What's going on everyone? Sam here with late in sports cards ripping 10 box Tuesday 10 box absolutely impeccable photo mixer number 142 random team style. Here's a look again at your random results again. Sorry that the stream cut out a little bit like during the random. I did upload the random to YouTube so you'll be able to see the entire random take place and we went through everything again so it should be good to go. As always you can find these on the website under the results tab as well as the link that's in chat. So good luck everybody. Did I upload those? I did not. Here I'm going to upload those to the website really quick. My bad before we get started. Sorry Donnie. Not uploading the random. I won't let it happen again I promise. Don't fire me please. Please not fire me. There's your guys' results. All right let's do we'll do elite first. Uh yep 22 Donner's elite football. That's true for Joey. For you Joey I had a way with breaking absolute that night. That was unreal dude. Unreal. Unreal. There's there you go Sarver. Kenny Pickett. Pen pals auto. Boom. On a card. There you go. Congrats John. John S. in YouTube. We'll nag that for you John. Congrats buddy. There you go. Bass and bass. First pack. Austin Eckler to 99. I'll be a good eBay listing for you. We're a good hole in Steelers in the Super Bowl of five years. I don't think that's coming any time soon. Sarcasm is always good to say. There's Trevor Lawrence to 75 for the Jags. Spellbound. Back to the future. Cadarius Tony to 149 for the Giants. Nice one there. That's Jerome Ford eight out of 24 for the Browns. I don't think that's really saying much to be honest Shane because I don't think either of those teams are going to win a Super Bowl anytime soon unfortunately. You may win one before the Ravens but the Ravens aren't going to win one for a while and neither of the Steelers. I think Steelers have a very chance of winning before the Ravens. No. Hassan Haskins to 399. If the Ravens lose them are yes. If the Ravens keep them are no. Are you ready for a rebuild here? Probably. Rookie on deck Kyle Hamilton. Bass. Andrew Booth Jr. to 999. McChubb playmakers. There's Craftsman Clyde Edwards-Hallaire on the Jersey Card not numbered going to the Chiefs. Fields playmakers. Bass. Segwan Barclay to 399. Well I'm not going to 19 contenders next I think. It's got to be something big coming out of 19 contenders eventually. Justin Herbert. Oh, sorry. Did you have a lot though? Oh we got talked. I was kidding. It's like crying. I might. The Marvin Leal to 999. After all it was my third birthday. That's true. It's my hat year. I think it's my third birthday though. Bass. Where are my presents? You just get to the top of it for me. That's your present. Happy birthday buddy.  What an awful birthday.  Oh my god. I would have rather had no presents. It's some near whites in 999 for the raiders. It's surrounded by toddlers. It's a daycare here. It's a daycare. It's surrounded by toddlers. That's what Sean always said like when it was you guys uh you Bryson and Alex. You know he's be like it's like you guys would like be laughing at something and Sean's like let me guess they're getting fussy because they just woke up from their nap. He's like their parents pay so much money to put them in daycare here. It's an expensive daycare. There's Miles Sanders to 399 for the Eagles. I'm just earning my dad's money back by being here. Exactly. That's an expensive daycare for him. It is an expensive daycare. Now you're not even getting paid. You're paying to be here. Sean would always go like I've raised my children. I'm not doing it again. Sean Askin to 75 for the Titans.  I'd rather have gotten no presents than had that. All right one box of 19 contenders. Good luck everybody. So you're not wrong. That was a pretty bad birthday. Like the whole like I'm staring at my toddlers thing does maybe you think of the part on Spaceballs. Hero watch them. Who's the toddler in this building anyway? Nice Byron Murphy for the Cardinals. Nice one there. Congrats Arizona. Starting corner over there. So when I do the dice roll it'll just go for both contenders boxes. Okay. Four showed me that. Oh nice. Julian Love for the Giant 16 out of 25. Champ ticket. Nice one there. Jay Love before Jordan Love. I hope so. I hope so David. That wouldn't be fire. Yay. Yes. Yes you do. This is my life though. My life. Just plastic sleeves and cardboard and pictures of men. There is Juan Thornhill. Nice one there. Congrats on that. Chiefs. He's losing it man. I've been losing it for 30 years. Yeah dude. If you want to be a loopy this is where you are loopy. Redemption. We've got David Montgomery. Rookie Super Bowl ticket. I think that's a one on one. I think so. Hold on a second. Super Bowl ticket variation RPS. Hold the phone here. I know the Bears have been to the Super Bowl in a while. There's football. Hold the phone. Hold the phone. Everybody hold the phone here for a second. Of course it is. It's a one on one. Yep. One of one. Yeah. Wow. Super Bowl ticket. One of one. David Montgomery. It did expire. I think that was Tom or Tommy had the Bears. Yes. Tom C. Congrats Tommy. I mean give it a chance. See if they will get it in for you but that's pretty massive dude. Pretty massive. Don't write Bears on it. I do want to take a picture before you write Bears on it. That's cool. Later Kenzie. Okay cool. Thank you. You can throw it in a mag and then I guess un-mag it after. I'll just leave it outside the mag. Fair. It's a redemption after all so I can't get it damaged. All right so one two three top four five six bottom this will go for the entire or both contenders boxes both 19 and 21. It's gonna be a five.  That'll go with McKeel Harry. That's kind of wild. We just pulled a Super Bowl ticket out of 2019 contenders. That card's been stuck. Yeah. That card has been stuck in a case for years man and we just freed it and I hope they have it man. If not you'll probably get some decent credit for that. Is the content is the duels or the other contender not vertical or are they both horizontal? No, they're both up and down. I think it's both. They're both horizontal. There's one contenders I feel like that's vertical here it is. I forget which I agree. I know which one you're talking about. Yeah. Oh you know you could just put it in the mag and then just stick note it on the back. Kentucky to your contenders Kyler Murray. Well I want to take a picture of it. That's why. You bought. What?    There's nice James Connor. 25 out of 99 championship ticket but that was gonna be an auto. Got trolled there for a second. Thanks.  It doesn't feel good does it? It's not. I got points coming up in this one. Random to all at the end only 250 and random to everybody. Levion. All right I'll take it out of the bag. All right let's do no huddle now. I'm not afraid to hit a child. Jose no huddle. Good luck. That's actually kind of insane dude. That's kind of wild. Glass mosaic. Case it. Joe. Burrow. Go into the bangles. Holy cow dude. That's Barry G. Congrats Barry. That's sick. That's nasty. Hey look Sam it's you. Oh get that away from me.  I hear all back flip. I gotta start saying that again Elucis. I forgot about that. Thank you. Go you better. You should just do a backflip. Do an IRL backflip yeah. You need to train. I hurt myself. Introductions breeze saw. There's a Michael Carter purple to 50. Just want some tiktok video where it's like a five step tutorial. You can do it in 30 seconds. Must be legit. Tiktok's telling me to do it then yes. Romeo Dobbs disco. Disco to shot Bateman. Okay we're seeing that. It's like a person like doing a tutorial for a backflip. I don't know. Well I do this move then do this move and then combine them all together and then you do backflip. So first everyone. It's like okay. Danny Gray. Like yeah I'd like to see that one work. I'm not someone who's built to be doing backflips.  That is Larry Johnson. Nice one there. That's going to the chiefs on the no huddle. Trayvon Walker Mosaic. What's up Caden? Tristan Worfes Mosaic. That should be your New Year's resolution. We'll do a backflip by the year. Yeah. Yeah you have the end of the year. That's like 11 months. I'll start training for that in December 31st. Silver, Kyler Gordon. It's only been using your time. Joe Montan. I'm learning how to do a backflip. It's not a good use of my time. Why not? I'm hurting myself. You know how many people you can impress? Like you go to the car show and be like hey would you give me that if I did a backflip right now? To our Chase Thayer Masters. It's actually not a bad point. Jair Alexander. $50 for me to do a backflip for you. No many cards are you walking out with for free? Yeah honestly. Start hustling people. Blue Dair card $75 for the Raiders. $24. Dude imagine the YouTube clicks. True. I get one of ones by doing backflips. I'm on Ross St. Fram to $75. Car show dealers hate this guy. Mosaic. Not Mosaic. Disco. John I think you'd give himself a concussion. I'd break my neck probably before anything.  Yeah there's Chris Godwin Silver and Cup of Cup on the Mosaic. Probably not off the top of my head to be honest Kaden. Let's do 21 contenders. Number to 10. Seven of 10. Anthony Schwartz, Trey Sermon. I'll just I'll do a dice roll for this one right now. One, two, three, top four, five, six, bottom it's a little lower numbered so it's going to go three and going to go to the top with the browns. One to the top. Interesting. That's probably wicked short printed. Erin Robinson for the Giants. Nice one there on the blue. That's one of those short prints. The blue. Sharp Bateman. Kaden's probably worth between a dollar to a million dollars. Somewhere in that ring. That was helpful. That was the point I had no idea. Lance Supernatural. Jason Pinnock. Let's go into the Jets. How do you find out how often a retired player is like signing? You just got to see how many sets they're in or if they sign like a contract with Penini then you'll know that MVP contenders Russell Wilson. So it's just like researching essentially. Yeah that's a big thing. We're keeping up to date with the product. Yeah because like recently like Patrick Peterson, nice Pat Pete, 21 out of 25 playoff ticket for the Cardinals. That's cool. That's out of last year's contenders. That's nasty. That's one of the vet tickets. Pat Pete. Well I mean contenders is a little different than Leaf but what was I going to say? Like recently like Kevin Garnett signed with Penini again to start signing autographs. So a lot of times when they sign a new contract with Penini or Topps or whatever it might be they'll generally start being in more products. Does that like, does Penini and Topps just have that on their website where they're like, oh sign this deal with us? Usually I'm like, I usually just find it on social media. I'll see like somebody, somebody else will know. I have no idea where to find it. Darren Hall for the Falcons. I'm pretty sure Montana has like an exclusive deal with Leaf.  That is the Ami Brown on Card Auto for the commanders of the year contender Kyle Fitz. Dude the glass of the Zag looks pretty slick. It's clean. Yeah it's really clean. Even though it's Joe Burrow it's still clean. It kind of would kind of be cooler if they they had like a mosaic parallel or it's like the mosaic silver instead of just the silver because that would make more sense but yeah it's still pretty cool. Let's do XR, 22 XR. Let's see if you get one of my schticks for this one. Oh boy. You can pull the right card you will. Now we didn't but that's kind of nasty. That's gonna be George Pickens rated R on the acetate short print. Nice one there, John with the Steelers. Nice Pickens. Rogers 2199. Derek Stingley the 249. George Carl Aftis Rookie. Coraline Sutton and Daniel Jones. We have Sam Howell 70 out of 75. Rookie Excellence. Nice one there. You need to be 18 years or older to get the rated R. No kids alone. Facts. There's Christian McCaffrey to 249. Calvin Austin to 75. And Traylon Burks Rookie. Bass and bass. Got Kennedy Brooks at 35 out of 49. For the Eagles. And John Mechie, Jumbo Jersey 55 out of 75. All right let's do Mosaic Choice now. He's right there for him. Oh those three cards. Yeah pretty much. Sweet. You have to mag a little bit. Joe Naimeth Silver. Deontay Johnson-Mose. We've got Kway Walker. They forgot to put the auto on. Nice. Yeah. This autograph is guaranteed. Anna Kway Walker. What autograph is guaranteed? There's no autograph on there. We'll send the empty box and wrap with the Steelers. Sorry about that Steelers. Come on. No I will not sign it. At least it is guaranteed. Yes it is guaranteed. Hang on we can put a sticky note out and see him signature and then they can just take the sticky note. That is Josh Allen to 88. Terry Slate Jr. to 88. Good god. Cameron Hayward to 88.  Bricks are over. There's uh what did I say? Did I say Steelers or something? I meant Packers. We're going to the Packers. Yeah. Packers. My bad. Kyle Phillips for the Titans and Matt Corral for the Panthers. Sam this is the only time your autograph can be certified by Benini. Oh great. You're throwing it away. Great. Oh is every Kway Walker like that? That's interesting. Origins. You want me to throw this in the red. Sure. I mean why not technically? It's supposed to be technically. Justin Fields to 299. There's Saquon Barkley to 199. Kway just took a look at him and sent him back. That is DeAndre Hopkins and Amon Ross St. Brown. They didn't pay him enough. He was like nah. Got Traylon Birx 18 out of 199. That's enough of me dawg. Nah. Followed by A. Zemir White. On-Card. Rushing Stars 10 out of 25. Nice one there for the Raiders. And Garrett Wilson. rookie jersey auto going to the Jets. There you go Brett. Congrats Brett. Nice Jets hit for you buddy. That's due absolute. All right let's see a Kaboom come out of here. Why not? Why not us? Why not now? Kaboom. Stoppin' us but us Donnie. Exactly. Is that a Russell Paul? Who said that? I don't know. Yeah someone's definitely said that in the past. Oh glass. That'll work. First up by Storm is Christian Watson. Jared Goff. There's a glass redemption. One of the short printed inserts that is of Jameson Williams. Go to the Lions. Congrats Detroit. Nice one there. Nice. He's going to be a huge role next year. Yep 100% agree with that. Lewis C9 to 275 for the Vikings. And Alec Pierce 56 out of 99. Triple rookie jersey auto. Him and like Amonora have a good chance to be one of the better duos. Yeah 100% I agree with that. Probably top 10 to be saved. Tyler L. Geer rookie 9 out of 25. Stud. Fantasy Stud right there. Yeah. Matt Jones and Damian Harris. Fantasy Stud for this guy right here. There's Mark Andrews 24 out of 99. I'm sorry would you finish? Not last. Did you were you over 500? No. Going to the Ravens. And nice one here. Bob Creasy 7 out of 50. Going to the Dolphins. Congrats Dolphins. Cool one there. A little bit of damage on the bottom right corner. Send an empty box and wrapper with the Dolphins buff. Sorry Dolphins. Next year when you need to make a trade don't come to me. That actually ended up helping me out. Yeah I bet it did. I started Christian Kirk for a while. I bet it did. I started Christian Kirk like every game after that. But AJ Dillon wasn't garbage. Was he garbage for you or no? I didn't really keep up with him. Like toward the end when it didn't matter anymore like yeah but I guess he was a hitter miss. Who can hit a golf ball further? Me or Donny? Donny. That is Jordan Davis to 50. I'm not even gonna joke about that. We don't need the that's not really a question. Yeah that's not a question at all. I'll be the first one to admit that's not a question. Basin base. That is Kyle Pitts on the quad 30 out of 99. Tools of the trade. Tools owed to trade for the Falcons. And Crystal Labe 14 out of 20. Nice one there for the Saints. Rats on that Saints. Wow. The one thing I can confidently say. Spectra 2022 Spectra. That I'm the best at in this building is probably hitting a golf ball. Yes 100%. Nobody is even close on that one. Maybe Caleb is close. I haven't seen him play yet. Can't make that assumption yet. No I can go up and hammer the ball still Joshua. I still hit the ball far but Donny's just good. I can keep it in play. Yeah. That's Frank Gore. 299. You started getting better like as it went on. Yeah. Oh yeah. Trayvon Walker rookie Spectris 99. That's not bad actually. Elucis. There's Kenneth Walker. That's a nasty patch on the meta. Three color jumbo patch for the Seahawks. You're gonna like this one. 5 out of 15. How about a Brent Selick for the Eagles. Oh nice. That's sick. A little throwback. Yeah. Eagles legend. Elucis to give you an idea. My three wood goes about 240. That's Tate Johnson 250. One of 50. Yeah you got your driver like in the 300s I'd say. It's honestly probably less than that. 35 out of 75 is Justin Fields. Depends if I can get rule. Oh very true. Yeah downhill or anything. Yeah. And another nice one here. 71 out of 75. Kenny Pickett. Two colored RPA. Boom. Going to the Steelers. Nice one there. Bratz Pittsburgh. Get that in a mag for you. Interstellar Darnell Mooney to 60. There you go John. Not too bad man for that Steelers spot. Bass. We've got to 75. Marcus Colston on the championship gear. That's kind of nasty. And 125. Carson Strong. Four colored RPA for the Eagles. Sorry. Here he goes. And last pack of Spectra. Then we go on to Impeccable Foto. Hyper John Lynch to 75 for the Buccaneers. Romeo Dobbs Rookie. Got 11 out of 15. Pierre Strong Jr. Help here you want to come out here. Patriots. And Jalen Tolbert. Two colored RPA. Like the Texas wedge about 40 out. Open green. Grab the eight iron with a firm punch. Oh yeah. Oh yeah. That's a big move dude. People love doing that. My buddy in college used to do that all the time. Well yeah because once you get the ball rolling the quicker you get the ball rolling the easier it is. Yeah exactly. Because like you can kind of guess like what you know how the terrain is going to take the ball. 22 Impeccable first off the line. So we'll have our first off the line parallel. We'll have probably a bar card. We will have a bar card. And yeah. Oh that's a nice one. Going to the Bengals. Smart Chase. That's Jersey number one of eight. Nice one there. Congrats Bengals. That's kind of nasty. Keenan Allen to 75. Aaron Rodgers to 50. We've got going to the Ravens. David Ajabo three out of 35 on the Sticker Auto followed by a Trent McDuffie four out of 10 for the Chiefs. Nice one there. And Chris Long Super Bowl Auto for the Eagles.  And Cooper Cup 22 out of 35 on the Indelible Inc. For the Rams. Nice one there. That is on card. And last pack of the break. Good luck everybody. That is Wanda Robinson seven out of 19 on the Silver Bar Auto. Nice one there. Got seven out of 19. Congrats on that Giants. Nice Wanda. We'll get that into a Mac for you. Let's do a quick points random random to everybody here. All right. Good luck everybody. Going to roll the dice. Whatever team is on top after seven times. We'll get the points. Good luck. One two three four five six seven Colts going to the Colts. Congrats Colts Colts Virginia Tech. I was going to say I was going to ask you if you're a big Chuck Clark guy who's played at Virginia Tech. It's never mind who else went there. One Thornhill go there with Sea Virginia Cavalier. We've got Pierce Strong Jr. Patriots. Markies Colts and Saints. Kenneth Walker Seahawks. Justin Fields Bears. Mark Andrews Ravens. That's Kyle Pitts Falcons. That is Traylon Burks for the Titans. John Match. Yeah. John Matchy Taxons. Clyde Edwards Hilaire Colts. We had Autos. They're going to be Trent McDuffie Chiefs. David Ajabo Ravens. Cooper Cup Rams. Chris Long Eagles. Brent Selick Eagles. Carson Strong Eagles. Jalen Tolbert Cowboys. Chris Olave Saints. Bob Greasy Dolphins. That is Alec Pierce for the Colts. Jameson Williams Lyons. Garrett Wilson Jets. Xamir White Raiders. Quay Walker. Yeah. Packers. Kennedy Brooks Eagles. Sam Howell for the Commanders. Diami Brown Commanders. Darren Hall Falcons. Pat Pete for the Cardinals. Jason Pinnock Jets. Aaron Robinson Giants. Larry Johnson Chiefs. Juan Thornhill. There he is for the Chiefs. Julian Love Giants. Byron Murphy Cardinals. Canary Stoney for the Giants. Can I see the Redemption as well there? Next to you. The Magma. Thank you. We had two Kenny Pickets.  Nice ones there for the Steelers. Wandaille Robinson 7 out of 19. Going to the Giants. On the Silver Bar Auto at an impeccable photo. We had a David Montgomery Rookie Super Bowl Ticket Variation. RPS one of one. Going to the Browns. I mean the Bears, not the Browns. The Bears. And Glass Mosaic Joe Burrow. Going to the Bengals. Fitting. I would pull this card with me on his body and the thumbnail. You know what? There is also. Yep. That'll do it for the break guys. Thanks again for the fill. Next up, personal.


Alright guys, first item, system of particles. So if ever you find, if ever difficulty in physics, this name will come first. System of particles. So why students find this chapter difficult? Because there are multiple things here. In this chapter they have a number of things. So we have this habit as just mugging up or trying to do it last minute of the exam preparation. So what happens is that if lot of information is there, you do not understand the link between the information or you do not do enough problem practice. Then you will get confused in this chapter which comes up when you might be still confused in the other chapter because of lack of problem practice. This chapter will double it if you do not pay attention. If you ever miss, let's say 30 minutes of the class, you are daydreaming about something or someone, you are thinking about something. And you do not pay attention. The entire chapter is gone. This is like a chain. Why I am telling you all this? Because the basic chapters are over now. So these will form a basics. And then here is a chapter studying a special case about the motion. For example, you always have patient and some velocity. It is moving like this. You never consider that while moving, for example, masses and a pulley system, you draw free body time, you get the answer and you feel happy about it. But then going forward, you are considering multiple particles together. For example, if there are like zillion molecules in this room, you are not going to study one molecule at a time. What is this molecule doing? It becomes senseless. So you need to understand how collective behavior is what? As a collection of all the particles, what are they doing collectively. So this is what this chapter tells you and this is closer to the. So we have learned the basics from special cases. Now we are making it slightly generic. And when it comes to each and everything is a system of particles. This theory itself, multiple point masses, you can put small, small, small masses, you can go to the atomic level. The atom is, let's say, smallest particle of this. You can say electron and this thing also. So there are zillions, millions of those particles are there of which the TV is made up of. So this is one entire, it will look like a single object, but this is actually a system of particle. But this is a special kind of system of particle. There can be system of particles like this cap and the pen. This is also a system of particle. When I am studying cap and pen together, two particles I am studying together. So this is also system of particles only. But they are moving. The motions are not point, will move along with that point. There is a definite relationship between these two. So their motions are related in some way. So studying this kind of system is easier because knowing the motion of one particle, you can predict the motion of the other particle. But if system of particles have loose particles like this, then you can predict knowing one particle's motion. This kind of system of particle which doesn't get deformed or there are some relation, this is called rigid body. So we are going to study a special kind of system of particle which is a rigid body later on. Right now I am going to just introduce a concept of system of particle. How to study any system of particle? Whether it is rigid body or collection of particles like this, they are moving dependent on each other. I think we have already started studying the system of particles. Can't be theory is one. We have studied the entire, all the gas molecules together, what they do. So we have already started studying the system of particles. But here we are going to study it in a different way. We are going to, we are trying to apply the neutral second law of motion. Then we are trying to find out the velocity of the system as a whole and so on. So this is slightly different but we have already started understanding the system of particles. Whereas have we studied the system of particles as in multiple particles together? System of particles here, right? You have found out that we have already studied the system of particles. And flutes, what is flutes? Is it a single particle? No, multiple particles are moving. So even flutes system of particles, so we have already started studying system of particles. First time we are studying it exclusively. So when we are studying system of particle exclusively, we don't know anything. So we will start from the scratch, fine? So when we were, suppose I study, let's say particle. Like you remember, what is the first thing about the motion that we should study? It's a point object. In kinematic, no, see that is different. You study and displacement. But before even, that is an assumption. How you start studying it? The first one is the location. Which location will you tell? Location means starting from 0, 0 to 2, 0 and 2, 2 and 0, 2. So you can't tell me that, right? Location is a coordinate, right? So first thing we are going to learn here is how to get that system. Suppose there are multiple masses scattered everywhere, how can a system, right? So please write down location of a system. Center of mass. Have you heard of the center of mass? This is called center of mass. It's a point. Have one mass here, which is 1,082 masses, only these two masses. So please write it down. I'm using the content, okay? I have my own way of. So don't match it up with, okay, this we have learned, this we haven't learned. We cover everything when the chapter gets over, then you can see. Yes. So the location is closer, this is more on the location, right? So rather than finding, suppose this is my coordinate axis, this is the other coordinate axis, x and y, let us say. And the position vector of this mass is r1 and position vector of that is r2. I am trying to find the position vector of center of mass, right? So position vector of center of mass will be the weighted average so that the position vector comes closer to the average mass. So it will be m1 into r1, m2 into r2 divided by m1 plus m2, okay? Does it make sense? Suppose m don't count the number of numbers you have. Similarly here you are finding the weighted average, now the weight of the position vector r is its weight, getting it? So this is the center of mass location and this is for only two particles. Suppose there are multiple 10 particles then going to the formula m1 r1, are you getting it? So I have particles and then there will be infinite particles also. So do you know this? This summation, summation of mi of mi. This is the center of mass location. Make sense of these particles. So let us try to see whether we can find, given the x and y coordinates of 1000 kg in 1 gram, what will be the x and y coordinate of the center of mass, okay? So if the position vector x i cap plus, similarly that is what I do, r, c, u and vector will be x center of mass, i y center of mass. This will be equal to summation of xi i cap plus y i j tan divided by summation of mi, getting it? So this I can write as summation of mi xi divided by summation of mi i cap plus summation of mi y i divided by summation of mi j cap. So what will be x center of mass? You just equate the i component, y component also. So x center of mass will be x1 plus m2 x2 and so on divided by m1 plus y center of mass will be equal to m1 y1 like this divided by the total mass of the system, getting it? Is it straight forward? Okay, so you must know what is x center of mass, y center of mass, because we are going to use this question. Do this question. This is 1 kg binary square. The silent of the square is 1 units. You need to find out the center of mass of this entire system. The system has 5 particles. Simple. 1 into 2 into 1 plus 3 into 1 plus 4 into 0 plus 5 into 0.5 divided by 15, some of all the... And similarly y c n. Y c will be what? 1 into 1, 2 into 1 plus 3 into 0, 4 into 0. 5 into 0.5 divided by... Isn't it simple calculation? Identifiable locations. Particles. Point masses. Are you getting it? It is a big circle which is not located.  Then I will say that this m1 into different point masses. Get it? If I divide it into small point masses, then this will give me that summation equal to capital M1 mass. m2 let us say mass m2. So m1 x1, m2 x2 and so on divided by m1 plus plus m2 x2 divided by m1 plus m2. Now tell me what is the first term in the numerator? This is what? 1 into center mass of m1's location, m2 into x2 divided by m1 plus m2. This will be total center of mass. So if there is a bigger mass, you multiply its center of mass plus m2 into its center of mass and so on divided by... ...points to be noted. It is uniformly distributed. Then the center of mass is location. You can see that x is equal to m1 x1 divided by m1 plus m2 and so on. If mass is uniformly distributed, all the components are distributed. If mass is uniformly distributed, n of symmetry, portion of mass, the intersection is center of mass. Because it should... If mass is uniformly distributed, it will not have to be made up of whole... ...where the center of mass, which is not regular shape and size. Then I go because there will be infinite particles, time of symmetry to help me out. Then how to find the center of mass location? The summation will integrate that. And this is how it will happen. So x center of mass is summation of m1. Now I am saying that suppose there is a big mass, a regular shape object. Here up this big mass is there.  The location of dm is x. So the numerator will become what integral of... So first of all it is x and dm. For a particular... Similarly here, this is a formula which you have to solve for different objects. Any doubts? No? Okay, now do one thing. Take a rod. This is a uniform mass distribution rod. Mass is n, length is n. Find out the center of mass using this formula. We know that in the next scenario, the mass locations, but they expect you to do in all the ordinary exams. That's the answer. Because you have not... So you should pay attention here. You should know something complicated here. So integral of s is going from here to here. The masses are distributed as constant. 0 to l, x dx cancels, l by 2. kg per meter. It will be center of the rod. So where... We tell. That into length is the mass of location. It will not be like simple state part. This is my y coordinate.


All right, so if we're going to be able to use the tools that we've developed to study problems with lots of molecules, let's say Avogadro's number of molecules, then we need to know how to take the factorial of large numbers so that we can use them in the binomial coefficient or the multinomial coefficient. So to show why that's a problem, let's think about this example. What is the value of n factorial when n is 1,000? So what is 1,000 factorial? So if you have a calculator nearby, of course, you could try to use your calculator to answer this question. So why don't you go ahead and pause the video for a second and type in 1,000 and find the factorial button on your calculator and see what you get when you do that. So if you've paused and come back, what you found is that when you type 1,000 factorial into your calculator, you get an error. That number is so large that your calculator can't calculate it, can't display it. And the reason for that is if I calculate 1,000 factorial, what that means is 1,000 times 999 times 998 times, et cetera, until I get down to 3, 2, 1, and then I can stop multiplying. So those numbers, this number is like 10 to the third. That number is pretty close to 10 to the third. There's a lot of numbers in a row that are pretty close to 10 to the third. They're not all of that big. But if they were all 10 to the third, then that would get 10 to the third 1,000 times. That's something like 10 to the 3,000. It's not quite that large, but 10 to the 3,000, there's not enough digits in the exponent for your calculator to display that number. So your calculator simply can't display a number as large as the result of that calculation, which is why we can't use a calculator to calculate this problem. What we can do instead is something physical chemists do a lot. And there's a question we can't calculate the answer to. We decided we wanted to ask a different question in the first place anyway. So instead, let's imagine that I want to know what the natural log of 1,000 factorial is. So this is the log of the factorial. So that's the log of 1,000 times 999 times, et cetera, 3, 2, 1. If you remember your log rules, in particular, if you remember that log of a product, a times b is equal to log of a plus log of b. So a log of a product is the sum of the natural logs. So this log of this complicated product is the log of 1,000 plus the log of 999 plus. And so on, down to the log of 3, log of 2, log of 1, right? So that's progress. That's something we can do on the calculator. So all I'm doing is adding together 1,000 numbers. They won't overflow the calculator.  And we'd get a number that the calculator can, in fact, display. That's tedious, of course. We don't want to sit down and add the plus button 999 times in order to find the answer to this question. So we'll find a way around that. Let me point out first that if I weren't doing this for 1,000, if I were doing it for some arbitrary number, then what I'd get is log of n plus log of a number 1 smaller plus. And then keep doing this until I get log of 3, log of 2, log of 1. For any arbitrary n, a more compact way of writing that down, of course, is sum up the log of every number where that number runs from k all the way up to n, log of 1, 2, 3, 4, all the way up to log of n. So that's using summation notation to write down what the log of n factorial is. So that's beginning to suggest how we can use a simpler method to find this answer. The sum of all these logs, let me show you what that would look like if I were to graph it. So here's k in this direction. I'll show what log k looks like in this direction. Log k has that sort of shape. Log of 1 is 0, log of 2, log of 3 are other numbers. So I'm combining log of 1 plus log of 2 plus log of 3. I'm adding those numbers up, and I'm doing that all the way up until I get to whatever number I'm interested in, which has its own logarithm. So another way of writing this sum, the sum of all these logarithms, log of 1 is 0, add to that log of 2, add to that the log of 3, and so on until I get up to the log of n. So I want to sum up the areas of each of these little rectangles that I've drawn that have a height of log 2, log 3, log 4, and so on, and have a width of 1. But we know how to calculate the area under this curve, which is exactly what I've described here. The area of these rectangles is very similar to, not exactly the same as, but very similar to the area under that green curve. That's what we know from calculus is calculating the area under the curve is like doing an integral. So when I say the sum of a bunch of things, letting k range through a range of values, that's an awful lot like, let's say, ln of n factorial is not exactly equal to but is close to the integral of log k. So the sum has become an integral. The value of k is still ranging from 1 to n, except now I say integral of log k dk, where k runs from 1 to n. So all I've done here is I've converted the sum to an integral, kept the integral the same as the inside of the sum, and now I'm integrating over values of k instead of summing over different values of k. And the picture is just there to illustrate that why these are both doing the same thing. It's worth pointing out that in calculus class, the way we initially calculated integrals is using a sum to approximate the true area often in calculus, what you want to do is find the area under the green curve and you approximate it with a bunch of skinny rectangles. In this case, what we actually want is the sum of the rectangles. And we're approximating that with the value of the integral. So this is the approximate result. That's the result we actually want. But now that we've written it as an integral, we can do the integral. That's not integral of log k is perhaps not one that's easily commonly memorized, but it turns out the answer to the integral of log k is k log k minus k. If you want to double check, that's true, and I would encourage you to do this. Positivity right now, take the derivative of k log k minus k. A little bit of simplification happens, and you'll find that the derivative of this quantity is log k, which proves that I'm right in telling you that the integral of log k is k log k minus k. I want to evaluate that in this definite integral between 1 and n. So plug in a capital N. I've got n log n minus n. And from that, I subtract 1 log 1 minus 1. So the logarithm of 1 is 0. So that term goes away. This minus 1 term doesn't go away. There's two negative signs. So my end result is that this is equal to n log n minus n plus 1 after the two negative signs combined. So what I've found is that the log of n factorial is not exactly equal to, but is approximately equal to n times the log of n minus an n plus a 1. And in fact, the only time we're going to use this formula is when n is a pretty large number like 1,000. If n is a small number, 6 factorial, you wouldn't use this formula. You'd work it out by hand or you'd plug it into your calculator. If n is 20 or 50, your calculator can handle it. But when n gets to be very large numbers in your calculator can't handle it, then we're going to use this formula. And if n is a number like 1,000 or much larger, then including this 1 is not very important compared to the n. The 1 is lost in the least significant digits of this number. So we often ignore that 1 because it's so much smaller than n. And if we write that the log of n factorial is n log n minus n, this equation put in a box, that's the expression we call Sterling's approximation. So this is a way of estimating the value of the log of n factorial when we can't get it by direct multiplication or from a calculator. So I can show you an example of how that works. Let's go back to our initial problem. We wanted to know what 1,000 factorial was. And we then changed the problem and said, OK, maybe we'd be happy enough knowing what the log of 1,000 factorial was. So when n is 1,000, the log of 1,000 factorial, according to Sterling, is 1,000 log of 1,000 minus 1,000. So that's easy enough to do on the calculator. We can plug those numbers into the calculator. And we find when we do that, then we get 5,908 points, something or other. So roughly 5,908. What that tells us, log of 1,000 factorial is 5,908. If I really want to know what 1,000 factorial is, all I have to do is undo the logarithm by taking the exponential of both sides, so e to the 5,908. So 1,000 factorial has the value of e to the 5,908. You might now think, OK, that's great. Now all I have to do is go to the calculator and ask what e to the 5,908 is. But then we're back to this problem. e to the 5,908 is a larger, large enough that your calculator can't display it. So don't be tempted to ask your calculator what that number is. What we'd really like to know is e to the 5,908. We're not used to thinking of powers of e. We're much more used to thinking of scientific notation, powers of 10. We'd like to know is that 10 to the what? So I'll tell you that is another one of the log rules to remember is that is 10 to the 5,908 divided by the logarithm of 10. Because that's a formula that I often have to rederive for myself, I'll assume that you don't remember it either. So the trick I used right there was to say, if I have e to the something, and I want to know is that equal to 10 to the something else, I'd like to know what the value of x is. The trick to remember to derive this formula is let's take the natural log of both sides of this expression. So if I take the natural log of e to the a, that's just a. So I'm taking ln of both sides of this expression. So natural log of e to the a is a. Natural log of 10 to the x is x times natural log of 10. So then if I rearrange this equation to figure out what x is equal to if I divide by log 10, so the power I have to raise 10 to get the same thing as raising e to the power of a, that power is a divided by log 10. So that's where I got this result. e to the 5,908 is 10 to the 5,908 divided by log 10. So if I continue with that problem, I find that 1,000 factorial is 10 to the 5,908 over log 10. If I ask the calculator what 5908 divided by log of 10 is, that works out to be 2,566 or so. So in the end, what we figured out is that we can find an estimate for the value of 1,000 factorial. 1,000 factorial is 10 to the 2,566. So a number that is 2,566 digits long, a number with four digits up in the exponent. So it's large enough your calculator can't display it, but we can still on paper derive an estimate for what that number is. And it's important to remember that this is only an estimate. It's wrong by a little bit because of this approximation of approximating the sum with an integral, but it's often good enough for us to do some calculations with. So now that we know how to use Strowing's approximation for calculating large factorials, we can start using that to calculate some chemical properties of real systems.


Welcome to Dispatches from India, a show by People's Dispatch, where we bring you some of the top stories from across the country, what Indians are talking about and the impact it will have on politics, economy and society. First we get into our News This Week section. Five Indian states went to the polls in February and March 2022, we now have the results. The Legislative Assembly elections were held for the states of Uttar Pradesh, Uttarakhand and Punjab in the North, Goa on India's west coast and in the country's northeast Manipur. The BJP, which is the ruling party at this centre currently emerged as the single largest party in all but Punjab. But was this a victory one on the basis of good governance? Or did a campaign of bigotry and hate and targeted welfareism triumph? And India Chakravarthy, Senior Journalist, explains. So it is pretty clear that what we are seeing here is that the BJP is completely in command of the biggest and when I say the BJP, I mean India's ruling party, the Bhaskya Janta Party, who is now widely seen across the world as a right-wing party which is driven by religious nationalism, which is the majoritarian nationalism of Hindus and English, which is the majority religion as most of your viewers would know. It is perceived as that, although the BJP itself that says that we are not that, but widely even by voters it is perceived like that and what these local state elections have done. The fact that the BJP has swept India's largest state in terms of the number of seats it brings to the parliament house at the centre, it determines almost 15% of the seats in India and more often than not decides who's going to be the prime minister in the country. The fact that the BJP has swept it, retained it and the fact that it has the biggest other national party, the oldest national party, Indian National Congress has been wiped out virtually off the board of every state that it existed in tends to show us that the BJP's rule is now almost unchallenged. It's become the party of rule. It is the dominant party around which all other issues will be, all parties will have to react and the opposition is fragmented and in some senses this is great for those who believe in a unitary system, a centralized authority and strong state, but those who believe in pluralism, more dialogue oriented democracy, definitely they should be worried about it. However, a few things to know. As I said, one of the elections was in India's largest state called Uttar Pradesh and in Uttar Pradesh we have seen in the past there used to be a lot of fragmentation of the vote. For the first time we are seeing a two-party system emerge or a two-race horse emerge in Uttar Pradesh and that could hold a lot of interest later on because the gap between the first party which as I said is the ruling Indian National Party, the Bhartya Jamta Party and the next which is a regional party has reduced. So in two years can that gap be surmounted? In another few years can it be surmounted? That's the question to watch out for which will have significant impact on future governments whether these will be coalition between regional forces or the central national party continues to rule. The other point that I'd like to make is that Indians have seen that unemployment is a huge problem in India. Employment is actually reduced in absolute numbers compared to the fact that population has grown, employment has reduced and this started well before COVID hit India. It started in 2017 and it has continued and we have not recovered from that yet it does not seem to affect the Bhartya Jamta Party, India's national party because it follows a two-pronged strategy. One is a religious nationalism, a nationalism which brings the majority together. It believes in that policy. It picks up on that and it builds on that. It's critics say that it is a politics of polarization, anti-minority polarization. As I said the BJP will never accept it so the support the BJP will not accept it. At the same time it also follows the policy of handouts and feeding of subsidies to the poorest people. No jobs mind you but just a government sustenance of their subsistence level which means they just are able to have two meals a day. It is made cheap for them. Some facilities are given to the poorest and that has allowed them to subsist which has become extremely difficult. Post reforms, post pro-market reforms in India where the poorest have actually become even poorer. Their growth, their real income has been absolutely stagnant from whereas the rest of India, the top one percent of Indians, top 10 percent of Indians have become very rich. The BJP is able to maintain this tension, get a lot of votes from the poor. So we are seeing a politics in which there is monopoly, the top big business which is getting a lot of concessions from the government in budgets and the poorest are being sustain this. So the money funding comes from big business and the votes come from the poorest of the people. No jobs, no progress, no economic development. This seems to be the politics that we are going to see for the next few years. Still the opposition comes together and there is a certain degree of coordination at that level. Regional elections in India have a particular and particularly under reported impact on women. This cycle, the implication has been exacerbated by the wide-ranging consequences of the COVID-19 pandemic to get a better understanding of the issues faced by women as well as the challenges faced by the people's movements in the country. We spoke to Mariam Dhavali, the General Secretary of the All India Democratic Women's Association, a mass Pan India organization. The impact of the results of the elections that have been declared on 10th of March are going to have a very adverse reaction in our country. We know we are aware that the ruling regime is extremely authoritarian and clams down on any kind of descent. This is going to really hamper building a social, political, economic movement on people's issues. But on the whole, women as a part of the population will have to struggle because the price rise and the issues connected with women's lives are going to worsen. They have made a slew of policies and promises, which we are sure they are never going to keep. The attack on women is also going to increase because in this past seven years, we have seen because of propagating the regressive Manusmuti ideology, women have been targeted in every sphere, right from employment, right from education to even carrying out their day to day responsibilities. The increase in violence on women, the decreasing sex ratio, the women being thrown out of the educational sphere, all this is taking us back into the dark ages and which the BJP RSS very much wants and is propagating. So the days to come are going to be of very severe challenges for us and the Indian population that believes in a secular democratic India will have to come together and the All India Democratic Women's Association is going to mobilize women further and trying to intensify its struggles to preserve the rights of women that we have won all these years through very hard struggles and also in the defense of our constitution and the rights that the constitution gives us. We now move to our in focus section where we take a deeper look at some of the burning issues in the country. For this story, we go to the Kanyakumari district of the state of Tamil Adu where those employed in temples are facing a variety of issues regarding livelihood. These include salary, promotion and retirement benefits. These workers are under the Hindu religious and charitable endowments department of the state government. Ironically, it is the left wing center for trade, Indian trade unions, C2, which has taken up their issue. We bring you this feature on the kind of problems the workers are facing and what they are doing about it. And finally, the Kashmir Valley was known for its beauty much before it was turned into the most militarized place in the world. For generations, people have kept alive traditional art, craft and music including traditional methods of production of daily use items. But the current generation of crafts people are finding it close to impossible to even subsist much less thrive in the economic and political reality of today. These artisans artisans may well be the last of their kind. That's all we have for you today. To read up on more such stories visit our website www.peoplesdispatch.org and follow us on Facebook, Twitter and YouTube. See you next week.


This is the SF Productions Podcast Network. That wonderful TV year, 1991. From the Pop Culture Bunker, I'm Mindy. And I'm Mark. You can check out our audio podcast, How I Got My Wife to Read Comics on iTunes, or on our website, sfpodcastnetwork.com. I've collected TV guide fall preview issues over the years and thought it would be fun to talk about which shows made it, which didn't, and which ones we actually watched. Now I have to give credit to Ken Reid's TV Guidance Counselor Podcast for this idea. Both the TV industry and TV guide stepped back a bit from the overstuffed previous season. Six fewer new shows, while TV guide went back to a single fall TV preview issue. They had four the previous year. So starting on Saturday night, The Turkelsons, NBC, and Oklahoma Family fights off debt after the husband leaves the family. Apparently it's a comedy. Connie Ray and William Shallert star. In the second season, the show was retooled and renamed almost home with the family moving to Seattle. The show also moved from film to videotape while Perry King and a young Brittany Murphy joined the cast. A total of 33 episodes aired. Nurses on NBC, a second generation spinoff with progenitors, the Golden Girls and Empty Nest. The action takes place in the same hospital where Dr. Harry Westin, Richard Mulligan, works. The show was designed as a vehicle for Stephanie Hodge, who played one of the nurses along with Arnisha Walker and Jeff Altman. David Rashi joined the cast in season two. Then Lonnie Anderson came in on the final season as the hospital administrator, at which point Hodge was gone and Anderson became the star. There were plenty of crossover episodes, of course. The Commiss, ABC. Michael Chiklis stars in the Stephen J. Cannell dramedy about a small New York town police commissioner. He's also a family man with wife Teresa Saldana and son Jack, Cack Erickson, Erickson. What a name. That's Cack Erick Erickson. Cack or cash? Oh, cash. It is cash. I think I got it wrong like three times in a row. So a blend of police drama and family issues. John Segan, later Melinda McGraw, then back to Segan, played his lieutenant. The show ran for five seasons. It was originally planned to air on CBS, but a disagreement with Cannell forced the network change. Two TV movies followed the series run. PSI Love You, CBS. This awkwardly named crime drama starred Greg Evigan as an undercover cop and Connie Selica as a con woman. She agreed to also work undercover to keep out of jail. The pair posed as a husband and wife working for Earl Holloman at his detective agency. But it's still a police operation? TV Guide noted that Selica can't pull off a Bronx accent. The show is set in Palm Springs and Sonny Bono, the actual mayor at the time, made appearances. This Glenn Larson production lasted all of 13 episodes. By the way, the awkward show name referred to the PI's phone number 5888 or PSI Love You. Moving on to Sunday, the adventures of Mark and Brian NBC, real-life local shock jocks Mark Thompson and Brian Phelps star in an early reality slash prank show. Well, it worked on radio, but not so much on TV. Despite having the NFL as a lead-in, the show sank and most of the episodes were burned off in the next summer. Eerie Indiana, that's one we recognize on NBC, a bizarre comedy drama from the makers of Unsolved Mysteries starring Marshall Teller as a 13-year-old investigator in a creepy Midwestern town. Justin Shankarow played his buddy. The pair kept running into weird people and events, like a woman who kept her twins stored in vacuumware every night to keep them young. The rest of the family and the town had no idea this was all going on. The show wound up first on the Disney Channel, then Fox's Saturday morning lineup, along with a rebooted series later. The original run was only 19 episodes. Man of the People, NBC. James Garner returns to TV in the show about a grifter that ends up in city council after the death of his ex-wife. He continues scamming while helping his new constituents. Kate Mulgrew played the mayor. This 30-minute sitcom lasted 11 episodes with two more unerred. Garner called the series short-lived and rightly so. Pacific Station on NBC is a Barney Miller pastiche starring Robert Guimet as a veteran cop assigned to a crazy precinct near Venice Beach. Richard Lippertini, Megan Challenger, Tellager, and Rob Liebman played the other cops with Joel Murray as the lead detective. It ran from September to October, then pushed back to December before ending a 10-episode run with three more unerred. Guimet would return to series TV almost a decade later for Sports Night. Rock on Fox. Charles S. Dutton stars as a Baltimore garbage man dealing with his family in what began as a traditional family sitcom. Ella Joyce played his wife with a younger brother, Rocky Carroll, and father, Carl Gordon. As all of the cast were primarily stage actors, the star wanted to move the show to be aired live. After a tryout the previous year, season two aired live each week. This updated show would begin with a monologue from one of the cast speaking directly to the audience. This experiment, the first scripted show since the 50s to go live an entire season, only resulted in a minor ratings bump. Apparently, the actors were so professional, three of them had just completed the stage run of August Wilson's The Piano Lesson that it didn't feel live to the audience, a.k.a. they didn't screw up. The show was critically acclaimed, but never did well in the ratings. I don't think I watched it. No. Herman's head on Fox was a surrealistic sitcom about a Greek chorus of personalities inside the mind of the lead, William Ragsdale, a fact checker for a magazine. He seemed normal on the outside, but there's a constant struggle in his brain. Angel, Molly Hagen, represents sensitivity. Animal, Cann Hudson Campbell, represents lust. Wimp, Rick Lawless, represents anxiety. Genius, Peter McKenzie, represents intellect. Jealousy, Bobcat Goldwaite, and God, Leslie Nielsen, make guest appearances. They all appear in what appears to be a large attic filled with stuff from Herman's memories. In the real world of the show, the Simpsons Hank Azaria and Yarlene Smith play his buddy and a research assistant, respectively. Jane Sibbot played another fact checker who would do anything to get ahead. The show never did well in the ratings, but it did run for three seasons with the lead character dying in a car accident in the final episode. Leif plans for a fourth episode for a season which came from a writer posting on an early BBS message forum involved switching to Sibbot's head with new personalities. That reminds me so much of the Disney movie Inside Out. I wonder if that's where they picked up a shadow of an idea for it. Maybe. On Monday, there were no changes in the schedule that year. Amazing. On Tuesday, we have All Fly Away on NBC, a period drama set in the U.S. south in the late 50s with the main theme being race relations. Regina Taylor starred as a black housekeeper for a district attorney played by Sam Waterston just before his long run-on-law in order. Jeremy London and Catherine Harold also starred. The series became more and more intertwined with the civil rights movement over time. The show won two Emmys and 23 nominations, but was gone in two seasons due to bad ratings. A TV movie wrapped up the storylines. It's often enlists of series canceled too soon. Creators Joshua Brandt and John Falsy had already created St. Elsewhere and would go on to Northern Exposure. Home improvement on ABC. This mega hit came from the give-a-stand-up-his-own-sitcom factory. Tim Allen plays Tim the toolman-tailor host of a cable TV show. He generally acts before he thinks, which gets him into trouble. He's also convinced he can fix anything which results in physical comedy. His wife Jill, Patricia Richardson, and kids played by Zachary Ty Bryan, Jonathan Taylor Thomas, and Terran Noah Smith all watch off to the side. His show within his show includes Richard Karn as Al his sidekick and Pamela Anderson later Debbie Dunning as the tooltime girl. Tim could always ask mostly unseen next-door neighbor Wilson, the voice of Earl Hindman, for family or work advice. The gimmick was that you saw the top of Wilson's head over the shared fence. The kids grew up and moved out over time. People got married, what you usually see in long-running sitcoms. The show ran for eight seasons in the top ten for all of them. It's been running in syndication ever since and can be seen on Hulu and Antenna TV. Homefront on ABC. Another period drama this time dealing really more of a soap opera with G.I.'s returning to Sweethearts who had found someone else while they were gone plus racial and union issues. Kyle Chandler, Mimi Kennedy, Tammy Lauren, Wendy Phillips and John Slattery were just part of the large cast. The show would run for two seasons and won a number of awards for Emmys, a WGA, and a People's Choice. Wednesday we had the Royal Family on CBS. Red Fox returns to TV as a retired mailman ready to enjoy life with his wife played by Della Reese. In what became a TV trope, their divorced daughter played by Mary Ann Ada, along with kids, Silver Gregory, Lauren State, and future Glee star Naya Rivera decide to move back home. Whackiness ensues. Well, not so wacky. Just a month into the series, Fox had a massive heart attack during a rehearsal. Ironic, since his best known role of Fred Sanford faked them a lot. And he died later at the hospital. The death was written into the show, and 227's Jack A. was added to the cast as Reese's half-sister, later changed to her adult daughter. After a promising start in high ratings, the show was gone in 13 episodes with two more unaired. Teach on CBS. Phil Lewis stars as a token black teacher at a boys' boarding school. Colonel Achilles Alicio, who comes up with these names, Joshua Hoffman, Ken Lawrence Johnston, and Jason Christopher played the students, along with a yuppie played by Jack Nosworthy. 13 episodes were produced, but only four ever aired. Sibs on ABC, a sitcom about sisterhood, not to be confused with sisters, with Marcia Mason, Margaret Collin, and Jamie Gertz. Alex Rocco played Mason's husband with the Simpsons' Dan Castellanetta as her ex-boss. Despite the talent involved in front of and behind the camera, James L. Brooks was the exec. The show never caught on. It ran eight episodes of that fall, then three more the next spring, with 12 more never aired. Despite this, there was an attempt to revamp it as related by birth, minus Mason and Rocco. They just ceased to exist while the other characters moved on. The pilot didn't make it to series. Good and Evil on ABC. Susan Harris brought us the story of two more sisters. In this case, Terry Gar and Margaret Witton. Gar's character was the cold CEO of the family's cosmetic empire, while Witton played a sensitive scientist involved with stopping viruses. Their mother, Mary and cell days, still ran the empire, though. Mark Blankfield, Lane Smith, Seth Green and Brooke Theiss were part of this large cast for a corporate soap parody. Blankfield's character was blind, and his physical antics got the network in hot water with the National Federation of the Blind. It was a moot point. Only six episodes aired, with five more were actually produced but never seen. On Thursday, pros and cons on ABC with James Earl Jones is character from Gabriel's Fire Returning. This time in a more lighthearted series, his wrongfully sentenced PI moves to LA, teaming up with another PI, played by Richard Krenna. Bowen's character instantly changed from being dour to almost manically happy, which had to throw viewers. He also married his love interest from the other series played by Madge Sinclair. At one point this show's title was even more of a pun. It was going to be called Bird & Cat. Jones played Gabriel Bird and Krenna's character was going to have the name Cat. 12 episodes and out. Drexel's class on Fox, yet another attempt to make Dabney Coleman who always played sour, unsympathetic roles into a big star. Not sure why the networks ever thought this would fly. He plays a guy with massive tax debt, forcing him to take a job as a teacher to fifth graders. Jason Biggs, Heidi Ziegler, Damian Cagnolotti and Matthew Lawrence played the students while A.J. Langer and Brittany Murphy, there she is again, played Drexel's teenage daughters. Edie McClurg played the principal. The show pivoted partway into more of a standard family sitcom with the school left mostly behind, but it only ran for 15 episodes. FBI The Untold Tales on ABC. Pernell Roberts hosts this early reality series Recreating FBI Cases, that's about it. The show ran for a total of 13 episodes over two seasons. Sounds like filler for ABC. Moving on to Friday. Princesses. CBS. Julie Hagerty, pre-nanny Fran Drescher and former model Twiggy played New York roommates all trying to find their way in life. Twiggy played role-former princess, hence the show's name. Matt about Hughes, Leila Kenzie played Hagerty's sister. Now there was a great deal of friction among the actresses with Hagerty walking off after four episodes. Drescher contacted directly the head of CBS programming to recommend a recast, but he acts the show instead. Eight episodes were shot, but only five aired. Now, this is, I thought this was interesting. TV Guide said that Drescher's gum-chewing Brooklyn sticker routine was wildly overplayed. Two years later, a version of that same character would become CBS's Queen of Comedy, like into Lucy, doing the same bit. Step-by-step on ABC. It's a mainstay of ABC's TGIF from the Miller Boy at sitcom factory. Patrick Duffy and Suzanne Summers all is forgiven, love ABC. Co-star is a divorcee and a widow, each with three kids. Why do I suddenly see a set of character boxes in my mind? Brandon Kahl, Christine Lackin, Josh Byrne, and Stacey Keenan, just off my two dads, Angela Watson, and Christopher Castile play the kids. The parents had their own child together in the fourth season, standard operating procedure in family sitcoms, with Emily May Young playing her once she's shot from birth to five years old in two seasons. The medical term is Soros, soap opera rapid aging syndrome. Jason Marsden played a boyfriend of perfect strangers, Bronson Pinjo arrived as a business partner for Summers character. In the final season of Seven, the show moved from ABC to CBS, who is trying to build their own TGIF clone. Brooklyn Bridge on CBS. Yet another period piece, this was the year of them, a gentle comedy set in Brooklyn in 1956. The show centers on Alan, Danny Gerard, a 14-year-old in a Jewish family. Louis York and Amy Aquino are parents, with Happy Days Marion Ross as matriarch Sophie. They're just part of a large cast of relatives and neighbors. The show was well received by critics, winning a Golden Globe, a PGA, and four viewers for quality television awards, along with 13 Emmy nominations. The series ran for two seasons. The Carol Burnett Show in NBC. She's back for another shot at Variety Show Glory just on another network. It's literally the same show, except with new supporting players. Richard Kind is the only one I recognize. She even brought her Good Luck Charm Jim neighbors in for the premiere. Despite running all of two episodes per IMDb, weeks apart, so really more like specials in a series, it was nominated for three Emmys. The ultimate challenge on Fox. Michael Adamley and Heather Thomas host this early reality show about daredevils and stunt performers that only lasted a few weeks. Flesh and Blood on NBC, a driven D.A. Lisa Dar wants to find her birth family in this sitcom. In Walk's Redneck Arlo, David Keith who insists he's her brother, he's actually a con man, dragging his three kids in to live with her. Perry Gilpin, Pre-Phraser, plays her secretary. 12 episodes, four of which never aired. Pellis Gard on CBS, a Steven J. Cannell crime drama starring D.W. Moffat and Marcy Walker. He's a reformed jewel thief. She's a PR chief for a huge hotel chain. They go to a different locale each week and stop a disaster at one of their hotels using questionable methods. Oh, and he's also secretly the son of the Hotel Empire's owner. Including the two-hour pilot, three total episodes aired with five more left for the housekeeper. Reasonable doubts on NBC, a pre-NCIS Mark Harmon and a post-children of Lesser God Marley Matlin co-star as a police detective and assistant D.A. He's all about bust the perps while he's into the rights of the accused. There's a lot of arguing going on. The show ran for two seasons with Matlin moving on to picket fences and Harmon to Charlie Grace. So, let's recap. In 1991 out of 28 new series, there were 11 hits to find us lasting more than one season. The Torkelsons, nurses, the commission, rock, Herman's head I'll fly away, home improvement, home front, step by step Brooklyn Bridge and reasonable doubts. With 17 misses for a phenomenal 39% success rate, the previous year was only 26%. I don't think I watched much TV in 1991. None of these stick out as things that I particularly watched a lot or loved. What about you? I was probably watching early MST at that point. There you go. And he's still watching early MST at this point. So, you can check out our audio podcast, How I Got My Wife to Read Comics on iTunes, or on our website sfpodcastnetwork.com From the Pop Culture Bunker, I'm Mindy And I'm Mark. Thanks for watching.


Hey there chameleons, it's Camille and today I'm finally bringing you my next hair dye tutorial I decided to do a three-section ombre because I love the depth it gives as well as getting to have several colors in at once This time I actually used permanent dye to get rainbow colors Which up until this point didn't exist and you'd have to use semi or demi permanent dye I love how perfect this color is for spring and how vibrant and happy it makes me feel Before this my pink had faded for about five months and my roots have grown significantly So it was time for a change the night before I put coconut oil in my hair to minimize damage from chemicals I had help with my hair this time by a pro named Julie who's been doing hair for longer than I've been breathing She started by brushing out my hair to make it easier to work with and then parting it down the middle and sectioning it off Since my ends were darker we used one part clear all professional power bleach Makes with one part of 30 volume developer to lighten them This will even out my hair so when we color over it that will come out even as well Fun fact oatmeal is a great source of fiber One important thing about bleach is when you use it you should make sure the hair is saturated So it doesn't come out all blotchy because trust me you really don't want to have to re-bleach your hair If you have dark hair getting a stylus to help lighten it can be a huge help before dying The way we applied the bleach was by starting at the bottom and getting all that covered and then using the brush to feather The bleach upwards so there would be no harsh line between the bleached and the other hair Then I flipped over that section and feathered the other side as well We let the bleach sit and do its thing for about half an hour And then I got to stick my head in one of those cool hair sinks, which is very exciting We rinsed out all the bleach and then washed the hair to stop the reaction and get rid of any remaining bleach Then we conditioned and paddle brushed out my hair again to detangle it and make it easier to blow dry The reason we used a blow dryer on my hair is because otherwise we'd have to wait five years for my hair to dry And ain't nobody got time for that. I know Julie has better things to do than watch my hair dry Next we sectioned the hair to make it easier to apply the dye We used the brand spanking new flair me line by Clarell Professional, which is a line of vivid permanent dyes These dye molecules are smaller than the semi-permanent ones and are used and react differently as you'll see This dye was made for DIY and is very easy to use at home to come up with your own creations We mixed one part power to the purple and one part ten volume developer and Applied this straight to the roots bringing it down a couple of inches over the lighter hair The ten volume developer is used so that the dye deposits the color onto your hair without lifting it to lighter levels like higher volumes do Permanent dyes always look white out of the tube and slowly oxidize once exposed to air to show its true color Which is a dark purple? I found it so neat how you can actually watch it turn from white to light pink to a dark purple right before your eyeballs To apply this dye just brush it on from the roots going towards the end of your hair Making sure you saturate all of the hair you're dying This is easier if you work with smaller sections of hair Flip it over to get the other side and always brush towards the ends I'm also feathering the end so it makes a smoother transition into the next color Julie used a small comb to feather the dye even more very clever Next we mixed one part clearly you which is a clear dye diluter with one part power to the purple to get a lighter purple than last time This is going to be the transition color from the dark purple to the lighter ends It's crazy how much the color changes when oxidized This was applied the same way as before but this time feathered on top and on the bottom So it will blend easily between all of the colors Saturate the top and the bottom and blend the two colors together I really like using my hands when I dye my hair as you know and find it easier to blend this part with my Fingers rather than a brush because you can really get all up in there, you know Lastly we mixed one part make them blush pink with one part developer and well made them blush pink What else are you gonna do with that color? It actually makes it really nicely with the lighter purple and was super easy to blend Especially when I use my fingers and yes, you do need to wear gloves when working with this kind of dye Look at how bright the pink turns Now that we really made them blush I'm gonna sit for 30 minutes for the dyes to process during this time go ahead and eat some oatmeal Next you'll need to rinse out all of the dye until the water runs clear Shampoo to get everything out and then use your best conditioner to rehydrate your locks Julie wrapped my hair in a towel bun, which was so cute Then I put in product and finger comb to style and waited for my hair to air dry After a hard day's work, we came out with this lovely purple to pink ombre, which I am loving for spring I hope you all enjoyed this video and found it helpful Thanks to Claire all professional for making this possible and to Julie for having mad skills I have links to everything down below and if you liked this video, please subscribe for more content like this Comment telling me and Julie what you think about these new dyes Thank you chameleon so much for watching. I wish you all a happy healthy life, and I will see you in the next video kisses


The study found that palm fruit juice, PFJ, can help prevent type 2 diabetes mellitus, T2DM. It does this by reducing hyperglycemia and lipid levels, as well as improving insulin sensitivity. This effect is dependent on the amount of all palm phenolics OPB in the PFJ, with higher doses being more effective. This article was authored by Julia Balsinger, Andrei Ponchak, Ravigadivi Sambantha Murthy, and others.