Rotational Kinematics Physics Problems, Basic Introduction, Equations & Formulas

This physics video tutorial provides a basic introduction into rotational kinematics. It explains how to solve rotational kinematic problems using a few simple equations and formulas. It covers topics such as angular velocity, angular acceleration, angular displacement and time. It contains plenty of examples and practice problems.
Intro to Rotational Motion:
• Rotational Motion Phys...
Angular Velocity:
• Angular Velocity Physi...
Angular Acceleration:
• Angular Acceleration P...
Intro to Torque:
• Torque, Basic Introduc...
Intro to Inertia:
• Inertia - Basic Introd...
________________________________
Parallel Axis Theorem:
• Parallel Axis Theorem ...
Rotational Dynamics:
• Rotational Dynamics - ...
Rotational Kinetic Energy:
• Rotational Kinetic Ene...
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-tuto...

[@TheOrganicChemistryTutor]

Physics PDF Worksheets: www.video-tutor.net/physics-basic-introduction.html Full-Length Videos & Exams: www.patreon.com/MathScienceTutor/collections Next Video: kzbin.info/www/bejne/oJiXlmuNaZmSe5Y

[@cooperlane7147]

Saved my ass in Calc yesterday, about to save my ass in Physics and will save my ass in Chem tomorrow.

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i have the same classes right now i better save my ass aswell

[@thetrailtrekker4030]

You are a God. My teachers refuse help me because they say I am a lost cause and stupid. You help me pass these tests and prove them wrong. Thank you

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Teachers used to do that to motivate students like u..dont b mad at them..they r just doin their job🤗

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@@warrenpadilla2304 how is "you are a lost cause and stupid" supposed to be motivating..This teacher refused to help him and even told him to give up basically by calling him stupid and a lost cause. Refusing to help a student who is willing to learn and be better is not calling doing their job, its called being insecure and unprofessional.

[@88GTA]

DDAA the teacher could help after/outside of class more exclusively, ur answer is semi-valid, however nobody that would say such a thing to a student should be hired as a teacher.

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U got it mate

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@@warrenpadilla2304 A teacher's job is to teach students that they are bad but can get better. Not to teach them that they are bad and will never get better.

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[@solomonmathew1084]

Thank you!! I only got 3 questions wrong on my physics exam😎 49/56

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My whole exam was 4 problems 🥹

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whats the best way to study?! i need help, struggling in physics 1

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How your teacher explains it: ~~~~~~~ How the OCT explains it: --------------------

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@Winston Apollo this guy and the guy claiming this works look like bot accounts and I doubt anyone fell for it but I wanted to give a heads up just in case

[@tamago9026]

Had an entire mechanics exercise on this as graded homework without having ever been introduced to the concepts during a lecture. Thanks for what you do

[@reallynotnetflixceo4674]

Huge thanks for this video! Cleared up a lot of confusion I had prior to watching this.

[@christabelrewe749]

I have exams on Friday. the only hope I have of excelling is this God-given teacher, thank you so much, Sir

[@datboi1861]

This actually isnt that hard once its explained properly. Thanks.

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[@tonjohn_]

6:53 This had me confused and 18:26 this killed meeeee LMAO

[@Armageddon613]

In question 2 part c you ask what the linear speed of a point at the edge of the rotating disk is and just multiply the angular velocity by r to find this. Correct me if I'm wrong but would this not depend on where we are assesing the speed of the point on the edge? If it's on the bottom of the wheel then it would be 0, if its at the top then it would be 2v. You have to specify where to solve that part

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[@someone8245]

thanks, very helpful. one thing tho, i try to solve the question on my own so when i pause the video (on pc) the title shows up on the top and i cant see the question so you could maybe move the question statement a bit in future videos :)

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[@rubentuting525]

how about normal and tangential components of acceleration?

[@waffaabouassaf1415]

you find theta by using W*T and anther times you used theta = W*t+1/2 omega *t^2 what is the difference?

[@banbantv3518]

I dont know but the second time the answer if we use w×t is 810 but when he used w*t+1/2omegat^2 it was 405....!?

[@vinitjadhav6555]

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[@lidiyaabebe4124]

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[@erickgaray463]

awesome video, you're teaching me a lot lol. For that final question, i paused your video and noticed time wasn't in there. so i solved for time using the kinematic equation, got t then solved for theta using the other equation but i got something completely different. my question is, when im given enough variables to solve a question should i just solve it instead of trying to find EVERY variable? cause once i plugged in T to find theta i got some weird shit. And what i dont understand is why that didn't give me the same answer as the final answer.

[@reallynotnetflixceo4674]

Not sure if this answers your question, but I am pretty sure I did exactly as you. I solved for time using one of the kinematic equations, and since we can treat Delta time as strictly the final time (since we can treat our initial time as zero), you're able to solve for time, then continue on with the only other kinematic equation that has theta as a variable (the one he didn't use since he didn't solve for time) and solve for theta that way. My answer was the same as his, however if you aren't careful with plugging your time into the theta equation as it was 1.3 repeating, (I just input roughly 1.3333333 ) for my time to get it as accurate as possible, your final answer can be changed slightly. If you enter time strictly as 1.3, your answer will be off by about .4. Hope that makes sense to you.

[@wengeance8962]

for the final question and final answer in revs, is it possible to find the time it is accelerating for?

[@manankalani0409]

yeh

[@TreasureObidike]

Thank you so much I finally understand this... I'm so happy rn 18:54

[@banthatiwisdom6783]

For final angular speed we suppose to find Wf as we have W0, Alpha and Time. And you found Angular displacement instead.

[@abishaimuddamalle7804]

So whenever Im converting from radians to revolutions my calculator always gives me something different from yours. My calculator is in radians but idk if thats the issue. For example when you converted 150 radians to revolutions I got 235.62 revolutions as opposed to your 23.87 revolutions. Pls help

[@lukasnolta9510]

multiply out 2 X pi manually first and then divide by that result and you should get the right answer. I had the same issue as you at first.

[@driesbrosens3089]

normally if you do 150/(2*pi) you schould get the right awser. you did 150/2*pi . your calculater will do 150/2 first (so 75) and then multiply it with pi, in wich case you will get 235. so it's important to put 2*pi in between ( ) or else it won't work. (sorry for the bad english)

[@kayla177]

@@driesbrosens3089 I had the same problem, make sure 2pi is in parenthesis

[@johnvincentcruz5648]

@@lukasnolta9510 thankyouuu it seems like 2yrs ago but your comment helps me.

[@jessicahorton5236]

Make sure to put parenthesis around your 2pi!! I was having that same issue but adding the parenthesis seemed to fix it

[@rutii.a6428]

Thank you very much!

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[@user-wu2rm3bh4y]

Many people wonder why radians do not appear when we have radians * meters. Here is an attempt at an explanation: Let s denote the length of an arc of a circle whose radius measures r. If the arc subtends an angle measuring β = n°, we can pose a rule of three: 360° _______ 2 • 𝜋 • r n° _______ s Then s = (n° / 360°) • 2 • 𝜋 • r If β = 180° (which means that n = 180), then s = (180° / 360°) • 2 • 𝜋 • r The units "degrees" cancel out and the result is s = (1 / 2) • 2 • 𝜋 • r that is, half of the circumference 2 • 𝜋 • r s = 𝜋 • r If the arc subtends an angle measuring β = θ rad, we can pose a rule of three: 2 • 𝜋 rad _______ 2 • 𝜋 • r θ rad _______ s Then s = (θ rad / 2 • 𝜋 rad) • 2 • 𝜋 • r If β = 𝜋 rad (which means that θ = 𝜋), then s = (𝜋 rad / 2 • 𝜋 rad) • 2 • 𝜋 • r The units "radians" cancel out and the result is s = (1 / 2) • 2 • 𝜋 • r that is, half of the circumference 2 • 𝜋 • r s = 𝜋 • r If we take the formula with the angles measured in radians, we can simplify s = (θ rad / 2 • 𝜋 rad) • 2 • 𝜋 • r s = θ • r where θ denotes the number of radians (it does not have the unit "rad"). θ = β / (1 rad) and θ is a dimensionless variable. However, many consider θ to denote the measure of the angle and for the example believe that θ = 𝜋 rad and radians * meter results in meters. Mathematics and Physics textbooks state that s = θ • r and then θ = s / r It seems that this formula leads to the error of believing that 1 rad = 1 m / m and that the radian is a dimensionless derived unit as it appears in the International System of Units (SI). In the formula s = θ • r the variable θ is a dimensionless variable, it is a number without units, it is the number of radians. When confusing what θ represents in the formula, some mistakes are made in Physics in the units of certain quantities, such as angular speed. My guess is that actually the angular speed ω is not measured in rad / s but in (rad / rad) / s = 1 / s, s^(-1).

[@aymanediouri3847]

i love u teacher

[@paulmale5615]

Very good explanation....

[@rulthlessrudy]

10:48 isn’t that final linear velocity formula? Is linear speed the same? I thought it be thetha/t (18 sec) no?

[@surajsingh-yg6yw]

10:02 why no of Rev coming out wrong if we calculate it through wf omega final 45 rad/s

[@fheiz8802]

stoopid

[@louisezero3129]

It's the same answer if you use the final velocity

[@yiweizheng4897]

very useful, thanks

[@user-hv6ef9ie1g]

9:13 Using the definition of Angular acceleration, Angular acceleration = delta omega/ delta time. Which means it's (2,5) = delta omega/18. Which means Delta omega = (2,5)(18) = 45. Since omega initial is zero, then 45 is omega final. Which to be fair, the video also said that omega final is 45. However, for part b, the video uses an equation that are not explained how it come about. If i didn't square the time and didn't divide it by 2, then the answer for part b would be different (this shouldn't work like this). Any explanation?

[@user-wu2rm3bh4y]

My guess is that actually the angular speed ω is not measured in rad / s but in (rad / rad) / s = 1 / s. If we say that the measure β of the angle is θ radians, we mean β = θ rad, and θ is the number of radians (it does not have the unit "rad"). For emphasis we can say that θ is measured in rad / rad, since θ = β / (1 rad) and θ is a dimensionless variable. When we use mathematical formulas to obtain formulas in Physics, we have to know what the variables represent. What I consider a mistake, is present in the literature, it is not only in this video. Therefore, I will leave another comment with the detailed information to be examined.

[@anonylolo324]

For part a) of the first question, could u basically just use the equation for period(T), as this is 5 mins and rearrange for 2pi radians, then divide your answer by 2pi?

[@christanjhayyap2015]

In 10:50 isnt that the average angular acceleration? Even though the answer is the same when you find the average linear acceleration it is still wrong to use omega...you should use velocity in finding average linear acceleration

[@johnmarioncastillo1210]

Thanks my friend

[@fahadabbas5252]

why didn't we use theta=omega t in 2nd problem to find revolutions>?????

[@day_pilot]

i have a physics exam tomorrow ill update depending on how well it goes

[@mathadventuress]

3:12 isn't average notated with a line over it?

[@taracheng345]

Thanks!

[@noor-bg9du]

you're awesome

[@sanviseth123]

This help me alot

[@KingII_]

Why did you assume the radius on the first question

[@justfizz415]

Love you man

[@gastivechipoba481]

Awesome 💯

[@AdityaMajumdar-vi1kt]

for question 2 part b cannot i just have used theta=angular velocity * time??

[@michaelaong1174]

Thank you

[@lightning4780]

I would like to point out at 9:17 you didn't input time in WoT, so it came out wrong. So if you put in the correct formula, 0(18)+1/2(2.5)(18)^2 = 423 rad

[@franceeanngregori6654]

0 multiplied by 18 is still 0. The one in the video is correct

[@horsfallprosper5909]

Why did you use ¢= (Wo+Wf)t/2 instead of ¢ = Wot + (at²)/2

[@Nicole-vp3oh]

How come for 1b you have to concert back to radians? Is theta not in degrees? And is revolutions always in degrees versus radians?

[@Toa_13]

It’s because the big booty bitches couldn’t see me

[@looneybugsybug5333]

Good stuff m8

[@dzunisanilishaba9281]

love u my guy

[@anifixworld6546]

Organic is the best

[@Hailee123]

Ugh I always forget changing the units....

[@jenromeave4793]

just read the given quantities with emphasis on the units then say it again and again. eventually you’ll think something is wrong because the unit for this quantity (say, velocity) should be in meters not centimetres

[@bobu5213]

11:35, why is it 0,5 over a radian?

[@Prism_JTN]

Because the 0.5 is the radius so he divided that radius over rad becase for every 0.5 m covered 1 rad have completed as well. With that he can cancel the other rad and have m/s which are the units for velocity.

[@poroporo8859]

You really don't need to put the over 1 rad as it's always one, and anything divided by one is itself.

[@guliyevshahriyar]

Thanks.

[@kostas71374]

instead of d =vot + 1/2at^2 my book says x=Xo+Uot+1/2at^2

[@jijicomel]

thanks alottttt!!!!

[@scootermcdoogall2781]

in question 3c where did the radians go 4rad/s^2 x .3m = 1.2m/s^2

[@user-wu2rm3bh4y]

My guess is that actually the average angular acceleration α is not measured in rad / s^2. The unit is (rad / rad) / s^2 = 1 / s^2. When we use mathematical formulas to obtain formulas in Physics, we have to know what the variables represent. What I consider a mistake, is present in the literature, it is not only in this video. Therefore, I will leave another comment with the detailed information to be examined.

[@captainshap317]

The goat

[@shailkumarjain]

Hello everyone , if somebody could help... as i have learned that we can't apply kinematics motion equations when acceleration is not constant. here in circular motion ,acceleration is not constant as of changing direction so how come we are applying those equations to find the answer, ,kindly advise please. thank you..

[@satarupadebsinha3413]

awesome

[@LithasWorld]

Sorry but where did you get the radius for example 2 @(11:33-34)

[@rulthlessrudy]

It’s in the question at the end in parentheses. He just converted from cm to meters

[@LithasWorld]

@@rulthlessrudy ohh my bad , didn't notice 😅 Thanks.

[@kostas71374]

Instead of 'd' my books says 'X-Xo'

[@malik7126]

its the same thing x-xo is delta x or distance

[@cheeesonator]

It means final X minus initial X. Which is the change in X. Which is the total quantity of X. The o means initial, the X with nothing implies final. Everything of a certain quantity is final minus initial.

[@kostas71374]

@@cheeesonator hahaha thanks for the answers. I had my exam 2 days ago... and i dont know if i passed or not it was a difficult exam.... will update it xD

[@kostas71374]

@@cheeesonator PASSED!!!

[@cheeesonator]

KoSTas M fuck yeah man! We’re all gonna make it brah

[@smfinch99]

Omega... I mean Theta...... (haha seriously tho love your videos)

[@SamWilletts-yt8rd]

For question 2, my formula sheet says theta=initial theta + omega t + 1/2 alpha t^2. Yours didn't have omega t. Someone explain please :)

[@Dark_matician]

Come again please. I can't seem to understand you.

[@NZC_Meow]

Theta is angular displacement The formula should be Theta = (initial omega × time) + (alpha × time squared) Yours is wrong because if you want theta as the subject of the formula, why would it be on both hand sides of the equation. And his formula didn't have the initial theta. It has the (initial omega × time)

[@ninoxyruzremedillo8591]

There's no need to put t cuz the initial omega is 0, so if you multiply initial omega which is 0 by the time, you'll get zero cuz any number multiplued by zero is equal to zero

[@banbantv3518]

9:10 Wait why not use w×t instead ... The answer comes out to 810 so it is wrong but why Someone help...

[@bernadetteashleytirtadji5672]

I know this is late but w x t is what u used when the acceleration is 0, but in this case it's 2,5, that's why you use the other formula :)

[@ferasbaker3954]

3:17 3:54

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There is a special place in heaven for you my guy. If I ever meet you in person, I would love to take a picture and shake your hand

[@paytonmarino7498]

anyone else stay the extra 30 seconds at the end to see if there was a post-credit scene like a marvel movie :(

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Godbless u huhuhu u save our lives huhuh usto mo hakdog libre ko? Huhuhuhu thank u huhu

[@strugglingcollegestudent]

Did everyone get 64 revolutions for 2b?

[@slkvideos9111]

my teacher is making me watch this

[@michaelaong1174]

Hi, ineed your help, how were you able to get 23.87 on question number 3 letter a? I've tried it on many calculators now yet I can't het the same answers as yours...help please

[@nonorv3095]

I guess you missed the t from ex.2

[@ashbym9968]

The angular velocity is 0 so it would've canceled time out

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vevolution

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Saving my ass again.

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❤

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(2)

[@chasegaddis418]

I am very sorry to complain like this, I love your videos, but please if you ever make more, do something about the amount of compression or whatever that is on your voice. I literally have a hard time listening to it.