I caught chicken pox in the late 80s when I was 12 years old and it hit me really hard. I was essentially bedridden for two weeks. My family didn't have cable, so during the day my only TV options were soap operas and The Mechanical Universe on PBS. I didn't understand all of this at that age, but when I got to high school and took calculus and physics, it all came flooding back, almost making me into some kind of mathematical Jason Bourne. I'm sure the experience of binging on this show played a big part in me becoming an engineer.
Wow stickyfox you became an engineer due to this show.that is a fine story.by the way I saw this show fairly a lot back in the late 1980's to but I was in my late teens,five to six years older then you were.
The swimming pool diving scene at 3:30 was shot at the old Industry Hills Aquatic Center. The diving scenes from "Back to School" was filmed at the same pool.
1. What was one of the great mysteries of physics regarding gravity?All bodies fall with the same costant accelerartion. 2. What 2 objects are dropped together in a vacuum near the beginning of the video? A penny and a feather. 3. What 2 objects were dropped simultaneously on the moon to demonstrate Galileo’s findings? A Feather and a hammer. 4. State Galileo’s Law of Falling Bodies: All bodies regardless of their weight fall at excaytly the same rate once the effective air resitance is removed. 5. According to Galileo, the distance fallen is proportional to which numbers? 1 unit of distance in the first time in the row 3 unit in the second time in a row. 6. Define instantaneous speed: 7. How does an object’s acceleration change during free fall?
I not able to continue my education beyond the 6th grade. However, after trying to follow along with this series, in part anyway, I am rarely compared with the poorly educated. Thank you, CALtech
Can someone explain (simply) to me why in a very very large vacuum constant acceleration from gravity (of a very large object) would not lead a falling object to fall faster than light? What prevents that?
Even if I have the force of gravity acting on an object in a VERY tall vacuum chamber long enough to mathematically achieve the velocity of "c", Einstein's physics (theory of special relativity) tells me (us) the object would gain mass before achieving "c"; in fact, it would achieve infinite mass before reaching the speed of light. The faster it goes, the heavier it will get...
@@JasonMayes There are a lot of things that happen as an object approaches 'c', like mass increase and time/distance dilation. It will happen to the feather and the hammer basically equally. There really isn't any noticeable effect until you get close to c, so our intuition kind of fails us, and we have difficulty imagining it. It also requires so much energy that we can never see it on any macro level.
@@JasonMayes One thing came to mind, there's a concept that we are always "moving" at the speed of light. That is our speed through time is directly related to our velocity in space. If you are stationary, time moves forward at its maximum speed, and if you are at the speed of light, your movement through time is 0. Look up the Lorentz factor on wiki, you can see that as you approach c, time dilation sharply raises. But at 0 to 0.1c, there is no meaningful change. (0.1c is 18,600 mi/sec or 67 million mph).
I just recently have been watching this show on youtube for the first time since I last saw it on PBS in the late 1980's(and in color to).I have always rather liked the use of the amusement park in this episode to explain the law of falling bodies!
@29:02 - I am used to acceleration of gravity, a, being about 10 meters per second, t, and the formula being 1/2 at². It was strange to hear that the rate was 5 mps. I guess it depends on what formula is taught.
Esse segundo episódio foi muito bom , conseguiu ensinar a lei da queda dos corpos de uma maneira muito interessante e convincente , ao mesmo tempo mostrou um pouco de cálculo de derivadas de maneira simples . Eu percebi o uso de produtos notáveis , propriedade distributiva e fatoração de polinômios no vídeo , coisas que se aprende no ensino fundamental .
De acordo com a Lei da queda dos corpos de Galileu , um corpo cai com aceleração constante , com velocidade proporcional ao tempo de queda e cai uma distância proporcional ao quadrado do tempo de queda .
Terminal velocity in our atmosphere is arounf 120 mph (wiki) this can be increased by streamlining the object. Radiation decreases as the square of the distance from the source. That velocity of a falling body increases as the square of the time from the start was a profound discovery. Now if we only knew what gravity is. Thankfully it will always obey Newton's laws. Thankfully also laws, equations and derivatives have been worked out by genius for the common man to use,
Can someone explain me how galileo knew the constant c is numerically 16? And although the constant acceleration for gravity is 32ft per sceond squared, why the distance reached after first second is just 16ft? I think it should be like 32ft , 32+32=64 ft, 32+32+32=96ft but by formula it gives 16ft, 64ft, 144ft. I missed something?
First, think that "c=ab^2" is the same as "c=a(b^2)". So, you have the equation "s(t) = c(t^2)". If you make t = 1, you have "s = c(1^2)", then "s = c". With that in mind, you should conduct a simple experiment to find the distance a body falls in one second. The video says the distance was "16 feet, just a little under 5 meters". Maybe you will find a similar result if you conduct the experiment.
It missed to capure the story of how The idea of acceleration,its formal logical intuition became institutionalised and vocalised in the accademic world. What is the etymology of the word-" acceleration"?
Gravity is an acceleration not a force And it is constant. (GM÷r^2)= (h÷t^2) h = height (where from the object falls) t = time taken by the object to reach the ground. But there is a problem Suppose, h = 383400km How much time will take the object to reach the earth? What will be the gravity experienced at this height?
I think most people intuitively understand gravity pulls down on everything equally without the help of galileo or newton. no one is going to think a small rock will not drop just as fast as a big rock. and they know a feather doesn't drop as fast because it is less dense and the air they can feel all around them holds it up a bit.
But if Einstien is correct and the equivalence principle is correct, then a body the jumps off a roof is no longer under the effect of gravity. They are now an initial reference frame. It is the earth that is moving upward towards the body accelerating 9.8 meters upward.
Thanks a lot, really extraordinarily structured series, YET one huge pedagogical blunder, you guys missed out on the steps HOW to arrive at s(t) = ct^2...
Actually they didn’t miss it. Galileo conducted series of experiments on rolling ball on inclined plane. He calculated distance fallen at each interval of time and he noticed that the distance fallen increases as time increases and he observed that distance fallen actually follows odd numbers.
that was interesting but i was hoping for a complete explantation instead of just calculus , by taking different forces , resistance and air into consideration
we have always observed objects falling in air resistance that we got used to it, but in vacuum there is no resistance hence for us it feels its a hammer(or any heavy object on which effects of air resistance is minimal). So every object seems like hammer...
That's a great way of thinking about Newtons law f=ma. Imagine your on the moon and you drop a hammer onto one foot and a feather onto the other they will both hit at the same time at the same speed, but the force of the hammer due to its mass will hurt like hell unlike feather.
C is a constant. Remember all objects falls at the same rate. And after one second of falling, the body will have fallen 16 ft, or ~5 m. C is that distance (16 ft).
distance proportional to time squared,is this the accurate way to read it ?? why i feel it is vice versa, as one unit of time met squared unit of distance.
As you insert values into t (t=1, t=2, t=5), you will increase the distance s to the square root, as s=c t ^2. So t=1 => s=c 1^2=c and t=2 => s=c 2^2=4c and t=5 => s=c 5^2=25c. So that as the time t increases by one, the distance s increases by that time squared. Its more helpful to look at the equation, rather than the linquistic explanation. The mathematics work out, and are quite simple, but the explanation can be hard to understand and lead to misunderstanding.
The logic behind all objects falling at the same rate in a vacuum is rather simple and obvious. What is a 10 kg object other than ten 1kg objects stuck together? Is it logical that sticking objects together would make them all individually fall faster? Obviously not. The logic can be extended all the way down to subatomic particles. Would each particle fall faster just because they're stuck together in one mass? Here's something odd about gravity though. How can objects stay in orbit without constant acceleration being applied? Centrifugal force is the result of force being applied, not just something coasting on its own inertia. Objects should logically be pulled toward the earth and their speed around the planet increase until it hits the surface, like a skater pulling their arms in. How can simple inertia counter the pull of gravity? It doesn't matter if you attribute gravity to a force or a curvature of spacetime. Either way, something that causes movement toward the earth should require constant force to counter, but it apparently doesn't. That's an unsolved mystery of gravity.
Log-antilog relative-timing ratio-rates Perspective Principle in e-Pi-i instantaneous infinitesimal coordination-identification positioning system. We require the ancient music-math proportioning of Scaling to make sense of the Measurement Problem reciprocation-recirculation @.dt Singularity-point here-now-forever pure-math Perspective. The Singularity-point Fluxion-Integral instant flow of relative-timing convergence-divergence in flash-fractal i-reflection Superspin Superposition-point synthesis of vertices in vortices=> Feynman type representation of Euler's e-Pi-i sync-duration Unit Circle modulo-geometrical chemical bonding of plasma shell-horizon Newtonian Fluxion-Integral "Corpuscles". The Physics of Galileo's Musical Mathematical Measurement reciprocation-recirculation potential.
Firstly, there is no such thin as vacuum, you can call it sub pressure, but no vacuum, absolute Vacuum is impossible. Secondly, there is that little thing called terminal velocity. And thirdly instant uniformed acceleration is impossible cause yet another little thingy called inertia. Put this all together using square root is just dumb idea.
Terminal velocity is an equilibrium point between forces, secondly the concept of universal gravity itself is self evident, thirdly it was poincare and Einstein that continued To unlock what gravity is.
I caught chicken pox in the late 80s when I was 12 years old and it hit me really hard. I was essentially bedridden for two weeks. My family didn't have cable, so during the day my only TV options were soap operas and The Mechanical Universe on PBS. I didn't understand all of this at that age, but when I got to high school and took calculus and physics, it all came flooding back, almost making me into some kind of mathematical Jason Bourne. I'm sure the experience of binging on this show played a big part in me becoming an engineer.
Wow stickyfox you became an engineer due to this show.that is a fine story.by the way I saw this show fairly a lot back in the late 1980's to but I was in my late teens,five to six years older then you were.
I believe you will find that an extended period of childhood convalescence was the beginning of many STEM careers.
It’s sad to see what the PBS is broadcasting now these days…
Very sophisticated graphics/animations for 1985, IMHO...
17:15 is my personal favorite
I love how this sneakily tricks the audience into doing calculus.
I watched this series 19 years ago. It's a towering achievement as important as Carl Sagan's Cosmos and Jacob Bronowski's The Ascent of Man.
Kenneth Clarke's Civilisation is also great, its about art.
The swimming pool diving scene at 3:30 was shot at the old Industry Hills Aquatic Center. The diving scenes from "Back to School" was filmed at the same pool.
1. What was one of the great mysteries of physics regarding gravity?All bodies fall with the same costant accelerartion.
2. What 2 objects are dropped together in a vacuum near the beginning of the video? A penny and a feather.
3. What 2 objects were dropped simultaneously on the moon to demonstrate Galileo’s findings? A Feather and a hammer.
4. State Galileo’s Law of Falling Bodies:
All bodies regardless of their weight fall at excaytly the same rate once the effective air resitance is removed.
5. According to Galileo, the distance fallen is proportional to which numbers? 1 unit of distance in the first time in the row 3 unit in the second time in a row.
6. Define instantaneous speed:
7. How does an object’s acceleration change during free fall?
You are an absolute G
THANK YOUUU
Thank you for uploading this series, Caltech. This is gold!
David Louis Goodstein (April 5, 1939 - April 10, 2024)
I just looked up the professor....he just recently died.... RIP 🙏🏽
@@philipsankot8003 😧 RIP!
I not able to continue my education beyond the 6th grade. However, after trying to follow along with this series, in part anyway, I am rarely compared with the poorly educated. Thank you, CALtech
thank you caltech, your teaching style is really great
Here in 2021 and this stuff never gets old.
Can someone explain (simply) to me why in a very very large vacuum constant acceleration from gravity (of a very large object) would not lead a falling object to fall faster than light? What prevents that?
Even if I have the force of gravity acting on an object in a VERY tall vacuum chamber long enough to mathematically achieve the velocity of "c", Einstein's physics (theory of special relativity) tells me (us) the object would gain mass before achieving "c"; in fact, it would achieve infinite mass before reaching the speed of light. The faster it goes, the heavier it will get...
@@tw4982 but in a vacuum heavy object and feather fall at same acceleration?? What am I missing? Appreciate the comment though thank you.
@@JasonMayes There are a lot of things that happen as an object approaches 'c', like mass increase and time/distance dilation. It will happen to the feather and the hammer basically equally. There really isn't any noticeable effect until you get close to c, so our intuition kind of fails us, and we have difficulty imagining it. It also requires so much energy that we can never see it on any macro level.
@@jboy55 thanks
@@JasonMayes One thing came to mind, there's a concept that we are always "moving" at the speed of light. That is our speed through time is directly related to our velocity in space. If you are stationary, time moves forward at its maximum speed, and if you are at the speed of light, your movement through time is 0. Look up the Lorentz factor on wiki, you can see that as you approach c, time dilation sharply raises. But at 0 to 0.1c, there is no meaningful change. (0.1c is 18,600 mi/sec or 67 million mph).
The animation looks amazing! This is awesome!
and this is from 1985 too.
I just recently have been watching this show on youtube for the first time since I last saw it on PBS in the late 1980's(and in color to).I have always rather liked the use of the amusement park in this episode to explain the law of falling bodies!
Great to have these available
@29:02 - I am used to acceleration of gravity, a, being about 10 meters per second, t, and the formula being 1/2 at².
It was strange to hear that the rate was 5 mps. I guess it depends on what formula is taught.
I imagine galileo happy in heaven when he saw the experiment done by the astronauts.......
Absolutely well done and definitely keep it up!!! 👍👍👍👍👍
Esse segundo episódio foi muito bom , conseguiu ensinar a lei da queda dos corpos de uma maneira muito interessante e convincente , ao mesmo tempo mostrou um pouco de cálculo de derivadas de maneira simples . Eu percebi o uso de produtos notáveis , propriedade distributiva e fatoração de polinômios no vídeo , coisas que se aprende no ensino fundamental .
animations are so good and i never thought that we can do diffrentiation like that we were just taught formulas in our school
It’s interesting to me that the SI units are not being used in the explanations.
The USA does not generally use SI units.
Most of ph1 is in cgs
Great series. Was on a lot here in Chicago.
De acordo com a Lei da queda dos corpos de Galileu , um corpo cai com aceleração constante , com velocidade proporcional ao tempo de queda e cai uma distância proporcional ao quadrado do tempo de queda .
At @14:25
Why is the change in distance and change in time zero?
Put it on 1.25 or 1.5 to save time
Nooooooooooooo! Boredom builds character!
Is very fast to understanding.
Love the way this video explains everything ❤
Why do we subtract s(t) from s(t+h)? Same question for subtracting v(t) from v(t+h)
Same doubt..and at 12:44 why c = 16
S(t+h) and s(t) are two different positions. We subtract to get the differens, the distance between them.
This series if very comfy
this is really great, thanks for uploading
Where do I buy tickets to the concert for this music!?!?!?
Terminal velocity in our atmosphere is arounf 120 mph (wiki) this can be increased by streamlining the object. Radiation decreases as the square of the distance from the source. That velocity of a falling body increases as the square of the time from the start was a profound discovery. Now if we only knew what gravity is. Thankfully it will always obey Newton's laws. Thankfully also laws, equations and derivatives have been worked out by genius for the common man to use,
Who in their right mind would thumb down this classic?
The window washers @ 1:45
Can someone explain me how galileo knew the constant c is numerically 16? And although the constant acceleration for gravity is 32ft per sceond squared, why the distance reached after first second is just 16ft? I think it should be like 32ft , 32+32=64 ft, 32+32+32=96ft but by formula it gives 16ft, 64ft, 144ft. I missed something?
First, think that "c=ab^2" is the same as "c=a(b^2)". So, you have the equation "s(t) = c(t^2)". If you make t = 1, you have "s = c(1^2)", then "s = c". With that in mind, you should conduct a simple experiment to find the distance a body falls in one second. The video says the distance was "16 feet, just a little under 5 meters". Maybe you will find a similar result if you conduct the experiment.
What is the rate of change of acceleration?
What is 'c'?
To derive by 0is always it's numeric of the derivative(from)
Watching it in 2022 from India feeling thankful to the creator..
It missed to capure the story of how The idea of acceleration,its formal logical intuition became institutionalised and vocalised in the accademic world. What is the etymology of the word-" acceleration"?
It would be greater if we had a full 1/2 hour of just Goodstein giving a lecture.
David Louis Goodstein (April 5, 1939 - April 10, 2024)
I just looked up the professor....he just recently died.... RIP 🙏🏽
Gravity is an acceleration not a force
And it is constant.
(GM÷r^2)= (h÷t^2)
h = height (where from the object falls)
t = time taken by the object to reach the ground.
But there is a problem
Suppose, h = 383400km
How much time will take the object to reach the earth? What will be the gravity experienced at this height?
I mean I get it but the they added to much affects when explain how they changed the equation with other ones and that got confusing.
I think most people intuitively understand gravity pulls down on everything equally without the help of galileo or newton. no one is going to think a small rock will not drop just as fast as a big rock. and they know a feather doesn't drop as fast because it is less dense and the air they can feel all around them holds it up a bit.
Makes sense, gravity effecting all atoms the same regardless of the ridged system it's in.
now this is me wondering in a new land of wonders
8:40 10:06 11:01 12:40 13:05
Ótimo vídeo ❤
But if Einstien is correct and the equivalence principle is correct, then a body the jumps off a roof is no longer under the effect of gravity. They are now an initial reference frame. It is the earth that is moving upward towards the body accelerating 9.8 meters upward.
What an interesting observation you've made.
Thanks a lot, really extraordinarily structured series, YET one huge pedagogical blunder, you guys missed out on the steps HOW to arrive at
s(t) = ct^2...
Actually they didn’t miss it. Galileo conducted series of experiments on rolling ball on inclined plane. He calculated distance fallen at each interval of time and he noticed that the distance fallen increases as time increases and he observed that distance fallen actually follows odd numbers.
that was interesting but i was hoping for a complete explantation instead of just calculus , by taking different forces , resistance and air into consideration
At 6:04 I'm not so sure the "feather" acts like a feather when it lands. Same for the hammer (acting like a hammer that is).
we have always observed objects falling in air resistance that we got used to it, but in vacuum there is no resistance hence for us it feels its a hammer(or any heavy object on which effects of air resistance is minimal).
So every object seems like hammer...
So, if you were on the moon, if a feather fell on your foot or a 25 lb anvil, it would feel the same?
bigpardner no.. Because force=mass times acceleration ...mass of hammer is more than that of the feather. So you feel more when hammer hits you
I agree. I was posing the question in response to other comment saying "every object seems like hammer".
That's a great way of thinking about Newtons law f=ma. Imagine your on the moon and you drop a hammer onto one foot and a feather onto the other they will both hit at the same time at the same speed, but the force of the hammer due to its mass will hurt like hell unlike feather.
David Louis Goodstein (April 5, 1939 - April 10, 2024)
I just looked up the professor....he just recently died.... RIP 🙏🏽
C is confusing me. What is C? the distance that is covered in the first second?
C is a constant. Remember all objects falls at the same rate. And after one second of falling, the body will have fallen 16 ft, or ~5 m. C is that distance (16 ft).
6:00
okey but how did they figure out the constant c at the first place !
I Googled that. Interesting.
Roses are red
Violets are blue
The psychedelic proof you seek
Starts at 15:52
I loved it
distance proportional to time squared,is this the accurate way to read it ?? why i feel it is vice versa, as one unit of time met squared unit of distance.
As you insert values into t (t=1, t=2, t=5), you will increase the distance s to the square root, as s=c t ^2. So
t=1 => s=c 1^2=c and
t=2 => s=c 2^2=4c and
t=5 => s=c 5^2=25c.
So that as the time t increases by one, the distance s increases by that time squared. Its more helpful to look at the equation, rather than the linquistic explanation. The mathematics work out, and are quite simple, but the explanation can be hard to understand and lead to misunderstanding.
The bounce must be studied
Wish I had seen this when I was 14
The logic behind all objects falling at the same rate in a vacuum is rather simple and obvious. What is a 10 kg object other than ten 1kg objects stuck together? Is it logical that sticking objects together would make them all individually fall faster? Obviously not. The logic can be extended all the way down to subatomic particles. Would each particle fall faster just because they're stuck together in one mass?
Here's something odd about gravity though. How can objects stay in orbit without constant acceleration being applied? Centrifugal force is the result of force being applied, not just something coasting on its own inertia. Objects should logically be pulled toward the earth and their speed around the planet increase until it hits the surface, like a skater pulling their arms in. How can simple inertia counter the pull of gravity? It doesn't matter if you attribute gravity to a force or a curvature of spacetime. Either way, something that causes movement toward the earth should require constant force to counter, but it apparently doesn't. That's an unsolved mystery of gravity.
The derivative is atomic weight of process
amaazing
Log-antilog relative-timing ratio-rates Perspective Principle in e-Pi-i instantaneous infinitesimal coordination-identification positioning system. We require the ancient music-math proportioning of Scaling to make sense of the Measurement Problem reciprocation-recirculation @.dt Singularity-point here-now-forever pure-math Perspective.
The Singularity-point Fluxion-Integral instant flow of relative-timing convergence-divergence in flash-fractal i-reflection Superspin Superposition-point synthesis of vertices in vortices=> Feynman type representation of Euler's e-Pi-i sync-duration Unit Circle modulo-geometrical chemical bonding of plasma shell-horizon Newtonian Fluxion-Integral "Corpuscles". The Physics of Galileo's Musical Mathematical Measurement reciprocation-recirculation potential.
This is what evey child should watch 😘
@14:30 She was, in fact, not fine.
very cool
If Oresme worked out gravitational acceleration in the 13th century why is Galileo given the credit ?
It is funny how long intros used to be.
The feather has preceptor tual power and bounce
Intro song please
$6.95 for a large pizza, I'm getting at least three
nice
It is prime
history of the word gravity?
Great
Did I hear Elon musk in the background at the end?
That not including the spirit
❤❤❤
cool
hola
TWCP
Oh please, please..someone check on the baby!!! 😱
bruh what the fuck is the intro, and why does it feel so long
❤👍
KRS
What a drag>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
WASSA
i like men
jordan`jojo`siwa
Firstly, there is no such thin as vacuum, you can call it sub pressure, but no vacuum, absolute Vacuum is impossible.
Secondly, there is that little thing called terminal velocity.
And thirdly instant uniformed acceleration is impossible cause yet another little thingy called inertia.
Put this all together using square root is just dumb idea.
Terminal velocity is an equilibrium point between forces, secondly the concept of universal gravity itself is self evident, thirdly it was poincare and Einstein that continued To unlock what gravity is.
The universe is not a machine. Why mis instruct every generation about he unknown nature of reality?
What reality? Physics doesn't claim to hold ultimate truth but rather a model to analyze it based on our own perceptions.
Cause 0$1t+hπ
Absolutely well done and definitely keep it up!!! 👍👍👍👍👍