern the changes to velocity and acceleration. For most of these questions, I really encourage students to try them with different values and see the relationship between their answers, because it's a really good way to learn. That way, when you see a question, you can already guess what type of answer it's suppose to have and can error check before handing in your papers to a marker. 👍

[@affanzakir6015]

how we can determine that if the problem belongs to absolute motion analysis or relative motion analysis

[@QuestionSolutions]

It depends on the givens and some critical thinking. If you're given angles with lengths that depend on a changing angle, then you can use relative motion. Also, most of these questions can be solved using more than one method, so pick the method you're comfortable with, but practice it all 👍

[@Kohler_Wood]

This is great. I wish more videos showed how to do this more intuitively and without all the terrible vector math.

[@QuestionSolutions]

Glad to hear. So sometimes, for problems, vector math is pretty much the only viable solution. Using scalar methods make it far too tedious and time consuming. It's all about what is the most efficient method in getting an answer. So try to become comfortable with vector math too :)

[@tausifislam7559]

you are a legend

[@QuestionSolutions]

Many thanks! :)

[@zhongli6546]

Sir at @5:42 , I chose the right side as positive. The value for angular velocity comes the same but positive as expected but during the calculation of angular acceleration it's not matching. How to fix this issue?

[@QuestionSolutions]

It's hard for me to say without seeing steps. Did you also pick the same directions for the acceleration equation as well?

[@zhongli6546]

@@QuestionSolutions Yes. For equation: a=-0.6(alpha.sintheta+omega^2.costheta), If right side is picked as positive, a=+16 while if left is picked a=-16 on LHS. But RHS is same for whatever direction taken because omega=angular velocity is whole squared. For this alpha=angular acceleration is varying sir.

[@fatimadaghmash1612]

I've got a question. In the first problem why did you plug in -2 as the velocity (y dot) if the slotted guide is moving upwards?

[@fatimadaghmash1612]

oh just realized its mentioned in the video. your videos are a lifesaver, thank you!

[@QuestionSolutions]

Awesome!

[@thefadulousonefleming7489]

Great video, but how do you know when to implicitly differentiate, rather than just doing in normally?

[@QuestionSolutions]

Normally, when you have an equation with distance, so "y" with respect to an angle, "theta." So I guess you can look out for the theta symbol.

[@mezonoor4022]

teacher firstly thank you so much why in the last question you take the velocity 0.15 m/s as negative ? while it is given positive

[@QuestionSolutions]

The velocity is assumed, so if the bar was extending, it'll be positive, if it's shortening, it'll be negative. 👍

[@hamanprnzhd6746]

Last example(bridge girder): Why did you plug negative 0.15 m/s for the velocity?

[@QuestionSolutions]

Movement to the right was considered positive. If it shortens, then it's a movement to the left. :)

[@abdallahindimi3484]

what if we are giving an angular velocity of a crank to start with and asked to find the angular velocity of a rod?

[@QuestionSolutions]

I don't know, it's really difficult to answer a question like that without seeing a diagram 😅 Is it asking you to solve it using absolute motion analysis or you have enough givens to use this method? If yes, then you can use the same methods shown in the video 👍

[@patrickfreiha494]

Thank you man I appreciate but i have a question why in the last question the velocity is -0.15 not 0.15?

[@QuestionSolutions]

Movement to the right is considered positive, so if it shortens, then it is negative. :)

[@inky3443]

For second question, how did you assume theta was the angle BDC and CBD not BCD?

[@QuestionSolutions]

It's shown in the question diagram. They labeled where the angle is. :)

[@pawan120989]

Nice

[@QuestionSolutions]

Thanks

[@wakeawake2950]

Nice video👍👍, plzz increase the frequency of ur uploads, then u will gain more subscribers by the way nice video. Thnk u

[@QuestionSolutions]

Thanks for your comment. Unfortunately, I have to balance my work and this at the same time. It's not so easy :)

[@camerontriplett9199]

This may be a silly question based on how I view the second problem, when x is positive in the left bound direction, then does that affect the axis of rotation of length CD?

[@QuestionSolutions]

Could you kindly give me a timestamp to the location on the video? I don't think I understand your question, sorry :(

[@camerontriplett9199]

@@QuestionSolutions the thing that I have trouble visualizing is what exactly is going on with length CD according to the final values we obtained at 5:50. If length AB is slowing down as it moves in the positive x direction, how come the value of the angular acceleration of length CD has the same sign as the value of the angular velocity of length CD?

[@QuestionSolutions]

@@camerontriplett9199 You might be confusing a few terms here but let me try and explain. First, the length of CD does not change, regardless of the position since you mentioned "what's going on with length CD". So I think your main question boils down to, how can angular acceleration and angular velocity be negative? So you have to use the right hand rule to figure out the direction of rotation. The vector itself points into the screen, negative z axis, which gives us a clockwise rotation. I show this at the very beginning when I animated the pieces moving to the left. You can see the arm rotating clockwise. Please see "scripts.mit.edu/~srayyan/PERwiki/index.php?title=Module_1_--_Angular_Kinematics" for further reading (scroll down to the angular velocity part). For angular acceleration, it just means it's slowing down the angular velocity since it's negative. I think mainly, you are confused about rotational directions, rather than angular velocity. Remember that the angular velocity vector in 2D problems will face in or out of the book, so it can be hard to visualize. If this isn't what you are asking, sorry, I still don't know what your question is 😅

[@camerontriplett9199]

@@QuestionSolutions ok, I understand the rotational axis of CD, so I was confused about the fact that it was already rotating clockwise while AB was slowing down, but since the angular velocity was negative and was slowing down, wouldn’t the angular acceleration actually be positive?

[@QuestionSolutions]

@@camerontriplett9199 It depends on the direction. So instead of thinking about angular velocity and acceleration, let's think about normal acceleration. Imagine we have a car, it's going at +50km/h, and there is a positive acceleration of +5m/s^2. Both positive, so that means the car will get faster and faster. Now imagine a car going backwards (we still assume forwards to be positive), so it's velocity is -50km/h, and the acceleration is -5m/s^2. What does that mean? It means the car gets faster and faster backwards, in simple terms, the car goes in reverse faster and faster. Now if the acceleration was +5m/s^2, and the velocity was -50km/h, what does that mean? That means the car is actually slowing down, while it's going backwards. Does that make sense?👍

[@danielntu3940]

what chapter and sub subject is that?

[@QuestionSolutions]

I don't really have that information, I am not sure what book you are using, which edition, nor do I have access to all the books out there that covers statics. In general, the title of the video gives a really good idea about what is being talked about, and what sub category it falls under. 👍

[@user-uy2uj6px3k]

Can someone help me out here? why is Y = 0.3cos(theta) and not -0.3cos(theta) even though it is pointing downwards?

[@QuestionSolutions]

There is no negative value because it's the distance of one of side of the triangle, in other words, it's just a length.

[@alperyasin710]

Hello sir, i am sorry for bothering. At 1:38 formula is -ab.cosC, but at 6:45 it is -2ab.cos, is it typo?

[@QuestionSolutions]

Please double check the timestamp 1:38, I am not seeing -ab.cosC? Also, it's no bother, just want to make sure we are looking at the same thing.

[@alperyasin710]

@@QuestionSolutions i am sorry, it was at 1:06

[@QuestionSolutions]

@@alperyasin710 Yes, that's definitely a typo. It should have been 2ab at 1:08. Good catch! :) Please see: www.mathsisfun.com/algebra/trig-cosine-law.html

[@alperyasin710]

@@QuestionSolutions sir thanks for everything, you are a life saver!

[@QuestionSolutions]

@@alperyasin710 You're very welcome!

[@ellyvatedaf]

How are you animating them?

[@QuestionSolutions]

Animated used After Effects