Uniform Circular Motion - IB Physics

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  • Опубликовано: 17 дек 2024

Комментарии • 183

  • @clarizeesmeralda3765
    @clarizeesmeralda3765 3 года назад +204

    This guy is so underrated , the way he teach is so direct to the point hands down

  • @marufhasan1732
    @marufhasan1732 3 месяца назад +8

    My brother used to see this now he's a engineer suggesting me to watch this video. This dude actually rocks

  • @philomenangoh6365
    @philomenangoh6365 2 года назад +46

    This man speaks the language of my brain cells

    • @AndyMasley
      @AndyMasley  2 года назад +7

      Aw that's so nice

    • @Avanti-zx7tm
      @Avanti-zx7tm 2 месяца назад +2

      @@AndyMasley i love your videos, they really clarify the concepts i learn in school,

  • @aycb8805
    @aycb8805 4 года назад +45

    It is so great that i finally found a lesson video that is JUST PERFECT !

  • @danieljatombliansky3515
    @danieljatombliansky3515 4 года назад +13

    SUPER HELPFULL, really, there aren´t a lot of videos explaining this stuff, thanks a lot

  • @runeknight2842
    @runeknight2842 4 года назад +130

    This guy teaches better than my teacher

  • @johnnyboy3390
    @johnnyboy3390 3 года назад +4

    Absolutely phenomenal job teaching this content, and $2,000 cheaper than my uni physics classes...

  • @ParthThapaChhetri
    @ParthThapaChhetri Год назад +2

    Absolutely nailed it. Have my exams tomorrow and your videos are the best one I can find on youtube, in terms of quality and going straight to the point ✨

  • @larsityosmarsilyet5933
    @larsityosmarsilyet5933 3 года назад +3

    dude really, . In just 14 minutes, you really taught better than anyone. I liked and subs to your channel. Keep going like that.

  • @AirbusBoeing-li5zi
    @AirbusBoeing-li5zi Месяц назад +3

    Thank you! I'm starting to learn this tomorrow and there is nothing on khan academy. The preview will be very helpful!😄

  • @highschoolphysics9459
    @highschoolphysics9459 3 года назад +7

    Very cool animations and timing for your teaching content. My students appreciate your work.

  • @11392ash
    @11392ash 3 года назад +4

    HOLY SMOKES, you broke that down SO WELL!!! Thank you so much

  • @Learning_with_Musti
    @Learning_with_Musti 3 месяца назад +2

    Best video I have seen on this topic.Well done Sir. You inspire me to be a better teacher

  • @kelvinthehuman
    @kelvinthehuman 2 года назад +1

    Waooo....amazing explanation, without a waste. Hats off to you, Mr. Masley. Greetings from the Dominican Republic.

  • @natrs2335
    @natrs2335 2 года назад +2

    Thank you so much, I understood in 15 minutes what I didn’t understand in class in 2 hours

  • @s9na-j2h
    @s9na-j2h 6 месяцев назад +1

    I’m in 12th grade and this channel is helping me so much this channel is underrated amazing video

  • @GoldenStoic
    @GoldenStoic 2 месяца назад +2

    You keep saving me, time and time again… Thank you sir.

  • @juliette0523
    @juliette0523 2 года назад +4

    You made it so much easier for me to understand this stuff, thank you so much!

    • @AndyMasley
      @AndyMasley  2 года назад +2

      So happy to hear that!

  • @jenniferbello-ld3rp
    @jenniferbello-ld3rp Год назад +1

    I have an exam on this unit and this video was really helpful. So glad I found this video

  • @sinan1322
    @sinan1322 2 года назад +6

    This video was pure miracle 😁 helped me a lot to understand this topic ! Thank you !!

  • @altonmiles4027
    @altonmiles4027 3 года назад +4

    Amazing video! Very concise and easy to understand. You saved me hours of studying so thank you

  • @yeetmeat1356
    @yeetmeat1356 3 года назад +31

    Are you going to cover the HL topics as well? That would be a big help, and thanks for giving us this type of quality content!

    • @AndyMasley
      @AndyMasley  3 года назад +15

      I'd like to! I'm still working through the SL topics. Unfortunately each video takes a while so I'm not sure when I'll be done with the HL material.

  • @mandysgainedmomentum9555
    @mandysgainedmomentum9555 2 года назад +1

    I am an IB physics teacher and I like this video. He is an experienced IB teacher although he looks young.

    • @AndyMasley
      @AndyMasley  2 года назад +1

      Skincare routine is key. Thank you!

  • @md_rifat_chawdhury
    @md_rifat_chawdhury 3 года назад +2

    LOVE FROM BANGLADESH. PLEASE MAKE MORE VIDEOS ON PHYSICS . YOUR TECHNIQUE IS REALLY GREAT.

  • @bautistabaiocchi-lora1339
    @bautistabaiocchi-lora1339 4 года назад +6

    Exactly what I was looking for, thank you sir.

  • @vandal3603
    @vandal3603 2 года назад +3

    Hey man, thanks for making this video, physics is alot harder than I anticipated, so vids like yours helps me out a lot.

  • @yabool2001
    @yabool2001 Год назад +1

    Man. It's awesome! Not overdone like many other movies.

  • @RinaNewhouse
    @RinaNewhouse 2 года назад +3

    Hi Andy!
    Your level of teaching is superb! I, in all honesty, learn the most from YOU! One thing, though: I believe the answer to a_c (time stamp: 13:48), is supposed to be 5.94E-1 m/s^2, or 0.594 m/s^2, assuming all previous answers to be correct, would it not? I calculated it twice, once on my calculator, and once again on Desmos, and both gave me the answer of 0.593609625668.
    Would you wanna quickly double check?
    Other than that super minor thing, I cannot thank you enough for posting these lessons for all of us to learn from. You are single-handedly getting us through our physics classes.
    Best,
    Rina

    • @AndyMasley
      @AndyMasley  2 года назад +1

      Yes you're correct! I made a mistake in that section

    • @AndyMasley
      @AndyMasley  2 года назад +1

      And thanks so much for the kind words, so happy the videos are helping!

    • @RinaNewhouse
      @RinaNewhouse 2 года назад +1

      @@AndyMasley It did help! I did well on my first exam because of you!

  • @jfrkhrfn
    @jfrkhrfn 6 месяцев назад +1

    bro literally i cant thank you enough. keep it up man.

  • @danhnguyenthanh7178
    @danhnguyenthanh7178 Год назад +1

    this guy answer my biggest doubt. why acceleration point toward the center? what is the role? why not in the same direction as the velocity?
    timestamp: 3:48

  • @Mouse-qm8wn
    @Mouse-qm8wn 11 месяцев назад +1

    You are a great Teacher please continue making videos 😊❤

  • @Palestine194
    @Palestine194 2 года назад +1

    very interesting lecture sir.....From Pakistan....well explained.

  • @amtulsyed5402
    @amtulsyed5402 2 года назад +3

    Very helpful and concise! Thank you!

  • @simsambros
    @simsambros 2 года назад +1

    This was the perfect video I could find for circular motion

  • @Opticsport
    @Opticsport 3 года назад +2

    my fav so far, thanks alot Mr. Masley

  • @Mrvicoloco666
    @Mrvicoloco666 2 года назад +3

    Hey ANDY, greetings from Ecuador, you just saved some my first classes. I was struggling a lot about how to introduce the important concepts of UCM. Master!!!

    • @AndyMasley
      @AndyMasley  2 года назад

      So glad to hear this was helpful!

  • @joudi.505
    @joudi.505 8 дней назад

    idk how but this 14 min is better then the 2hours lec
    thank u thats help me alot ✨

  • @levychipapa190
    @levychipapa190 3 года назад +1

    wow i just cant believe i just understood 70% of circular motion in jxt a few minutes wooow you dope man

  • @peter3900
    @peter3900 3 года назад +2

    Thanks so much really found this helpful even though im not an IB student

  • @sobky6378
    @sobky6378 2 месяца назад +3

    If I somehow pass this test tomorrow I’m gonna name my child after you

    • @AndyMasley
      @AndyMasley  2 месяца назад +2

      Please send updates

    • @sobky6378
      @sobky6378 2 месяца назад +2

      @@AndyMasley I think I survived, I’ll introduce you to Andy Masley jr when he’s born

    • @AndyMasley
      @AndyMasley  2 месяца назад +2

      Big day for me

  • @jamesluc6506
    @jamesluc6506 Год назад +3

    Your video is so great. I am in the middle of my May Physics Sl exam. I am sad for finding your channel late but also happy for finding it before my final exam. You explain it so well (much better than my teacher). I am pretty sure all your student get a level 7. Just wonder do you have some IA topic recommandation material that could be shared if you still have it (I know you have left teaching). Thank you for the great content.

    • @AndyMasley
      @AndyMasley  Год назад +1

      My advice for the IA:
      1: A good IA is often a middle school-level experiment with high school-level analysis. You don't need to do something crazy, just a simple experiment with a clear independent and dependent variable and a pattern that's either linear or that you can linearize.
      2: It's often helpful to look through the IB physics equations and find one that has two variables that you can test. As a very simple example, you could look at F = ma and measure how the acceleration changes when the same force is applied to different masses and rearrange the equation to be a = F(1/m) where a is the dependent and m is the independent variable. Working backwards like this from an equation to an experiment can make it easier to find something you can linearize and analyze in the data analysis section.

    • @jamesluc6506
      @jamesluc6506 Год назад

      @@AndyMasley Thank you so much for your helpful suggestion. I have another quick question, who will mark our IA? I have heard two statement where one says that the teacher marks your IA and one or two IA of your class will be sent to IB to be reviewed and they will decide to increase/decrease the mark of the IA marked by your teacher. And another one states that the teacher only gives you the predicted mark, the IB will review and gives you the final mark. The reason I asked it is because our teacher clearly tells us if we choose a SL topic, is it at most about level 5 and he always suggest us to choose hl topic ot outside the syllabus of IB, so I am concerned if he will be the person to give us the final mark for IA. Thank you very much!

  • @arindomchakrabarty2254
    @arindomchakrabarty2254 2 года назад +1

    Concepts, explained in a simple way.

  • @zh-vu7zc
    @zh-vu7zc 2 года назад +1

    Best Explanation. Appreciate it ❤️💐

  • @gloryeruka2501
    @gloryeruka2501 2 года назад +1

    What a great video 😲 thank you so much sir!

  • @DingusSquatfordJr.
    @DingusSquatfordJr. 3 года назад +2

    His explanation is nice and clear compared to my professor.

  • @Archie1981
    @Archie1981 7 месяцев назад +1

    Very well explained❤

  • @sabaalameer100
    @sabaalameer100 Год назад +1

    you made so easy to understand it

  • @moamr8002
    @moamr8002 Месяц назад +1

    Thank you man iam from Egypt 🇪🇬

  • @cloudy7817
    @cloudy7817 2 года назад +3

    my physics teacher cant teach for shit. thanks to u I (probably) wont fail my test lol.

  • @hoanggiabaotran9025
    @hoanggiabaotran9025 Год назад +1

    Great video, but I have a question regarding the Example Problem 1! The formula booklet stated that a = v^2/r = (4 x π^2 x r)/T^2, and in the video you used v^2/r to get a = 4.641. But technically, in the given variables, you already have r and T, so would it not be easier if you just substitute everything inside (4 x π^2 x r)/T^2? That is what I did, however I ended up having a = 4.626 instead. Could you help me verify what went wrong? Because essentially they should be giving the same answer.

    • @AndyMasley
      @AndyMasley  Год назад

      You're correct that those formulas are equivalent to each other. Ultimately physics has many formulas that can be rewritten based on convenience. F = ma could also be F = m(Vf -Vi/t) if the variables called for it. Our answers are so close that it's possible that I just rounded incorrectly!

    • @AndyMasley
      @AndyMasley  Год назад

      I might have used a slightly less exact number for pi, like 3.14 instead of 3.1415926 etc.

    • @hoanggiabaotran9025
      @hoanggiabaotran9025 Год назад +1

      @@AndyMasley I see. Thanks for replying!

  • @MikeStallings2023
    @MikeStallings2023 Год назад +1

    Outstanding teacher. What is "IB"? These lessons are valuable to people like me who have no clue what IB is. And this is very hard to google.

    • @AndyMasley
      @AndyMasley  Год назад

      Thanks so much! IB stands for "International Baccalaureate" it's a specific physics curriculum that I was teaching at my school

  • @danmike2305
    @danmike2305 2 месяца назад

    Very well spoken 👏

  • @zh-vu7zc
    @zh-vu7zc 2 года назад +2

    Sir , Do you have any videos on banking angles of road?

    • @AndyMasley
      @AndyMasley  2 года назад

      Yes! Here: ruclips.net/video/94krMSdxA48/видео.html

  • @harunosakura9798
    @harunosakura9798 3 года назад +4

    sorry I only have a question that why delta 0 = 2.pi ( 8:58) ?
    and thank you so much, I have learned this lesson for at least 15 times ( included learning from my teacher and internet ) and I still don't understand till I find yours. Its just too easy to understand, and the way you put all of the base-knowledge in just 14:01 video is just so amazing, it really helps me a lot.
    I have subscribed your channel after only 5 minutes watching yours, and hope that you will make more great video, especially 10 grade physics cause I'm at grade 10 now ^^
    hope you will answer my question soon.
    have a nice day !

    • @AndyMasley
      @AndyMasley  3 года назад +2

      So happy it's helpful! Delta theta is 2 pi because that's how many radians one complete circle is. If you need help reviewing radians use this: www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:trig/x2ec2f6f830c9fb89:radians/e/degrees_to_radians

    • @harunosakura9798
      @harunosakura9798 3 года назад +1

      @@AndyMasley omg thank you so muchhhhh

  • @jawaduddin1160
    @jawaduddin1160 2 месяца назад +1

    Hey there,first of all loved ur video...can u plz explain me what did u mean by net force

    • @AndyMasley
      @AndyMasley  2 месяца назад

      I have a video explaining it here! ruclips.net/video/K4wTddNMVSQ/видео.html

    • @jawaduddin1160
      @jawaduddin1160 2 месяца назад

      @@AndyMasley thanks man❤️

  • @vd4538
    @vd4538 8 месяцев назад

    Hi Andy, thanks for all your efforts in helping us all. I just had a small doubt for the second example problem... By using the formula I was getting 2 π x 149,600,000 x 10^3/ 365 x 24 x 60 x 60. Which was giving me the answer of 29,806 m/s. However you got the answer of 2.98 x 10^5 which is 298,000 m/s. I just wanted to ask if I went wrong in the calculations anywhere or was the displayed answer a typo? Thanks again.

    • @neotiwari3772
      @neotiwari3772 7 месяцев назад

      It is 2.98 x 10^4 m/s, he probably made a typo

  • @budderrrr4855
    @budderrrr4855 2 года назад +4

    you deserve my real teachers salary

  • @nsfw9087
    @nsfw9087 2 года назад +2

    I'm a little confused in example 2, isn't the earth's orbit around the sun not in uniform motion? (Kepler's law) orbit's shape is an ellipse, not a perfect circle.

    • @AndyMasley
      @AndyMasley  2 года назад +3

      Correct! It's actually an almost-perfect circle, the ellipse is usually exaggerated in diagrams, but it's technically not uniform circular motion. I find it has enough of the same properties as uniform circular motion (centripetal force and tangential velocity) that it's a useful example to explain UCM, but it's technically not perfectly uniform.

  • @abel_kidus
    @abel_kidus Год назад

    Thanks for making me understand the concept.

  • @cartoonic6039
    @cartoonic6039 Год назад

    I have a very simple but question.
    Why doesnt the object collapse into the point.
    Since the centripetal force is an acceleration is increasing with time it should get to a point where its high enough to pull the object towards its centre.
    For example:
    The electron in an atom if not for its stationary state it should be pulled towards the nucleus since the proton and nucleus attract but what keeps it moving in a circular path is the fact that they have fixed energy called stationary States so they can't lose energy.
    But objects in the real world dont have fixed energy level so what keeps them in circular path?
    Another example is that if we change the mechanics occurring on the body interms of force, The centripetal force will be the F=m×a but converting the objects tangential velocity into force its F=0 since it has no acceleration.Resolving the 2 forces the object is supposed to move towards the center so why does it still move circular

  • @nadirenuryasar2729
    @nadirenuryasar2729 8 месяцев назад +1

    example 1 should be 4626N since you shouldn't round up 11.7809... to 11.8

  • @iqrajabbar5287
    @iqrajabbar5287 Год назад +1

    V v v v v v nice....❤

  • @Mrabosaleh4ever
    @Mrabosaleh4ever 4 года назад +5

    Thank you

    • @nikolasolakov1232
      @nikolasolakov1232 4 года назад +1

      @@AndyMasley no he's actually right, after staring at it for a good 30 minutes and solving i saw that it is actually correct and its not 10^5 but 10^4

    • @JenniferRokks
      @JenniferRokks 3 года назад

      @@nikolasolakov1232 how?

    • @amznani2023
      @amznani2023 3 года назад

      @@nikolasolakov1232 how???

  • @akankshabhatt3357
    @akankshabhatt3357 2 года назад +1

    Thankyou so much for this video, was trying to make sense of this fromone of my mcat books and it just wasn't clicking.

  • @teguhgumilar6868
    @teguhgumilar6868 5 месяцев назад

    Hi , I am a physics teacher, can you tell us what application/software to make animation on your slides? Thanks

    • @AndyMasley
      @AndyMasley  5 месяцев назад

      Apple Keynote! Explained here ruclips.net/video/hW7vr8Tbsrg/видео.html

    • @teguhgumilar6868
      @teguhgumilar6868 5 месяцев назад

      @@AndyMasley would you like to share your slide to use ? thanks

  • @JoséAntonioBottino
    @JoséAntonioBottino 2 месяца назад

    In a Uniform Circular Motion, the linear speed (tangential speed) v remains constant.
    If the object makes n revolutions (cycles) in a time t, then it travels a distance s
    s = 2 • 𝜋 • r • n
    where n is the “number of revolutions”, n is dimensionless, n has unit rev/rev = 1.
    Since v = s / t, then
    v = (2 • 𝜋 • r • n) / t
    Since v = ω • r, then
    ω • r = (2 • 𝜋 • r • n) / t.
    This implies that
    ω = (2 • 𝜋 • n) / t
    If ω = 2 • 𝜋 • f, where f is the frequency, then.
    2 • 𝜋 • f = (2 • 𝜋 • n) / t.
    This implies that
    f = n / t
    or what is the same, the frequency f is the number of revolutions (cycles) per unit time (usually seconds).
    The unit of f should be
    (rev/rev)/s = Hz = 1/s
    equal to the number of revolutions per second [nrps = (rev/rev)/s, if the custom is to be maintained], and not in revolutions per second (rps = rev/s).
    The unit hertz (Hz) replaced the unit cycles per second, which was actually the number of cycles per second.
    Given that the period T = 1 / f, then
    T = t / n.
    Since the period T is the time it takes for the object to complete one revolution (one cycle), then the unit of T is:
    s/(rev/rev) = s
    equal to seconds per number of revolutions (second per number of cycles).
    As
    ω = θ / t
    and θ is the number of radians, θ is dimensionless, θ is measured in rad/rad = 1, that means that ω must be measured in
    (rad/rad)/s = 1/s = s^(-1)
    and not in rad/s.
    It is understood that in the formula
    ω = 2 • 𝜋 • f
    the unit conversion is
    1 (rad/rad)/s = 2 • 𝜋 • (rev/rev)/s
    so
    1 (rad/rad) = 2 • 𝜋 • (rev/rev).
    There the 2𝜋 allows us to go from “number of revolutions” (rev/rev) to “number of radians” (rad/rad).
    I will highlight the difference between the unit of angular speed, which seems to be 1/s and the unit of frequency which also appears to be 1/s. They are different. Hertz is number of revolutions per second (nrps) while angular speed is the number of radians per second (nrad/s, stretching the notation a bit).
    I will leave another comment where I show how to obtain the formula
    s = θ • r
    and what the variables represent.

  • @charleskoripamo7488
    @charleskoripamo7488 4 месяца назад

    Is it wrong to say the direction of the force on the object changes, therefore the direction of acceleration changes?

  • @Booooscared
    @Booooscared Год назад +1

    u absolute madlad

  • @berserkjr6154
    @berserkjr6154 2 года назад +2

    👍 ty for good videos

  • @motorcorp_0073
    @motorcorp_0073 3 месяца назад

    Perfect Video

  • @dullahanan4371
    @dullahanan4371 4 года назад +1

    I have a question in uniform c.m net force should constant

    • @AndyMasley
      @AndyMasley  3 года назад

      Yeah usually we assume the net force is constant. If the net force changes but the radius and mass stay the same, that implies that the velocity changed, so the circular motion is no longer uniform (at one speed).

  • @edinsonorlandodoradodorado9101
    @edinsonorlandodoradodorado9101 3 года назад +1

    Man, you are awesome, congratulations

  • @isoheilhsni
    @isoheilhsni 4 года назад +1

    This video was awesome
    Super helpful 👍👍👍👍

  • @yinkak3921
    @yinkak3921 2 года назад +1

    Doesn’t the formula for tangential velocity assume that there is no tangential acceleration?

    • @yinkak3921
      @yinkak3921 2 года назад +1

      Nvm just realized the title says uniform circular motion

  • @danielcendales1984
    @danielcendales1984 2 месяца назад

    I'm a little confused. w is in rad/s, and Vt = w*r, so Vt is in rad*m/s?

  • @amznani2023
    @amznani2023 3 года назад +2

    ok but how did you get the 2.98 x 10^5 m/s in example 2?

  • @Linhkinhbrods
    @Linhkinhbrods 3 месяца назад

    i can't understand the proof for the centripetal acceleration formula.

  • @maggiiuwu3022
    @maggiiuwu3022 2 года назад +1

    ur a king

  • @OscarSL
    @OscarSL 8 месяцев назад

    You had Vt's order of magnitude as 5, even though it should have been 4. (In example problem 2)

  • @yanyaZhao
    @yanyaZhao 6 месяцев назад

    May I ask why the time is 16 seconds.

  • @islamdowidar1930
    @islamdowidar1930 2 года назад +1

    Amazing

  • @jabbedcrab
    @jabbedcrab 2 года назад

    Correct me if im wrong, but when calculating Vt in the last example problem, the answer is actually 2.98x10^4, i kept getting the wrong final answer with 10^-5!!

  • @madhyapradesh8841
    @madhyapradesh8841 2 года назад

    Wow thank you so much sir

  • @karlalerma4231
    @karlalerma4231 3 года назад +1

    I need help :( so I have a problem " a 2.0 kg object is attached to a 1.5m long string and swung in a horizontal circle at a constant speed using a centripetal force of 192N. What is the speed of the object?" I'm very confused I looked up vids but can't find one for my scenario:(

  • @jamesmatheson9624
    @jamesmatheson9624 Год назад

    We need to investigate adding multiple rings aounrd the first ring and using smaller and bigger balls. In the rings to change the force to fully understand how the forces are changing

  • @zahraaalhadi4451
    @zahraaalhadi4451 3 года назад +1

    You channel is a real treasure (:
    but I wish you could download the slides you are explaining as pdfs

  • @nadirenuryasar2729
    @nadirenuryasar2729 8 месяцев назад +1

    example 2 is also wrong vt=2.98x10^4m/s

  • @suraphelendalu4070
    @suraphelendalu4070 3 года назад +1

    Thank you so much

  • @mahlanesophonia3080
    @mahlanesophonia3080 3 года назад +1

    THANK YOU SO MUCH

  • @sarahkim9546
    @sarahkim9546 3 года назад +1

    You are really good.

  • @alirazanasir5992
    @alirazanasir5992 Год назад +1

    Thank you

  • @vinayguduri2163
    @vinayguduri2163 3 года назад +1

    thank you very much sir it helped me a lot😁😁😄

  • @Mutabaruka-8
    @Mutabaruka-8 3 года назад +1

    This is really helpful.

  • @leylay1447
    @leylay1447 4 года назад +1

    Thank you this was very helpful!

  • @paulduggar5888
    @paulduggar5888 3 года назад +1

    Mr. Masley thank you so much i think i can get an A tmrw bc of u i didnt know UCM until just now

  • @joshuankrumah3532
    @joshuankrumah3532 3 года назад +2

    that what i was looking for

  • @blackhand441
    @blackhand441 9 месяцев назад

    Why is tangential velocity 2πr/T ?
    I thought it would be zero since there is no displacement 😢

    • @AndyMasley
      @AndyMasley  9 месяцев назад

      It's a poorly named term that the IB uses, tangential speed would make more sense! You're exactly right and the IB is just a little lazy with this variable

    • @blackhand441
      @blackhand441 9 месяцев назад

      @@AndyMasley Thank you for your reply

  • @basesixty6739
    @basesixty6739 Год назад

    tangential velocity for last question should be 2.98*10^4

  • @desisagreat1961
    @desisagreat1961 3 года назад

    Sir thanks so much. Please keep it up and do the exercise and examples

  • @shamelsinha1626
    @shamelsinha1626 3 года назад +5

    Ur the reason I ditched my textbook and no longer attend online class!!!