Rotational Kinetic Energy and Moment of Inertia Examples & Physics Problems

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This physics video tutorial provides a basic introduction into rotational kinetic energy. It explains how to solve physic problems that asks you how to calculate the final speed of a sphere rolling down an inclined plane using potential energy, translational kinetic energy and rotational kinetic energy. There's another problem that asks you to use conservation of energy to calculate the final speed of a falling block that is attached to a rotating pulley. The final speed of this block is confirmed using rotational dynamics, inertia, torque, and one dimensional kinematics. This tutorial contains plenty of examples and practice problems.
Intro to Rotational Motion:
• Rotational Motion Phys...
Angular Velocity:
• Angular Velocity Physi...
Angular Acceleration:
• Angular Acceleration P...
Rotational Kinematics:
• Rotational Kinematics ...
Intro to Torque:
• Torque, Basic Introduc...
Intro to Inertia:
• Inertia - Basic Introd...
________________________________
Parallel Axis Theorem:
• Parallel Axis Theorem ...
Rotational Dynamics:
• Rotational Dynamics - ...
Rotational Power, Work, & Energy:
• Rotational Power, Work...
Work Done By a Constant Torque:
• Work Done By a Constan...
Angular Momentum & Torque:
• Angular Momentum - Bas...
_________________________________
What Is Angular Momentum?
• What Is Angular Momentum?
Angular Momentum Problems:
• Angular Momentum Physi...
Angular Impulse:
• Angular Impulse
Rotational Motion - Review:
• Torque, Moment of Iner...
Full-Length Videos and Worksheets:
/ collections
Physics PDF Worksheets:
www.video-tutor.net/physics-b...

Опубликовано:

28 окт 2017

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Комментарии : 140

@TheOrganicChemistryTutor Год назад

Physics PDF Worksheets: www.video-tutor.net/physics-basic-introduction.html Full-Length Videos & Exams: www.patreon.com/MathScienceTutor/collections Next Video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-KbYejyiRsFw.html

@ishravlogs5382 6 лет назад

You are one of the best tutors. Thank you so much for explaining the topic so beautifully :)

@floridaman964 3 года назад

I need to get 100 on my next two quizzes and at least a C on my final to pass. Zoom classes failed me. Wish me luck boys, I'm going in.

@pinpon163 3 года назад

lmao same bro, professor just solves 4 questions per chapters and calls it a day. Going in dark today.

@floridaman964 3 года назад

Update: I aced last Friday's quiz on rotational dynamics. I have two more to go: thermodynamics and harmonic motion and the final.

@pinpon163 3 года назад

@@floridaman964 Just took my third exam, got a 90. I owe this dude half of my degree lol.

@janeh9962 3 года назад

@@floridaman964 good luck mate !!

@floridaman964 3 года назад

Update: aced harmonic motion the week before thanksgiving, just have thermo quiz this Friday left and my final next week.

@laurelwilley211 5 лет назад

Your voice sounds so smooth that it doesn't kill the vibe of the lo-fi I keep on in the background. Thanks for the help man

@danielmuzza5125 4 года назад

In 12 minutes I learned what I didn't in a whole course. Monsieur!

@iask_95 6 лет назад

Thanks Man!!! I did well on today's test because of you I can't thank you enough 👍🏽👍🏽👍🏽😊

@Cherry-wq1mb 3 года назад

thank you so much for these videos. you are wonderful!

@soniahshankoti6245 3 года назад

This was really helpful Thanks so much

@ZiphindiweDuba 4 месяца назад

Thank you soo much im Always looking for your videos whenever we start a new topic because i know you are mastering the introduction

@adarshkrishansharma5796 10 месяцев назад

Tysm bro you make it so easy to understand

@timm8610 6 лет назад

This man is my hero.

@zuhairalsaffar7001 5 лет назад

I like your teaching way thanks

@nasha07 8 месяцев назад

bro that alternative solution for the 3rd question really blown my mind awayyy

@boagootukile6219 6 лет назад

wonderful boss

@iban4849 5 лет назад

So can the derived acceleration equation be used on any system or is specifically on pulley systems?

@user-du6qx6bn5o 8 месяцев назад

Amazing content! thank you!

@stephensolanke430 3 года назад

Pls can you make videos and problems concerning the term "radius of gyration" in relation to problems in angular momentum.. I'd really appreciate

@ainikibluu 2 года назад

You saved my life

@ruthwossen943 4 года назад

thank u so much

@jastinloydsalaya2064 Год назад

thanks man

@owaiswani937 6 лет назад

My hero...

@yusebol 3 года назад

K.E=IW² K.E≠½IW² From I=½mr² and v²=r²w² K.E=½mv²=½mr²w²=½mr² × w² K.E=IW² Mistake sir,you taught me thou😻🔥

@susa9786 3 года назад

Inertia is mr², it doesn't have 1/2

@halberdoh8489 2 года назад

@@susa9786 yeah but the tutor said in the video that the inertia of the disc= 1/2 Mr^2, and then he replaced it with I which is supposed to be I=Mr^2, and thats where the extra half came from.( normaly RKE=1/2IW^2 , but not in this case as her I=1/2Mr^2)

@jharmley6882 Год назад

KE is equal to (IW^2)/2 and Impulse should be I=mr^2

@brianafonso8197 4 года назад

U are so goated bro

@rye-bread5236 5 лет назад

Is this why boxers use corkscrew punches? The rotation of the first increases the speed in a perpendicular motion?

@YogeshSharma-gl8yt 3 года назад

Thanks 👍😌👍

@ligawa361 Год назад

OVERWHELMED WITH GRATITUDES

@radudinescu1975 3 года назад

I have a question At problem 2 with the încline, he didn't mension anything about the 20 degrees in his formula. So if it was 45 degrees and 50 m height it would be the same risult. Is it correct? Please help.

@abhirupdey4339 Год назад

Quick Question... Wouldn't the equation for ke be Iw^2? Since the og equation for I is 1/2mr^2, in ke equation, wouldn't you take into account the 1/2 as well?

@fryPS Год назад

That’s what I was thinking

@TurdFurgeson571 5 лет назад

9:19 I know we get excited when we can start computing, but consider solving for v _before_ you start to plug in numbers, as OCT did on the previous problem. Doing so can help you keep your sanity and also prevent you from losing points on exams due to computation errors during the extra steps needed (factoring, dividing, taking the square root, etc).

@pinpon163 3 года назад

For problem 2, you can usually just use V=sqrt((4gh)/3) and shorten the steps.

@schizoid7543 Год назад

If the ball is a solid sphere yes

@datpham31415 5 лет назад

tnx :))))

@anestisniskou6313 4 года назад

on the sphere question, the force doing work , why is it mgh and not mgsinθ

@ayehufekadu1392 4 года назад

Sir why don't we consider tension in the third question

@mohammedisarezwani 6 месяцев назад

how did you find the 2/5 in q2?

@ibphysicsclassroom 4 года назад

please you must state whether its a solid or hollow sphere. their inertia are different

@sattendragopinath4674 4 месяца назад

Wait, for question 3, why can’t we just use mg for the tension force, since the internal forces (actual tension forces) cancel?

@masoud6398 Год назад

And also can we say cause the "M" is twice the mass of "m" so the "g" must be devided by 2. means 4.9m/s2 . Is it true or false?

@awptimized2734 5 лет назад

What program do you use to do the writing?

@TheOrganicChemistryTutor 5 лет назад

It's all in this video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-rBSuMooMYrs.html

@misheckmukala Год назад

How did came up with the inertia 2/5mr²

@yellowsunflower8834 Год назад

I need help. When how to use I=1/2mr^2 and I=mr^2 ??

@AsadNematv Год назад

I = 1/2 * m * r^2: This formula is used to calculate the moment of inertia of a solid disk (or a cylinder) about an axis perpendicular to the plane of the disk and passing through its center. Here, m is the mass of the disk or cylinder, and r is the radius. I = m * r^2: This formula is used to calculate the moment of inertia of a point mass (or a thin hoop) about an axis perpendicular to the plane of the hoop and passing through its center. Here, m is the mass of the point mass or hoop, and r is the distance from the axis to the point mass or the radius of the hoop.

@marielcinco5883 6 лет назад

Hi! On the second exam please where did he get the 2/5(inertia) ? thanks

@adamsmith2050 5 лет назад

That is just the formula for rotational energy of a sphere

@sparkle0859 5 лет назад

The moment of inertia for a sphere is 2/5mr^2

@indritduka2951 5 лет назад

Magmaflamess Gaming Thank you.

@lenael4747 4 года назад

@@adamsmith2050 and Sparkle08 Thanks 😊

@sashank6142 3 года назад

Heyy the moment of inertia of a uniform circular disk is 1/2mr^2 whereas the moment of inertia of a sphere is 2/5mr^2 and we have to calculate accordingly

@alialaweye6390 5 лет назад

in ex3 why we didnt write the epg for the pulley

@Elite_Academix 5 лет назад

Bcoz the pulley is fixed

@ImCHN24 5 лет назад

best

@PursuitToSuccess 4 года назад

question 3, 11:20 why is inertial mass = cM, then cM to1/2M

@bernardoamorim5113 4 года назад

c is a constant and the value of that constant for a solid disk (pulley) is 1/2. Hope this helps :)

@kennan7527 2 года назад

on the first part you equated I=mr^2/2 then on 2:10 you are saying mr^2=I why is it though?

@BrandonBaunach 6 лет назад

in the beginning you say inertia = (1/2)mR^2 and then at 2:23 you show that inertia = mR^2 without the 1/2, which is it?

@godlikeproductions7898 6 лет назад

brandonbaunach look up inertia equations for each shape..

@poketradeEU 4 года назад

In a) case the disk is full (solid) in b) case is empty , so the distribution of mass is different , making moment of inertia different

@kwanelensingo1528 3 года назад

Am lost too

@masoud6398 Год назад

Is it wrong to calculate "a" like this : ( 70- 0) ÷ 2=35 then 500÷35=14.2857s and then 70÷14.2857= 4.9m/s2

@anilkumarsharma8901 2 года назад

velocity into something is energyy so what is that quantity ????

@ghxstk2152 Год назад

QUICK ONE/; How was the 2/5 MR^2 and 1/2MR^2 found ? Basically where was the values which were used in place of inertia found and how ?

@ibxn6539 Год назад

2/5MR^2 is the moment of inertia for a sphere and 1/MR^2 is the moment of inertia for a disc. I'm not sure why but if you google them I'm sure there's an answer out there :)

@ogechindulaka1386 2 года назад

Why did you divide the moment of inertia by 2 in the first question

@sparkle0859 5 лет назад

Lmao this is gonna help in my AP physics 1 exam in exactly 12 hours from now... Thanks

@68506gan Год назад

why didnt we consider the work of the tension force in the second problem?

@samb.7395 Год назад

What tension force?

@anilkumarsharma8901 2 года назад

any app over it ????

@mezarebacxovreba7249 21 день назад

es ori amoxsna ro ceria da erti dedamotynulad grdzelia yle var meoreti rom amovxsna????

@samipdon3514 2 года назад

isnt inertia formula I=mr^2 tbt in the first portion of the video he does mr^2 /2 someone explain that to me

@virajbagga5923 4 месяца назад

If the formula for I is (1/2)mr^2, then wouldnt the formula for RKE just be iw^2 not (1/2)iw^2?

@Chris-mm6mn 2 года назад

For the pulley problem, how did he get inertial mass “cm” as 1/2M?

@palnatinagamma 2 года назад

Because it's inertia of circular disc

@mikisolomon9228 4 года назад

It is not the same when calculating with 1/2Iw^2and 1/2M^2R^2w^2

@YogeshSharma-gl8yt 3 года назад

Funfact : he always use values like 1.3 to make question so that we can listen to calculator sound😂😂😂

@emerald_eyes 7 месяцев назад

Isn't it going to do work? Torque times distance (mgh - torque*50/sin20 = mv^2 + Iomega^2/2)

@ntwohiu0252 4 года назад

Still not understand, can someone explain to me, what’s the difference of 1/2mr^2 and mr^2. (Sorry for my bad English)

@leocallebaut3548 4 года назад

Might be a bit late here. mr^2 is the moment of inertia of a mass of masses located at a distance r of their axis of rotation. On the other hand, 1/2mr^2 is the moment of inertia of a cylinder/disk about an axis with radius r. Different shapes have different formulas relating their moment of inertia. Perhaps you should watch one of his video's that explain in greater detail the moment of inertia. Hope this helped

@ntwohiu0252 4 года назад

Leo Callebaut ya thx a lot mate!!! At least you’ve replied my comment, I appreciate it !! Really thx

@artuniverse7296 3 года назад

You miss the mass of block when you working on the distance of block move

@tanmay______ 3 года назад

you don't need the mass of the block to calculate the velocity, it cancels out in the end

@arwaadel3704 2 года назад

it was amazing tutor i really appreciate u but i have one question from where did u get the 9.8 ?????

@diegoperez4486 2 года назад

its acceleration due to gravity

@arturoroche3782 3 года назад

06:59 Problem 3

@tonybada717 2 года назад

how did you get the 2/5

@unknown-ek7xp 2 года назад

different shapes of objects have different formula of moment of inertia......FOR sphere it is 2/5MR^2

@reneumeh8601 4 года назад

power level 9:45

@oladelerasheed4994 Год назад

You sub mR² instead of 1/2mR² ....from 1/2mR²w² .....why sir? You told us I= 1/2mR² 10:20 may 28 2023

@zahranirfan5008 2 года назад

angle 20 is not involved in equation?

@zahranirfan5008 2 года назад

question 2

@callummcmahon9939 5 месяцев назад

Hey tutor I think you made a mistake on RKE of Q1 part b. at the point where it is 1/2mr^2w^2, the 1/2 is part of the Inertia equation for a disk so when simplifying the Kinetic energy equation becomes Iw^2 not 1/2Iw^2, and will be double that of your answer. Please correct me If im wrong as I was stuck on this for a while. If you plug the numbers into the 1/2mr^2w^2 you will get double your final answer so I believe your final answer is incorrect.

@anonymoususer1112 4 месяца назад

This is what I thought at first, too; however, the coefficient of the inertia equation varies depending on the distribution of mass. Thus, because the general equation for inertia is mr^2, we can substitute it with "I" and still get the correct answer.

@abhishekcv29chandi69 3 года назад

Can someone explain what is C at 11:35

@o.v4069 Год назад

It is the constant value you change when the shape changes. In this case it is 1/2 because the object axis of rotation for torque is a solid disk.

@leeovib9284 4 года назад

Why is the inertia of the sphere is 2/5 ??????

@manmmtk 4 года назад

why

@FriesDotExe 4 года назад

for new people who are wondering about this too, the inertia of a sphere's formula, in general, is (2/5 x MR^2). The Inertia of a Solid disk in problem 3 would be (1/2 x MR^2)

@grahamflowers Год назад

There is no kinetic energy in a moving mass there is force Mv squared kinetic energy is the energy of consistent work from a consistent force regards Graham Flowers

@peterarthur7161 5 лет назад

I'm quite discombobulated, if inertia =1/2MR² and RKE=IW, then how come RKE=1/2(IW²)

@callynbarath4005 4 года назад

Inertia is equal to MR squared not half MR squared, the half is only used for disks as they have their mass distributed differently, which requires that constant term

@DigitalLifeguard 4 года назад

@@callynbarath4005 but the whole problem talks about disk, so shouldn't it be 1/2MR^2 all over?

@callynbarath4005 4 года назад

@@DigitalLifeguard the first example is a sphere, that has a different constant term because of its mass distribution, second one is a disk, that's why it'll have half MR squared

@DigitalLifeguard 4 года назад

Callyn Barath i am talking about problem 1, “ A 5kg disk” not the second one with the sphere

@callynbarath4005 4 года назад

@@DigitalLifeguard i watched it again, i believe he does use half MR squared when calculating the inertia of the 5 kg sphere, at the beginning when deriving the rotational energy equation he doesn't use it because it applies to all objects irrespective of their mass distribution

@lxq2874 Год назад

I dont get why the torque is in negative,, isn't it in clockwise direction? it will be a big thanks for anyone whos gonna reply me!

@Mik-gw7tv Год назад

If torque is clockwise, it's negative. If it's counterclockwise, it's positive. I don't know why. I know it's weird. Something to do with trigonometry....🤷‍♀️👍

@samb.7395 Год назад

@@Mik-gw7tv Hey clockwise is negative because in trig if you are told to draw a line with an angle of 40 degrees you don't draw it below the x-axis but above it, therefore above x-axis in the counter clockwise direction is positive.

@Mik-gw7tv Год назад

@@samb.7395 Ahhh interesting. Thank you for the answers.

@yasarali45 2 года назад

So. What about double cone kinetic energy 😁😁😁😁

@user-wj9wg5tt9c 9 месяцев назад

Inertia of an object is as equal to 1/2 mass of the object multiplied by square of radius of the object. So, we can write I = 1/2 mR^2 In the next part of Rotational Kinetic Energy, you have written I = mR^2. Can you please tell me why did it happened? -Thank you

@unahebere2690 2 года назад

Sighs😩 If only I could do without physics 🤷🏾‍♀️

@user-nt8jo2gy6y 8 месяцев назад

i love u

@isoheilhsni 3 года назад

The second way of third example was too long and hard I never have had that much time on exam 😬😬

@comfortamuley324 4 месяца назад

Pls I=uR^2 not 1/2uR^2

@tatiana1310 3 года назад

@tassinfaak 5 лет назад

Bro, add some BTC, ETH, Monero adresses so people can donate shekels.

@brUh-gq4kt Год назад

Your explanation is bad, we dont know all the macro whats behind all actions you say, at least slow down and explain little pieces to make sense all of it, like justify what have you just said not automatically take one as granted