Rotational Kinetic Energy and Moment of Inertia Examples & Physics Problems
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- čas přidán 28. 10. 2017
- 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...
Physics PDF Worksheets: www.video-tutor.net/physics-basic-introduction.html
Full-Length Videos & Exams: www.patreon.com/MathScienceTutor/collections
Next Video: czcams.com/video/KbYejyiRsFw/video.html
You are one of the best tutors. Thank you so much for explaining the topic so beautifully :)
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.
lmao same bro, professor just solves 4 questions per chapters and calls it a day. Going in dark today.
Update: I aced last Friday's quiz on rotational dynamics. I have two more to go: thermodynamics and harmonic motion and the final.
@@floridaman964 Just took my third exam, got a 90. I owe this dude half of my degree lol.
@@floridaman964 good luck mate !!
Update: aced harmonic motion the week before thanksgiving, just have thermo quiz this Friday left and my final next week.
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
In 12 minutes I learned what I didn't in a whole course. Monsieur!
thank you so much for these videos. you are wonderful!
Thanks Man!!! I did well on today's test because of you I can't thank you enough 👍🏽👍🏽👍🏽😊
This was really helpful
Thanks so much
Thank you soo much im Always looking for your videos whenever we start a new topic because i know you are mastering the introduction
Tysm bro you make it so easy to understand
So can the derived acceleration equation be used on any system or is specifically on pulley systems?
I like your teaching way thanks
wonderful boss
Amazing content! thank you!
bro that alternative solution for the 3rd question really blown my mind awayyy
This man is my hero.
how did you find the 2/5 in q2?
Pls can you make videos and problems concerning the term "radius of gyration" in relation to problems in angular momentum.. I'd really appreciate
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?
That’s what I was thinking
thank u so much
Is this why boxers use corkscrew punches? The rotation of the first increases the speed in a perpendicular motion?
thanks man
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.
thank you so much
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😻🔥
Inertia is mr², it doesn't have 1/2
@@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)
KE is equal to (IW^2)/2
and Impulse should be I=mr^2
Thanks 👍😌👍
My hero...
You saved my life
U are so goated bro
on the sphere question, the force doing work , why is it mgh and not mgsinθ
Wait, for question 3, why can’t we just use mg for the tension force, since the internal forces (actual tension forces) cancel?
Sir why don't we consider tension in the third question
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?
please you must state whether its a solid or hollow sphere. their inertia are different
tnx :))))
I need help. When how to use I=1/2mr^2 and I=mr^2 ??
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.
For problem 2, you can usually just use V=sqrt((4gh)/3) and shorten the steps.
If the ball is a solid sphere yes
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?
brandonbaunach look up inertia equations for each shape..
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
Am lost too
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).
OVERWHELMED WITH GRATITUDES
How did came up with the inertia 2/5mr²
Hi! On the second exam please where did he get the 2/5(inertia) ? thanks
That is just the formula for rotational energy of a sphere
The moment of inertia for a sphere is 2/5mr^2
Magmaflamess Gaming Thank you.
@@adamsmith2050 and Sparkle08 Thanks 😊
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
What program do you use to do the writing?
It's all in this video:
czcams.com/video/rBSuMooMYrs/video.html
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
best
velocity into something is energyy so what is that quantity ????
any app over it ????
in ex3 why we didnt write the epg for the pulley
Bcoz the pulley is fixed
on the first part you equated I=mr^2/2
then on 2:10 you are saying mr^2=I
why is it though?
es ori amoxsna ro ceria da erti dedamotynulad grdzelia yle var meoreti rom amovxsna????
question 3, 11:20 why is inertial mass = cM, then cM to1/2M
c is a constant and the value of that constant for a solid disk (pulley) is 1/2.
Hope this helps :)
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?
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 ?
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 :)
Isn't it going to do work? Torque times distance (mgh - torque*50/sin20 = mv^2 + Iomega^2/2)
Why did you divide the moment of inertia by 2 in the first question
why didnt we consider the work of the tension force in the second problem?
What tension force?
Still not understand, can someone explain to me, what’s the difference of 1/2mr^2 and mr^2. (Sorry for my bad English)
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
Leo Callebaut ya thx a lot mate!!! At least you’ve replied my comment, I appreciate it !! Really thx
isnt inertia formula I=mr^2 tbt in the first portion of the video he does mr^2 /2
someone explain that to me
For the pulley problem, how did he get inertial mass “cm” as 1/2M?
Because it's inertia of circular disc
how did you get the 2/5
different shapes of objects have different formula of moment of inertia......FOR sphere it is 2/5MR^2
it was amazing tutor i really appreciate u but i have one question from where did u get the 9.8 ?????
its acceleration due to gravity
It is not the same when calculating with 1/2Iw^2and 1/2M^2R^2w^2
Can someone explain what is C at 11:35
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.
angle 20 is not involved in equation?
question 2
You sub mR² instead of 1/2mR² ....from 1/2mR²w² .....why sir? You told us I= 1/2mR² 10:20 may 28 2023
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.
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.
06:59 Problem 3
power level 9:45
I'm quite discombobulated, if inertia =1/2MR² and RKE=IW, then how come RKE=1/2(IW²)
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
@@callynbarath4005 but the whole problem talks about disk, so shouldn't it be 1/2MR^2 all over?
@@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
Callyn Barath i am talking about problem 1, “ A 5kg disk” not the second one with the sphere
@@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
Lmao this is gonna help in my AP physics 1 exam in exactly 12 hours from now... Thanks
Why is the inertia of the sphere is 2/5 ??????
why
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)
Funfact : he always use values like 1.3 to make question so that we can listen to calculator sound😂😂😂
You miss the mass of block when you working on the distance of block move
you don't need the mass of the block to calculate the velocity, it cancels out in the end
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!
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....🤷♀️👍
@@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.
@@samb.7395 Ahhh interesting. Thank you for the answers.
So. What about double cone kinetic energy 😁😁😁😁
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
i love u
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
Pls I=uR^2 not 1/2uR^2
Sighs😩
If only I could do without physics 🤷🏾♀️
The second way of third example was too long and hard
I never have had that much time on exam 😬😬
:(
Bro, add some BTC, ETH, Monero adresses so people can donate shekels.
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