Rotational Inertia
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- čas přidán 28. 08. 2024
- 097 - Rotational Inertia
In this video Paul Andersen explains how the angular momentum of an object if a product of the rotational inertia and the angular velocity. The rotational inertia depends on the mass, radius and shape of the rotating objects. A sample calculation and several examples are included.
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All of the images are licensed under creative commons and public domain licensing:
Campagnoli, Manuel. English: Pointing Hand Icon, Thick Outline, 08012 2010. Manuel Campagnoli. commons.wikimed....
File:Leonardo-Flywheel-Screenshot.jpg, n.d. commons.wikimed....
“Flywheel.” Wikipedia, the Free Encyclopedia, March 3, 2015. en.wikipedia.or....
“Gravity and Orbits.” PhET. Accessed April 6, 2015. phet.colorado.....
“Leonardo Da Vinci.” Wikipedia, the Free Encyclopedia, March 26, 2015. en.wikipedia.or....
If i ever make it big i'm gonna hook you up man seriously your videos were so helpful to me and helped me get into my desired uni and course cheers man, people like you often go unnoticed and you deserve way more for how much you help people
Hope you made it/in the process
Real
I'm just discovering physics (or the study of, at least.) Went to college, but with a 6th grade education, (that's when I was expelled.) I didn't take any physics classes in college, my curriculum didn't call for it. I had never been exposed to the study of physics, but I am loving it. Just in a few hours tonight I was able to understand people when they talk about energy, and the transfer of it. Not to say that I expect it to always be easy. But it's fun, regardless.
It's so cool to learn that energy is never created or destroyed. It's just transferred. What we have is what we'll always have. That understanding brings into focus a lot of other laws that I've heard a million times just because they're famous, but I never really "got it." Newtons laws make total sense now. Takes energy to alter energy. I understood all of this video. It just made sense.
When he was talking about da Vinci's variable flywheel, I immediately thought of ice skaters, who will start a slow spin with their arms out, then slowly bring them in and their rotational speed increases. I may be using the wrong term here, but does that mean that it is inversely proportional since it can happen both ways, or is there another equation going on here? Perhaps it has something to do with going into the spin? I noticed they go from a straight line and take that energy into a tight spin with their foot, with one leg dangling out.
Well, I could go on. If anyone can suggest a friendly physics forum, that'd be great. Seems like I should take an introductory physics class, too.
So absolutely fascinating.
Well, just wanted to share my mini-awakening. Off to read more on it :)
You realize energy is never created or destroyed because we chose state variables in a way that made it never be created or destroyed.
Search up inelastic collisions. It doesn't always apply.
Energy is a way to get the properties of an object (like its velocity) and translate it to something else (like the height it reaches) without having to go through the icks of the process, of the kinematics in this case. As they discover more properties an object can have (like temperature, or rotational energy or whatev) they create more energy equations in a way that you can translate easily from one scenario to the other (for example, how far will burning this fuel get this car). You don't actually need energy to solve these problems, and at the beginning, no one used energy. I would suggest straying away from justifying things with energy until u really understand them physically.
Just some advice.
Bro absolutely hyped that you like physics! That is the kind of passion that we just never see from people outside of the subject. Please enjoy all it has to offer :)
@@joshuaronisjr Wait a second, so does energy even exist?
@@birhon Energy exists, , and has physical manifestations depending on the situation we're considering. And, as we discover more and more quantities with physical representations in our universe, we'll be able to create energy equations from those physical representations. But, energy itself is not a specific physical aspect of a system...at least as far as I've understood in my studies so far.
How are you doing now?
This helped immensely, thank you so much. I honestly depend on what these Physics Tutorials do for me to understand my class, and they haven't failed me yet. Thanks~ ^.^
You made me cry over how simple this is
you did not see walter lewiin
@@ezanagebregziabher5981 Two amazing teachers, Professor Andersen and Professor Lewin! :)
@@clumsyhes2103 True
I'm a engineering student almost in senor year. I still come back and review this stuff I learned years ago in physics.
Cool that you are a senior! Same here but I study medicine.
Thanks Mr. Anderson! This course saved my life!
Love the animations and the speed. Excellent video. Keep it up Mr. Anderson.
This formula I=1/2MR^2 could be figured out by using integration. And there is also an important concept "parallel axis" not mentioning in this video.
That's because this video is for AP Physics 1, which is algebra-based, so integrals are not a part of the curriculum.
Thanks Mr. Anderson, hope all is good
"Best useful channel of the year":)
you are the best dear teacher
thank you
omg I LOVE YOU.You were so helpful !!!
Lol
@@coreyhaskins7768 love you too
Thank you! Very clear and concise
sir your classes are so helpful.....
That was incredibly helpful.
I love the new videos, Paul!!!
Its so on point, thank you for this sir
what will be the rotational inertia in case of a solid and a hollow sphere? And can u plz explain how u calculated it?
great video
Very good!
holy shit that was like drinking from a fire hose
how dare you just spend 5 minutes to make me understand Rotational Inertia
Cause u searched that
Or it got recommended
That 5 minutes was worth it!
very helpful video
very helpful video, thank you!
Isn’t there a third form of inertia, vibrational? A pendulum, a vibrating string, all direct manifestations of some kind of inertia, but one that allows regular deceleration/acceleration somehow. Would love a video on this!
There are products of inertia, that become important with generalized 3-d rotational mechanics. Inertia takes the form of a 3x3 square matrix called the inertia tensor. The diagonal terms are the three moments of inertia about the three coordinate axes, while the remaining 6 terms are mixed terms such as Ixy, Ixz, and Iyz. There is a symmetry to these 6 terms, so it is really just 6 independent terms in total, that form this tensor of 9 terms.
Where we use Torque =I x alpha and Torque= F x r , please let me know
im glad cuz i found your channel
This was very Helpfull ,Thanks a lot
^^
Thank you sir
Ur r doing great job dude
How does this principle apply to sprinting on the track
Great video
Ok so take a full record and cut away all of the inside so you get A large hollow cilinder. Would its inertia be less or more then the full verdion of the record?
Nice lesson. Thank you.
Love from India ♥️♥️♥️
Well done sir!
How do you account for different mass configurations in writing I? You mentioned that the 1/2 is cancelled when the mass is moved to the outside of the disk. What happens if the mass is, say, condensed in a triangular wedge?
It's an integral. In general, it is I=integral r^2 dm.
Hello I was wondering if you could help me with a unique flywheel calculation please? If I had a way of magnetically supporting a huge flywheel like the one illustrated in your video (vinyl record). Lets say 50 meters in diameter. Is it possible to spin that flywheel with an outside rim speed of 1600 km per hour? Lets use for calculation purposes a material like cast iron.
Thank you it was helpful.
what tools do you use to produce the video ? keynote and screen flow?
Thank u for helping me
how can i calculate inertia(I) of a polygon
What actually is inertia ? Like kind of practical concept ? Please can you help me out ?
It is the tendency of mass (matter) to want to keep doing whatever it is doing. If an object is at rest, it wants to stay at rest. If it is in moving, it wants to maintain that motion (resisting acceleration, which is a change in motion). That's really the whole point in Newton's first law. More mass, more inertia. More ability to "resist change".
A way I think about it, and this will make more or less sense depending on how much you know about mechanical physics (impulse, momentum, and energy), is that inertia, or mass, is like a battery. Like a battery, inertia acts as a storage place for energy. If you have a ton of mass in a freight train, you essentially have a huge energy battery. The caveat of this battery is that the larger the mass/inertia, the harder it is to charge or drain the battery. In other words, a resting freight train has a ton of inertia, so it is hard to "charge" it, or get it to start moving, at which point it would store that "charge" in the form of kinetic energy. Once you get it going, you're going to have to work equally hard (pun intended) to drain that charge. In contrast, a toy car has a much smaller mass/inertia relative to the freight train, and so it is easier to charge up (pushing it across the ground with your hand, accelerating it) or draining its charge (halting it with your hand).
Anyways, that's one way of looking at inertia. If all else fails, just remember Newton's first law and remember that it's just saying mass is inertia, and that the inertia of an object resists changes in motion. Hope that helps.
Palidion woaaah great ! Thanks for writing such an understandable answer ! I appreciate ur understanding level 😀 thank yuh !! Thank yuh !! Thank yuh !!
A funny example of a large inertia would be of a fat girl wanting a kiss so she grabs you and you try in vain to get her off you... it takes alot of effort to stop her..
but if its a thinner girl well shes easier to kiss because its easier to pull her toward you ;) or push away if you did not want her to kiss you either.
Thank you so much
You said about how inertia starts to drop (spheres move down) when we decrease the speed of the flywheel. Since angular momentum is always conserved shouldn't inertia increase as angular speed decreases???
You probably figured it out after 3 years but no. Inertia only relates to the mass and the radius from the rotational axis. Rotational kinetic energy decreases as angular speed decreases.
Isn’t 1/2mr^2 the formula for a cylinder. A record is a circle
Thank you
amazingly helpful :)
Why can't you be my teacher in school.......
He's great at teaching!
But what is an object rotating in relation to?
I think this is the wrong formula. If a disk is rotating, in this case, I think it should be 1/4mR^2 (rotating about the diameter). 1/2mR^2 is rotation of a disk vertically.
really very niceeee
I don't understand the 1/2 in the formula for inertia. I thought it was it mass times radius squared.
+fawad3022 It depends on the shape of the object. If you look in most physics textbooks there should be a table of all sorts of shapes being rotated and what their I values are.
Thanks!!!
hey man i have a really cool invention that uses these principles and need peoples feedback on if it would work
If anyone can help, i was wondering why he was putting 1/2 in the formula when he was trying to find the rotational inertia?
+Shams Drawings it has to do with calculus. The 1/2 comes from the power rule of integration when the constant I is being calculated.
Got it. Thank you very much
dude pls prove I=MR^2
HAVE YOU FIGURED THIS OUT. I DONT UNDERSTAND
This is not easy, we just proved it in my physics class and you need to use linear algebra.
It took us two hours in total
@@549231 if i want to prove it what can i read ?
@@hozaifaessam6853 pick a book used for 2 sequential courses of linear algebra and then look up a proof online
5:06 should say " going to see a year which is half the TIME of what it is"...not distance - slight slip
Where's your physics video?
Where do the constants 1/2 come from
They come from calculus. The general formula is I = integral r^2 dm. You set up the value of dm to be an infinitesimal mass element, and you will see a spatial variable become the new variable of integration, after determining what dm is, in terms of that infinitesimal spatial variable, and constants. Then you carry out an integral across the dimensions of the shape.
For the case of a cylinder, you set up your infinitesimal mass element to be a thin cylinder at radius r from the center, with a thickness dr, and a height h. The term dr is the infinitesimal change in the spatial variable r. The volume of this cylinder is 2*pi*h*r*dr, since the thin cylinder unwraps into a rectangular prism of dimensions 2*pi*r by h by dr. This means the infinitesimal mass element dm= 2*pi*rho*h*r*dr.
Now we add this to the integral:
I = integral r^2 * (2*pi*rho*h*r) dr, from r=0 to R
Pull out the constants:
I = 2*pi*rho*h * integral r^3 dr
integral r^3 dr = 1/4*r^4 + C
Evaluate from r=R to 0, and get
1/4*R^4
Put it back together:
I = 2*pi*rho*h * (1/4*R^4)
Simplify:
I = pi*rho*h*R^4/2
Recall that rho = m/V, and V = pi*h*R^2
rho = m/(pi*h*R^2)
I = pi*(m/(pi*h*R^2)) * h * R^4/2
Cancel pi, cancel h, cancel R^2, and get:
I = 1/2*m*R^2
who the hell disliked this lol
The physics professors that suck at teaching
Those who tried to download this video.
people who's brains don't work like ours do
@@JimmyCrust Woah, chill out with that elitist Darwism bud!
those flat earth theorists did...
Love you
Please let me clear, how moment of inertia changes as the mass changes from centre to periphery.
How it becomes double at same velocity and mass .
that's cooooooll awesome
Tysm🙌
Thnkuuu so much
Love from india
Awesome Amazing good marvellous magnificent 😍😍💟💟💟🙏🙏
Very helpful!
a tesla turbine with a large diameter with and extreme low mass is what. a large diameter same eg. but extremely thin with a great mass. what happens. also cold dry air vr hot. then distilled water vs sea water. what vacuum force is created and it relation to torque.
The gentleman is throwing ideas and concepts and formulas right after another before developing it step by step, there are much better videos on youtube search for a moment of inertia
رائع جدا
Doesn’t I=Current?
Variable names get reused in different contexts all the time, and don't necessarily have anything to do with each other.
Make a simple potential limits of all the physical potential and found anomalies we see in nature from experimental data 🕉🕉🕉🕉
So simple
New to me anyhow
👍🥇
🙄😘😇
🌛 Tesla
This only explained the obvious. It still does not explain how all objects stick to the spinning ball Earth. In fact it explained how it's not possible.
Gravity.