This definitely one of the best explanations out there. I checked out several videos and they just gave the formula and told that moment of inertia is the rotational analogue of mass. This didn't make complete sense to me. As F=ma (linear 2law) , if F is constant, if mass increases the acceleration decreases. Similarly when torque was constant, if mass increased angular acceleration decreased which suggests the 'm' part in rotational inertia. Then you proved how the 'r' part comes into the picture. As the radius of the mass increased, given the torque constant, the angular acceleration decreased. This shows that m and r together form the 'm' term in F=ma as when the mass and radius of the objects increases, it resists rotation. Hence T=Ia as if torque is contant, m and radius are the determiners of the angular acceleration. We know that torque is proportional to fishy thing and the proportionality constant becomes mr^2 (I had a confusion as to why r^2 and not r but then when I calculated the dimensions using t proportional to a, t=Ia , I=T/a and the units was kgm^2). This clarity I got only after watching your video. Thanks alot. Do let me know If I have gone wrong anywhere with the understanding. I am definitely recommending you to my friends.
You are such a good teacher. You make physics so intuitive. I hope to watch more of your videos to gain a better understanding for how beautiful physics really is.
Thank you! It was actually someone else's idea to add that in there, but I thought it was hilarious, so I added it. I was afraid it might be too subtle. Glad you noticed!
This is the second time I watched yr video. The first time was explannation of action reaction force misconception, that was really good and I recommended that to a lot of friends. This video is also well made, its especially impressive that you tend to cover misconceptions and questions that students might come up with Thx so much
This is the Best Moment of Inertia explanation I have heard / read. Flipping Physics is the best. Great content along with superb explanations. Thank you.
Okay, seriously cool. I study statistics, which summarizes the dispersion of a probability distribution as its variance. The definition of variance equates to moment of inertia. Statistics therefore borrows the physics term, describing variance as the second central moment. With this lucid video, I now better understand variance.
Excellent demo and exlanation! May I suggest one correction to the notation? Near the @5:00 mark, the equation displayed is notationally incorrect. We can write the torque vector equal to the vector product of the radial vector and the force vector ("r cross F"), but when we write the equation in scalar form, the magnitude of the torque is equal to the magnitude of the radial vector times the magnitude of the force vector times the sine of the angle between the vectors when they are tail to tail, we need to drop the "arrows" on the symbols (or put the double- or single- bars around them depending on which notation you prefer for the "norm" or magnitude of a vector). Vectors cannot be stuck together without a "dot" or "cross" because that is an undefined operation, unlike scalar algebra where "a cross b" = "a dot b" = ab. I apologize for not being able to format mathematical operations in the comments.
Thanks. I am aware of this issue and, if RU-vid allowed uploading of replacement videos, I would upload a replacement for this with that correct. Unfortunately, RU-vid does not allow that. It's a bummer. Wish I were perfect, or at least able to fix my mistakes.
1:41 torque is a pseudo-vector😉 3:49 : vector *r* next to vector *F* with no symbol between. That notation exists but in a different context: *r* *F* is the geometric product of both vectors, not its cross product) (I put vectors in bold letters, easier here)? Don't you rather mean the norm of each times sin(θ) (where θ is the angle between *r* and *F* ), like so: | *τ* | = | *r* | × | *F* | ×sin( *r* , *F* ) ? (note for readers: here × denotes usual multiplication, whereas in *r* × *F* it denotes the cross product. Non anglo-sphere students might use ∧ for cross product) Very nice video
Why are you calling torque a pseudovector? I've never heard it referred to that in a physics context, unlike pseudo-forces. At this level, students have a hard enough time grasping that centrifugal force is a pseudoforce. Also, this is the first time I've come across the geometric product, though I vaguely recall coming across an inner vs. outer product. As this video is intended for introductory physics students, most of those subtleties are lost on the student so not worth mentioning. I usually say that operation is "undefined", which is not quite true but gets them to stop writing vector multiplication without the dot or cross symbol in some cases. When you only teach introductory courses you lose some of the more advanced mathematics, but it really does not need to come up in this context.
I watch this video six times. and every time's learn something new. so increase the watching frequency thet increase your knowledge and reduce fear about physic just like increase torque due to increasing the acceleration
Hi. if I were to investigate the effect of a particular variable on rotational inertia where I can get a graphable equation, which variable would you recommend? Great video btw
I enjoyed the video. However, I was expecting you to get to the fact that the acceleration of the 2 mass system is less than that of the single mass, just like with an Atwood Machine. We now have an additional 200 g of inertia, all with the same net force. Since more of the potential energy has to go to translational kinetic, a bit less goes to rotational. I can understand not wanting to go into this detail in your video. I know that you said "roughly" at the end, so I figure this detail is outside of the scope of your video. I probably would have mentioned this in my classroom, though. Thanks for making these!
Making these videos is always an act of restraint. Think of all the things that are _not_ in this video: - Free body diagrams. - The relationship between velocity of the hanging mass and the tangential velocity of the exterior of the pulley. - Friction in the axle causing torque. - Conservation of mechanical energy. This video is meant to be a basic introduction to rotational inertia. I felt it necessary to have one example with two torques because students often forget it is the _net_ torque in the rotational form of Newton's second law. Someday I hope to make a video which quantifies the "roughly" word you pointed out I used at the end. Trust me, quantifying that will take a full video of its own. You are absolutely welcome for the videos!!!
@@FlippingPhysics by its definition , mass always remains constant, unless it ownself is the creator of speed. In a gravitized environment, a rotating body is counter directional-one facing gravity and the other against it. Do this condition affect its momentum or inertia? Consider an object in an elevator going up and down.
@@gensyed Gravity doesn't affect moment of inertia. It will apply an alternating torque to an object, if not rotating around its center of mass, but it doesn't make the ratio between net torque and angular acceleration any different.
There has to be an easier way to explain this. Has to be. I just watched this other video that stated "the diver who is curled up will tend to stay spinning, whereas the diver who is stretched out will be less likely to spin". That makes sense. Buy then they said "the diver curled up has a low moment of inertia". WHAT???? How could he have a "low" moment of inertia when he is MORE likely to keep spinning---to "remain unchaged". Its so ridiculous.
@@FlippingPhysics thak you so much you saved my life! You're doing a great job. You have no idea how much its helping me! Ps: I have a really bad physics teacher at school
Sir i am your biggest fan from india ... And wating for you each video And i am your suscriber from 50 Sir may you provide your contact no. So it help me a lot ... Thank you
AJ Games Hacker. Know I appreciate your support. Also understand that I cannot give you my contact information. There are a large number of people who want to contact me and I just cannot communicated with all of them. I have to protect my time to be able to make videos to help you learn. I hope that makes sense. -mr.p
