In our last lecture, we had described the concept of force. Of course, in classical mechanics, force is well known. We discussed how we redefine it when we come to special theory of relativity. Then we realized that the way we define force in special theory of relativity, the acceleration and force need not be in the same direction. While in classical mechanics, if I apply force in a particular direction, the acceleration is also in the same direction. But in relativity, it is not like that. It need not be like that. Then we considered two special cases. One, when we are talking of only one dimensional motion, it means the force is being applied in the same direction as the velocity of the particle. And a situation in which force is applied perpendicular to the direction of velocity. In these two cases, we found out that the force and the acceleration will turn out to be the same. I mean, it will turn out to be in the same direction. So, these are the things that we discussed last time. So, we recapitulate. We discussed the definition of force in relativity. The acceleration in general is not in the same direction as force. We considered two special cases when force and acceleration are in the same direction. And this is what I have just now told. These are the two special cases. One, when the motion is along a line and the force is applied along the direction of the velocity. And the second condition, when force is applied perpendicular to the direction of the velocity of the particle. In last lecture, we had sort of said that we should, we will find out the equivalent of what we call as kinematic equations using these definition of force in relativity. So, we will spend some time today to discuss that particular aspect. Then of course, we will talk about the force transformation. So, this is the equation that we have derived earlier. Force multiplied by time. Let us just recapitulate the nomenclatures. U naught is the initial velocity of the particle. A force is applied in the same direction as the velocity of the particle. Once the force is applied in the same direction as the velocity of the particle and the motion is only in one direction, we are not talking about the vector sign. So, we have removed the vector signs. So, U naught is the initial velocity of the particle or we can even now call the initial speed of the particle. And a constant force is applied for a time t and after time t, U t is the final velocity of the particle. This is U t here. There is a U t here. There is a U naught here. There is a U naught here. And M naught is of course, the rest mass of the particle. So, this is the equation which we had derived last time, which relates force to the final velocity of the particle and the initial velocity of the particle. Of course, it assumes that force is constant as a function of time. So, my next step would be to find out this U t as a function of time so that I can directly get one equation from which I can find out the speed of the particle. This is the way the traditional kinematic equations in classical mechanics are written. So, let us attempt to do that. So, this is what I have written. The equation can be, this equation can be rewritten in a different form to enable us to calculate the speed after a given time t when a particle is subjected to a force F in one dimension motion. Of course, it essentially means reorganization of these terms because the equation has already been obtained. It is only sort of reorganizing the terms so that by direct substitution I can find out the velocity at a particular time when a constant force is applied to the particle. So, let us try to reorganize these terms. So, this was my equation which we had just now written and explained. I define a quantity A. A is not a very standard symbol. We just force divided by M naught rest mass of the particle. So, this I am calling as A which is some sort of acceleration in that sense because it has the dimension of acceleration. So, I am writing it capital A. So, if I take this, define F by M naught as capital A, then this M naught which is appearing in both these equations can be brought here. Once we brought it here, this becomes F upon M naught and this quantity will become A.  So, this quantity can be written as gamma U naught.  This quantity I take on the right hand side. So, once I have divided by M naught, this becomes this quantity becomes A t. M naught disappears from the right hand side of these two equations. This equation I take it to this side and write in the form of gamma U naught.  So, this term remains exactly identical except for M naught which we have already taken by replacing F by A. So, on the right hand side, we just have U t upon under root 1 minus U t square by C square. My idea is to write U t in terms of everything. So, what I will do? I will square this quantity and try to solve for U t. It is a simple, very simple algebra, but just to arrive at the equation which is comparatively simplified equation to determine final velocity. Because in most of the kinematic problem that we are used to in classical mechanics, essentially you are given a force or given an acceleration and you have to find out the velocity of the particle after a particular time. So, this is what I am doing in the next transparency. This is the same equation which I had written in the last transparency. This is exactly the same. I have squared it.   When I square the right hand side, this will become U t square and in the denominator, the under root will go away. So, it will become just 1 minus U t square by C square. This I take on the left hand side. So, this will get multiplied to this particular quantity is square. So, this is what is happening here. So, this quantity after squaring and bringing into the left hand side becomes 1 minus U t square upon C square. This quantity squared is put here becomes equal to U t square. Now, it is simple. We will try to organize the terms with U t square, collect all the terms which have U t square and those terms which do not have U t square and solve for U t square. This is what I am doing in the next transparency. So, this U t square term has just been taken on the other hand side. Let me just work it out.  So, if I take 1 and multiply this, this becomes a constant quantity and this I retain on the left hand side.  This contains U t square. So, I take it on the other hand side. So, this becomes U t square. This term will give you 1 and because this I am changing to the right hand side. So, this negative will become plus this whole quantity divided by C square. So, this is what this equation would look like. This is what I am writing in the next transparency precisely.  After that simple, I divide this quantity on both the both the sides. So, left hand side becomes this divided by this square and then I take under root. Once I do that, this is the value of U t which I get U t. Once I take the under root, this just becomes A t plus gamma U naught U naught which is on the numerator. This gets divided. So, this becomes 1 plus A t plus gamma U naught U naught square by C square and of course, because I am taking under root, so this becomes under root. So, this equation would tell me if I know what is the value of A that is F upon M naught. It means if I know what is the force and if I know what is the initial velocity U naught, then it will tell me what is going to be the speed of the particle after time t. Of course, it assumes very clearly that motion has to be only along a single line because if the motion is not along the single line, these equations will not work unlike kinematic equations where you could still take the components and write those equations. Here it is very clear because in that case force and acceleration would not be in the same direction. So, in this case one has to be careful. It is only for a one-dimensional motion that I can write this type of equation and as you can see this equation is much more complicated than the usual kinematic equation that we have been used to writing V is equal to U plus A t, things like that. Now once we have obtained this equation of velocity as a function of time, I may also like to find out the distance travelled by the particle in the same time t under the same conditions. This is an equivalent of kinematic equation that we write S is equal to U t plus half A t square which tells you that if you know the acceleration, then you know what is the distance travelled by the particle in a given time t. Of course, knowing the initial velocity U, so equivalent of that equation can be found out by integrating this particular equation and that is what I will do next to find out the distance travelled by the particle in a given time t. So, this is what I have written here. The equation gives the speed of the particle with initial speed U naught after time t under a constant force F. Of course, it is very clear. Let me repeat. I assume that the motion is in one dimension, force is applied in the same direction where the velocity of the particle exists. We can integrate the above equation further to find the distance travelled by the particle. That is what I said I am going to do next. And for that matter, let us just assume for simplicity that this is along the x direction because we are talking of only one particular frame. There is no question of transformation as of now. So, you have just a frame and you would like to know, you have a particular particle which is moving in a particular direction. Let us assume that this particular dimension direction is x direction just for simplicity. Therefore, once I try to integrate this equation, this U t can be written as dx dt because the motion is only along the x direction. Therefore, if I write this U t as dx dt, this equation becomes dx and I take dt on the right hand side. So, this whole thing into dt. After that, I can integrate it. This is what I have written in this particular transparency. 0 to x dx assuming that the particle starts at time t is equal to 0 from x is equal to 0. And of course, we assume that time starts from the time when we are trying to measure the distance and goes up to the time t. Here x is the total distance travelled by the particle. I have to integrate this particular equation. Once I integrate this equation, then I can find out what will be the value of the distance that the particle travels during this particular time t. Like before, I would like to take the indefinite form of this integral and solve. Of course, left hand side is very simple because this just gives you the value of x. Because once I integrate, I will get x and if you put the limit, this will just give you x. So, left hand side is obvious, trivial. Only the right hand side has to be integrated. Though the integral looks complicated, but you can see that this integral, as we will see, the integral can be evaluated simply. So, let us go to the next transparency where I write the indefinite form. That is what I said. Let us solve right hand side integral in indefinite form by using a substitution. So, I take a substitution and using that particular substitution, I will be able to solve this integral. So, this is the right hand side integral which I have written. I have removed the limits because I want to solve this in indefinite form just to make things easy. You could have done it the other way also if you like it. And I put the substitution, this particular quantity which is under the root that is 1 plus At plus gamma U0 U0 divided by C square. Of course, this quantity also is squared. This whole quantity here within the bracket, I write as some variable that I am just taking this variable to be p. Some variable which is here which is put inside the bracket. So, once I take this particular substitution, I have to change this variable of integration also from dt to dp. For that, I have to differentiate this particular quantity. Once I differentiate this quantity on the right hand side, I will get dp. But let me first try to differentiate this particular quantity. If I differentiate 1, I will get 1. I am sorry, I will get 0. So, that does not contribute to the differential. Once I start differentiating this, this whole square is multiplied by a constant 1 upon C square or rather divided by a constant C square and C square being constant. This C square will just remain as it is. In fact, that is the reason the C square I have taken on the other hand side. Then I have to differentiate this quantity which is on the numerator. If I differentiate that particular quantity, this is fx square or rather ft square. So, first I have to differentiate assuming ft to be one single variable. So, this becomes 2 times ft. So, this becomes 2 multiplied by this particular quantity in the bracket which is a multiplied by t plus gamma u0, u0. Then I have to differentiate this quantity in the bracket itself. Once I differentiate this quantity in the bracket, I have to differentiate. I have to find out df dt. And for that, this quantity is constant. Initial velocity is constant. Of course, then gamma u0 is also constant. Then this quantity when I differentiate, I just get a. So, this a is appearing here. So, this 2 is because of this differential and this a is because of this differential and this divided by C square I have taken on the other hand side. So, what I get? 2at plus gamma u0, u0, adt is C square dp. So, what I will do? Here, I have at plus gamma u0, u0. This particular quantity I will replace by C square dp. Of course, this multiplied by dt I will replace by C square dp divided by 2a. This is what I am doing in the next transparency. This was my original integral. This quantity I have written as p. So, this becomes under root p. And as we just discussed, this multiplied by dt can be written as C square divided by 2a multiplied by dp. This is what I have written. C square upon 2a is constant. So, I can take it out. And what remains here is the integral of 1 upon under root p which becomes integral of p to the power minus half dp. This will become n plus 1 which becomes 3 by, I am sorry, minus half. So, this becomes p to the power half must be divided by half. So, this becomes 2p to the power half. So, this is p to the power half is under root p. So, this is what I have written here in this particular transparency. C square divided by 2a multiplied by 2 root p. This 2 of course cancels out. And then what I get is C square by a under root p. So, this is rather easy integral to solve, not all that difficult. I substitute the value of p and then put back into the integral. Then I will get x as a function of p. In fact, p contains time. So, now the integral as I said becomes C square by a under root p. So, this quantity was p which we have defined which of course depends on time and depends on a which is f upon m naught. We can substitute back into the integral and we can write the solution of the full integral by putting the limits. So, if I put the limit, I had to, I mean the left hand side was very clear because it was just integral of dx. So, once you put the limit, you just get x. But here when you put the limit, you have to put the limit t and subtract minus, put t is equal to 0 and then get the answer. So, this is what I will be doing in the next transparency. Let me just write it so that becomes little clear. The quantity which was written here was C square by a 1 plus a t plus gamma u naught u naught square divided by C square. So, first quantity when I put the limit t, this quantity remains identical. So, when I put 0, then I have to subtract whatever I get by substituting 0. If I substitute 0, you will get C square by a under root 1 plus gamma u naught u naught, sorry there is no square here, gamma naught u naught upon C whole square has to be subtracted from it. So, this is what I am writing in the next transparency here that x is equal to C square by a, this quantity remains as it is minus C square upon a under root 1 plus gamma u naught u naught upon C whole square. So, as you can see that this equation is also much more complicated than the simple equation s is equal to u t plus half a t square which we have been using for kinematics in the traditional classical mechanics. However, this equation can give me the distance x traveled by the particle in time t, if the particle starts with a speed u naught and is under the influence of a force f and it has a rest mass m naught. So, a is equal to f upon m naught of course, assuming that the motion is purely in one dimension. So, these were the equivalent of the kinematic equations that we are used to in classical mechanics. Now, let us go to the next step which is crucial for us to arrive at the transformation of electric field and magnetic field that we are going to discuss as the last topic of this particular course. So, question is that if I know the force of a particle in a given frame, what will happen to the force as being viewed by another frame? This is what we call as a transformation. We have been talking of velocity transformation, we have been talking of momentum transformation. What it means that I know the velocity components in a given frame and I want to find out the velocity components of the same particle in a different frame. Similarly, I know the momenta or momentum components in a given frame and I want to find out the momentum components in a different frame. Now, my question is if I know what are the force components Fx, Fy, Fz, I would like to find out what are Fx, Fy, Fz in a different frame. In classical mechanics, they are expected to be same, but as we will be seeing that in relativity they do not turn out to be same. The force components also are frame dependent. Remember, F is equal to dP dt. So, once we are talking of transformation of momentum, let us look how we are going to transform the force. So, this is what I have written as transformation of force. With the new definition of force in place, let us try to see its transformation as we change the frame. I know the components of force in a given direction. What are the components of the force in a different frame? For that, what we will do? We will go back to the concept of four vector which we have been using earlier. We had defined the Lorentz transformation in terms of four vector. We have defined velocity transformation in terms of four vector. Then we define momentum energy transformation in terms of four vector. So, let us try to construct a force four vector and if I am able to construct a force four vector, obviously that will give me the transformation of force also. So, that is the way I would look into it. I will first try to define the force four vector. As we have said that earlier we had defined the momentum four vector as this. The notation that we have used, if you remember, is that these are the four components of the four vector. First three components are the x, y and z component of momentum of the particle. First component is px, second component is py, third component is pz and the fourth component of momentum, we normally call momentum or momentum energy four vector is dependent on the total relativistic energy of the particle and in the notation that we have used we write this as IE by C where E is the total energy, total relativistic energy of the particle. Obviously, if I have to construct from momentum to force, I have to differentiate with respect to time or I have to differentiate something, I have to differentiate this with respect to something which has a dimension of time. If I differentiate this with respect to dt, again we land into the same problem when we are trying to construct from a displacement four vector to a velocity four vector because dt is a frame dependent quantity. Time interval, if you take a particular time, the moment of the particle and it little later time, the moment of the particle take the difference, this delta t time is a frame dependent quantity, that is what we have discussed. So, if I differentiate this particular thing with dt, then I will not be able to get a four vector because in that case, dt will be a frame dependent quantity. If I have to construct another four vector out of this, I have to multiply or divide by something which is a four scalar which does not depend on the frame. This we have discussed earlier and if you realize, if you remember, it is the proper time interval which is a frame independent quantity. So, therefore, if I have to construct a force four vector from a momentum four vector, I cannot differentiate with respect to dt which is different in different frame. I must differentiate with respect to dtow, the proper time interval because dtow is a frame independent quantity. If you change your frame, dtow will not change. Therefore, if I have to take a force four vector, I prefer to differentiate this with respect to dtow. That is what I have written to generate force four vector. We have to differentiate with proper time which is a four scalar. Therefore, I define force vector four vector as dp d tau where tau is a frame, d tau is a frame independent quantity. If you remember whatever we have done at the time of velocity transformation, eventually I will write to write in terms of the force component in my own frame. If I am in a particular frame and in my frame, I would prefer to write this in terms of dt as measured in my own frame. While my definition gives the differential in terms of d tau, I can always convert this d tau into dt. So, if I know the velocity of the particle at that instant of time, then I can calculate gamma u, then I know that d tau is equal to dt divided by gamma u. This we have used earlier also in the case of velocity four vector. So, this d tau can be written as dt divided by gamma u. So, this quantity force can be written as gamma u dp dt. The advantage is that now I write this thing in a particular frame. If you are in a particular frame, you would like to know things in your own frame to construct a force four vector. So, it is better that I know things in terms of my own frame. So, my prescription is that I have to calculate the momentum four vector in my frame, then take a differentiate with respect to time in my own frame, but because this is going to be a frame dependent quantity. So, what I have to do, I have to multiply this by gamma u, where gamma u is 1 upon under root power minus u square by c square, where u is the speed of the particle measured in my own frame. So, if I know the speed of the particle, I know the momentum four vector, I know gamma u and using that particular dt, I can find out what is the force four vector. So, this is what I have said. The four components of the force four vector defined in this way would then give me like this. So, I take, I calculate in my own frame what is x component of the momentum, differentiate with respect to time as measured in my frame. This is this quantity. Take the y component of the momentum, differentiate with respect to time as measured in my own frame. This will give me the second component. I take the z component of the momentum, differentiate with respect to time in my own frame. I will calculate, get the third component. I know the energy of the particle in my frame. I differentiate with respect to time in my own frame. All these quantities are given in my own frame. Then I know what is the speed of the particle. I calculate gamma u, which is 1 upon under root 1 minus u square by c square. I know gamma u. I multiply this gamma u by these quantities. This four vector is now written in respect to everything that is known in my own frame. So, I know how to write it. So, the force four vector will be given by this particular quantity. All these quantities multiplied by gamma u will generate the force four vector. If you remember, this is exactly the way we had calculated or we have constructed a velocity four vector. Now, once we know that this is a velocity four vector, I am sorry force four vector, then I know how it will transform once I go from one frame to another frame, because this is the way force transformation, four vector transformation takes place. There is a standard equation. Let me just first read this thing. The first three quantities in the bracket are equal to the components of the force. Of course, once I say dpx dt, we have already defined as the force. dpy dt I have defined as fy, dpz dt I have defined as fz and the last quantity depends on the rate of change of the total energy, which we can write in terms of power, which we have done earlier in the last lecture. So, before going to the transformation, let me just rewrite this thing. This components the force and dE dt. Therefore, the components of force four vector can be written as gamma u. First component was dpx dt, which by new definition is fx, dpy dt is according to new definition is fy, dpz dt according to the new definition is fz. And if you remember, we had calculated d dt of E in the last lecture and that we have found out to be equal to power f dot u. So, dE dt I have written as f dot u divided by c. So, like the energy happens to be the fourth component of energy moment of four vector, time happens to be the fourth component of the displacement four vector. For the force four vector, the force component turns out to be power. So, once we have generated everything in terms of forces, if I go to a different frame, in general fx is likely to change, fy will change, fz will change, of course u will change and of course gamma u will change, because the velocity of the particle would change once I change my frame of reference. I can write the transformation equation as given in this particular transparency. These are my four components of the force four vector in a particular frame S. These are the components that I want to find out in a frame S. This is the transformation matrix, which depends on gamma. Gamma depends on v, the relative velocity between the frames. See remember, we have three different speeds. So, we should not get confused. There is a particle which is moving in S. Its velocity is being measured by an observer sitting in frame S. That is what I am calling as u. Same speed, the same particle is being observed by an observer in S and that observer finds the speed of the same particle to be u. So, that means second speed. Third speed is that the relative velocity between the force, between the two frames, which is always assumed to be along the x direction and all those things, which are the conditions of Lorentz transformation. That is v. So, we have three speeds and correspondingly we have three gammas. We have gamma u. We have gamma, which depends on v, gamma u, which depends on u. This is my transformation matrix, which if I have to open up to find out what will be fx relating to other components in S frame. That is what let us do it next. So, let us expand it. I have written this particular transformation matrix here just to save some time to make it clear. If I have to write gamma u prime fx prime, this will be gamma multiplied by this component, 0 multiplied by this component plus 0 multiplied by this component plus i beta gamma multiplied by this component. So, that will be the first term. So, let us just see first term. Once I multiply it here, gamma and gamma u will come out and there will be fx. There will be gamma and gamma u, which will also be similar. i square will make it minus 1. So, second term will be f dot u by c to beta. This is what I have written here as the first term. Gamma u prime fx prime, which is the first term on the matrix, column matrix on the left hand side is equal to gamma gamma u, which we have agreed will come out, multiplied by fx minus beta f dot u divided by c. Let us look at the second component. Second equation here on the paper is gamma u prime f i prime is equal to 0 multiplied by this plus 1 multiplied by this plus 0 multiplied by this plus 0 multiplied by this, which means gamma u prime f y prime is equal to gamma u f y.  And the fourth equation will be i gamma u prime, this quantity minus i beta gamma multiplied by gamma u fx plus 0 multiplied by this plus 0 multiplied by this plus gamma multiplied by this. Here also you will see that there is a gamma and gamma u. There is a gamma and gamma u, which will come out, which will take out of the bracket. So, these are gamma equations.   And this is the fourth equation gamma u prime i f prime dot u prime by c, which was the fourth term in the column matrix on the left hand side.  So, these are the expanded, this particular matrix equation has been expanded into the four equations. Now, we will try to simplify these equations by using a notation or using a equation, which we had obtained at the time of velocity transformation to write in a compact form, which is a useful form and which probably is much more useful as far as our, the future endeavors are concerned. So, this is what I have written. We shall use a previous result to simplify the force transformation equation. This result was obtained while writing the velocity four vector. This was my velocity four vector transformation. So, remember this transformation matrix is exactly same. In that case, if you remember, what was forming the four vector was gamma u ux, gamma u uy, gamma u uz and gamma u ic. And when we change the frame, it became gamma u prime ux prime, gamma u prime uy prime, gamma u prime uz prime, gamma u prime ic. Let us look at only the fourth equation, which is this equation, which is gamma u prime ic is equal to gamma multiplied by gamma u, I am sorry, minus i beta gamma multiplied by gamma u ux plus gamma multiplied by gamma u ic. I am looking only at the fourth equation. First three equations will give me standard velocity transformation. So, let us look just at this particular fourth equation, which is here. Gamma u prime ic is equal to this particular quantity. This we have done earlier, discussed earlier in great detail when we are discussing the velocity transformation. And by reorganizing the term on which I would not like to put my time here, this is what we get, gamma u prime is equal to gamma gamma u1 minus v ux upon c square. So, on the left hand side of the force transformation equations, the four equations that we had got, wherever gamma u prime comes, I will replace it by gamma gamma u1 minus v ux upon c square. Therefore, I will be able to get a clean equation writing fx prime in terms of other components. This is what I am writing by the next transparency. So, I have said, we use this equation in the expansion of force transformation equation. This was my first term, which we have obtained by expanding that particular matrix equation.  Just now, we have obtained by expanding that particular matrix. This is the equation, which I have written in the earlier transparency, which we had obtained from the velocity transformation, which relates gamma u prime in terms of gamma gamma u. So, gamma u prime is equal to gamma gamma u multiplied by 1 minus v ux upon c square. So, this gamma u prime here, I will substitute by this particular quantity gamma gamma u1 minus v ux upon c square. Once I do here, put it here, gamma gamma u will cancel from here. What I will be getting is 1 minus v ux upon c square, which will get multiplied to fx prime. And right hand side will just become fx minus beta f dot u upon c. Now, it is rather simple. I can just divide this quantity on both the sides and I will get fx prime is equal to a quantity, which I have been doing in the next transparency. I have divided 1 minus v ux upon c square. And remember, there was a beta and there was a c here. Just here, there was a beta, beta was v upon c and there was also a c here. So, this becomes v upon c square.  Maybe you will see the resemblance that we get from the equation, which was a time, when we are doing Lorentz transformation, when we are doing the time transformation, we are getting something like this. It is somewhat similar to that except that the fourth term here turns out to be f dot u. This will be the transformation of the x component of the force. Let us look at the transformation of the y component of the force. Of course, let me first, before we go, let me first discuss it, because this equation sometimes is written in a different form. So, let us first work out that particular form. Then we will do the y component transformation and the z component transformation. Just wanted to mention one more point that remember fx prime will also depend on f, the total force, which means that it will also depend on fy and fz. See, like in the case of momentum transformation, px prime also dependent on the energy, which depends on p square, which will depend also on the x, y and z component of momentum, not just on the x component of the momentum. So, similarly here, it will also depend on fy and fz. So, sometime this equation is written in a different form, avoiding to write this f dot u. So, let us just try to write that equation that form before we go to the transformation of the y component and the z component. So, what we do? We just expand this f dot u. So, fx is V upon c square remains like this.  So, here you have f dot u.   Just simply expanding and writing in this particular form. What I will do? I will take this fx common here. If I take fx common, I will get 1 minus V divided by u square, I am sorry, I will get fx 1 minus V ux by c square. So, there is a ux here, there is a V here. So, I will get V ux by c square. And that particular quantity will cancel with this particular quantity. Only as far as the x components are concerned. As far as these components are concerned, there is no cancellation. So, I can rewrite slightly this equation. This was my equation. So, as I said, fx 1 minus V upon c square, fx 1 minus V ux upon c square will cancel with this particular thing. And you will just get simple fx. These two quantities, there is no cancellation. So, you will get fx minus V upon c square, which is here, f y u y, which is here, plus f z u z, which is here. And of course, divided by 1 minus V ux upon c square, which is here. So, this tells you that fx prime is equal to fx minus all these quantities. Remember in classical mechanics, we expect V fx prime to be equal to fx. So, you can see very easily that when V is going to be very close to c, all these terms will cancel and just fx prime will be negligible. And this will give you fx prime is equal to fx. Now, let us go to the transformation of the y component. Of course, second and third terms both are similar. So, let us look first at the second term. This was the equation gamma u prime f y prime is equal to gamma u f y. This was my second equation, which we have got obtained from opening of the matrix. I use again gamma u prime is equal to gamma gamma u 1 minus V ux upon c square, exactly similar way. Here, there will be gamma. This gamma u will cancel from this gamma u on the right hand side multiplied by 1 minus V ux upon c square. So, this gamma will not cancel here. You just have f y prime into gamma into whole of this quantity 1 minus V ux upon c square divided by is equal to y f y. Therefore, f y prime is equal to f y divided by gamma 1 minus V ux upon c square. If you remember this was similar to the velocity transformation of the y component and because the z component equations are exactly identical. Therefore, I get f z prime is equal to f z gamma 1 minus V ux upon c square. Remember, in the s component, there is no gamma because that gamma has cancelled out. Here, gamma has not cancelled out, gamma u has cancelled out. So, gamma is retained in the denominator, just like the velocity transformation that we had got to obtain earlier. You can see that in non-relativistic limit, f x prime is equal to f x that we have discussed. You can also see that in non-relativistic limit, this will become 1. When V and ux are much smaller than c, this quantity is negligible in comparison to 1. f y prime will be equal to f y, f z prime will be equal to f z. So, in non-relativistic limit, we do get f x prime is equal to f x, f y prime is equal to f y, f z prime is equal to f z, but in relativity, forces also transform. In a different frame, they appear to be different. Now, let us look at the fourth component, which is component related to the power. So, power also transforms. So, once I go from one particular frame to another frame, the power will also transform. So, let us now look at the transformation of the fourth component of the fourth four vector, which is related to the transformation of power. This was my equation, which we have obtained by expanding the matrix, which was the fourth component equation. Again, I write for gamma u prime, gamma gamma u 1 minus V ux divided by c square. Here, there is a gamma gamma u, which will cancel. The i's will also cancel, which leads me to somewhat simpler equation, which is f prime dot u prime is equal to f dot u minus V fx divided by 1 minus V ux upon c square. So, this gives me the transformation of power. So, once I go from frame s to s prime, how my power changes? This is the transformation equation that governs that particular transformation equation. Now, let us look at the inverse transformation. This is tradition that whenever we write a transformation, we also write an inverse transformation. It means if my quantities are given in s prime frame of reference and I have to find out the equivalent quantities in s frame of reference, how do I transform? Like, for example, in velocity inverse transformation, my velocity components are given in s prime frame of reference and I want to find those velocity components in s frame of reference. So, that is what we call as inverse transformation. The prescriptions are simple as we have discussed the more of times that all prime quantities have to be changed to unprimed quantities and vice versa and wherever there is a V, replace it by minus V. It is as simple as that. So, that is what we are doing. We are writing now the inverse transformation equations just by changing the prime, I mean interchanging the prime and n prime and replacing V by minus V. So, this is my force component. So, on the left hand side, we have fx is equal to now fx prime. Here there was fx. So, this becomes fx prime. There was a minus V. So, this becomes because we have replaced V by minus V. So, this becomes plus. This becomes V upon c square f dot u, rather f prime dot u prime should be u prime divided by 1 plus V ux prime by c square. Similarly, f y will now become f y prime gamma 1 plus V ux upon ux prime by c square because V has been replaced by minus V. Similarly, here fz will be equal to fz prime divided by gamma 1 plus V ux prime by c square. So, this becomes my inverse transformation for force. Similarly, we can write the inverse power transformation also, exactly identical things. Here it becomes f dot, I am sorry f prime dot u prime plus V fx prime divided by 1 plus V ux prime by c square. On the left hand side, you have f dot u. So, prescription is simple. We do not have to spend too much of time describing this. Just as I said, interchange all prime quantities, make them unprime. All unprime quantities make them prime prime replace V by minus V. This gives me the inverse transformation. Before we close the lecture, let us look at a special case which is quite useful and illustrative and we will also be using in our next lecture. We consider a special case of a force transformation. Let us assume that there is a frame S in which this particular particle is instantaneously at rest. Of course, it is rest at that given time, at a later time because it is under the influence of force, so speed will change. So, it is no longer will be at rest in that particular frame. Assume that there is a frame in which at given instant in which I am interested in, this particular particle is at rest. So, whatever was the velocity of this particular particle at that particular frame, that particular frame seems to be moving in the same velocity. Therefore, this particular particle is at rest in that particular frame. In that case, u would be 0, vector u will be 0 and the force equations becomes somewhat simple equations. So, this is fx prime. This is the transformation of the x component because this particle is instantaneously at rest in S frame. So, u becomes 0. So, once u becomes 0, this whole quantity becomes 0. Of course, if u is 0, ux is also 0. So, this quantity becomes 0 and denominator we have only one which gives me fx prime is equal to fx. So, if we measure the force of the on the particle in S frame and that time when the particle was instantaneously at rest in S frame also it will appear to be at rest. I mean, it will have the x component of the force will turn out to be same.  Gamma being always greater than 1, your f y prime will be smaller than f y. And of course, because these transformations equations are similar for the z component, I will also get f z prime is equal to f z divided by gamma.  We just see that the force is smaller because f y components have become smaller in a frame in which the particle is not at rest. So, the force is large in the frame in which the particle is at rest which you can call sort of a proper frame. So, to end the lecture, we just summarize whatever we have done. We derived the equations similar to the kinematic equations in classical mechanics. We also defined force 4 vector and discussed the transformation of force. Thank you.


So, a super quick and easy way to shift between chords would be, let's say if you take C major here in root position C, E, G, you ask yourself what is the next chord, so I want the next chord to be A minor and we are in luck because A minor just has one different note compared to C major. The G for the C goes to A of A minor and all you do is retain the positions of the common notes and change to the unique note with a finger which works for you. Write them all down in a circle and the circle gives you a list of three shapes. You can do it from A minor, journeying to maybe an F major, journeying to maybe a D minor, journeying to a B flat major, maybe a D flat major, an F major which I already did and then F minor maybe, D minor and then back to C. But if there is nothing in common, retain the shape or the inversion of the previous chord.


I've been making something called Godot types, a collection of Godot prototypes to make small games and projects while I continue to learn Godot. I wanted to show my progress so far this week and it's open source. So you can go ahead and check out the code too if it's helpful. The first one I started with is smart input. You can see down here that we've got controller icons showing because I have an Xbox one controller plugged into my computer. Now if I go ahead and unplug my controller, which will turn it off because it's... I don't have batteries in it. The icons will change. I have a wired controller plugged in. Let me unplug that. Okay, so I unplugged that and you can see those icons changed. If I plug the Xbox controller back in and then power it on to connect it, those icons should change to be the controller icons if it connects. Come on, controller. It's funny how when working on things, it always works, but then when you demo it, it sure doesn't. Okay, great. We're connected and if I press the buttons on the controller, it shows the controller icon. Now if I go and press my keyboard, it changes to the keyboard icons. This seems like a weird place to start, but I really like those aspects of making games, those UI and the user interface and the user experience. Figuring that out was not too bad. I used the underscore input callback to check what the last input was and also check for the controller connected and disconnected events to change and it prioritizes controllers because if you have a controller plugged in, I think it's safe to assume you want to use a controller and then if you press your keyboard, it changes back to keyboard. So that's where I started smart input. Then I knew I wanted to make a bullet hell game, so I thought let's start with bullet patterns and you know, quick aside, you can turn off sound effects because wow, that was annoying. So you can see here, we've got an enemy firing straight, a single shot. Here's an enemy firing double straight. Here's a spread shot wiggly, they're following a sinusoidal pattern. And then we've got spread straight, we've got circle straight, and then we've got spread arc. This was a really fun exercise in building these different patterns in isolation. And for, you know, me as I'm using the game, I thought it'd be neat to show you how that works. So in Godot, I just have enemies in the scene tree. And then over here, my apologies, that's a little small. You can select fire pattern and bullet movement to change those. So that was a way where I took, I know I wanted to make a game, but I wasn't so sure how to make all these different firing patterns. I haven't done that in Godot yet. So I made this first, then I, all those enemies are scenes in Godot. If you don't know Godot, it's probably boring as heck, but drop them in the bullet heck. So this is a shoot them up game, where you pilot this little ship, got a health bar, I'll get damaged. And you can see my health decreased by one, enemies spawn in waves and we have those stars moving. There's the same number of stars, they just have random speed and alpha values and placement. So when they reach the end of the screen, they go back to the top, they get some randomized and they come back. You can see I added the smart input down in the lower left. So now if I switch to the controller, we can do that. And I really like making shoot them up. So they're fun. I would like to make a full game of one of these figuring out the waves was interesting. It's just an array of ones that spawn in each wave. And I turned the sound effects off, but the sound effects work too. Maybe I should turn those back on eventually. When I back out of this, I will. You can see the spawn. If you just hold the fire button, it's a slower rate of fire. And if you mash it, it's faster. We won. Anyway, let's turn sound effects back on so you can see that. I also made a platformer called Devil Boy. And let me go into there. So Devil Boy is this platformer kind of like Mario uses assets from Kenny one bit style. And I learned a lot about tile maps, tilesets, physics, that kind of stuff, camera that follows the player. And it shows a windscreen. So that's Devil Boy. Then the latest one I made is called Bunny Blaster, which isn't too dissimilar. It's kind of like a Mega Man game where you also use this Kenny assets. And there's platforming. There's one way collision so you can jump up, but you won't fall down. And that was fun getting bullets working and basic enemy logic and AI. That's it for Godo types for this week. Next up, I'm going to work on making probably a visual novel, a JRPG, kind of like the old Dragon Quest and Final Fantasy's. I'm going to make a strategy RPG kind of like Fire Emblem, just the foundational parts of it and action RPG, just learning about top down tile sets. And then when I'm done with those, I'll move on to 3D. We're it's March 12th. So yeah, almost near halfway through the month. And then once March reaches an end, I'll go ahead and move on to actually making and completing finished games. But so far, so good. Continuing to enjoy Godo. And if you want to check these Godo types out, you can go to the itch page, which is brechalupa.itch.io slash Godo types. And you can run it in the browser or download it for your operating system. There's also the source is on GitHub at github.com slash brechalupa slash Godo types. And it's all public domain. So if you find anything useful, you can use it yourself. Made it with Godo skeleton, which I made a video about previously. It's been quite nice and useful. That's all I've got this week. Thank you and see you next week. Bye.


52 Reasons to Hate My Father by Jessica Brody Lexington Larrabee, almost 18, is looking forward to receiving her $25 million trust fund promised by her father. With it, she can party as long as she wants, anytime she wants. Her life has been one of luxury with no responsibility, and she's looking forward to being completely in control. However, on the morning of her birthday, her father has left new instructions. In order to claim her trust fund, she's going to have to work in different jobs for a whole year entry-level jobs, 52 of them. This is something she knows nothing about, and now she realizes not only is she going to have to show up, she's going to have to do the work. How do you turn on a vacuum cleaner like she doesn't know? Will she do it? Can she do it? What other choice does she have? 52 Reasons to Hate My Father by Jessica Brody.


The reason why the narcissist has to cause as much pain as possible The narcissist has to hurt you They're never satisfied They're comfortable with dysfunctionality So it may seem as though they have to be uncomfortable at all times They have to be dissatisfied with whatever you're doing because then they can justify what they're doing And then they can keep doing what they're doing. They need to cause chaos and drama They need to have a problem with you, but although they claim there's all of these problems They continue to remain around you They're still a part of your life They're still trying to mold you into what they want you to be Instead of just leaving you alone They act like it's because they're concerned about you They love their family They want to make things right and that's why they can't go But if you've watched my videos You will know that this is all a lie They're only around you because they're getting something out of it Narcissists are only concerned with their own interests They don't care about what happens to you Which is why once you've spent enough time with them You become an emotional wreck They drain your bank account While they're portraying this image as though they're going to do whatever they can to support the family because of course Narcissists are always favoring and encouraging traditional family structures and values And that's why you can't get them away from you Because they're so tied to this image and how it makes them look And also the benefits that they get from being with you It makes their lives very convenient That's why they're always standing in the center of the room and they won't leave That's why you can't even go into the kitchen to make something to eat Without them bothering you Without them talking at you About something that's not relevant or important to you Because they're only concerned with their own interests Everything has to be at their convenience Everything has to aid them There always has to be a problem They always have to be dissatisfied with something They have to cause chaos and drama Because they are emotionally dependent on these situations They have to externalize however they feel about themselves They have to have an excuse for why they're doing what they're doing So that they can get supply for as long as they need it from you Which is why any interaction you have with them Is always emotionally charged They're always trying to manipulate your emotions It's like it penetrates your skin And you always feel down whenever you're around them They have been using their emotions to get what they want for a very long time They're like big babies Their words don't really mean anything What they're saying never makes any sense They don't really accomplish anything with their actions It's all from their emotions From their temper tantrums From pretending to be nice to people That's what gets them what they want Which is why whenever you're around them You feel emotional It's like a skill that they have Some people know how to make you feel really good They can make you feel safe and secure Where you want to open up to them While narcissists have the opposite effect They make you want to shut down and close yourself off They say mean things Often without even realizing the effect that it's having on you Because they're so self-absorbed They lack empathy They cannot share your experiences Which is why it always feels like you're on your own Being in a relationship with a narcissist Is lonelier than being alone Because at least then you have your own company You can attend to yourself While with a narcissist you can't even do that Because they demand all of your attention and focus to be on them But no matter what you do for them They're always dissatisfied It's like there's constantly something wrong all of the time And it's constantly affecting you This is the effect of this skill That narcissists have mastered They know how to make you feel down They know how to make you feel bad about yourself Just like some people know how to make you feel good about yourself But with narcissists it's the opposite Because how we treat people Is a direct reflection of how we feel about ourselves When someone feels good about themselves You feel that Just as you can feel the narcissist's self-hatred Because they project it outwardly onto you and make you identify with it Until it becomes a part of you and then they feel relieved They blame everyone for their problems It's like a part of who they are It's a characteristic trait It's what they do They hold you responsible for everything And they use that to justify what they do When they have to punish you When they have to cause as much pain as they possibly can But they're often not even dissatisfied with anything They just use it to create the environment that they like It gets them what they want It gets their needs met They make you feel like there's always a problem But then you soon discover There's no problem at all Because they're actually comfortable in dysfunctional environments Because then they can be in control If they create the problem They can then provide the solution A solution will always be in their favor It will always benefit them And it will always be at your expense Which is why the situations where they are really dissatisfied Is when there's no way for them to complain When you give them everything that they need When you give them everything to make them feel comfortable That is when you will see them act up the most That is when they will have a breakdown That is when you will see the problems Things will just come out of nowhere Suddenly and unexpectedly Things that you never could have anticipated That is when you will really see them panicking Because they have to have an environment Where there is something to complain about They need to have a crisis Where you need to fix something Because something is wrong And if you don't do it You're bad But no matter what you do You're always going to be bad anyway They take up all of your time with you having to fix all of this stuff But when you get rid of all of the problems That is when you will see the real problem Which has nothing to do with anything in the external environment The real problem exists within them Which they are trying to hide by putting the finger at everyone else Because they're never in situations where there are real problems It's always a situation where it's good enough so that they can exploit everything It's not going to be a dangerous environment But they will always make you feel like something's wrong They will always try to keep you in a fearful state Because that's what gives them control It provides them with emotional support It regulates their emotions It makes them feel comfortable within themselves Thank you for watching I hope this video resonated with you Please like, comment, share and subscribe If you were like the Nate My PayPal link is in the video description Coaching Inquiries You can email me at coachingnetandarchsafiver.co.uk Thank you for watching and I'll talk to you soon


So let's see the credit memo first. Let's do that option first and see what it looks like. So I'll make a credit memo for AAA, and then I'm gonna say it's for the same inventory one. We're just gonna reverse it exactly. And then same thing here. So it looks perfect. We're gonna reverse it exactly. We could have the same issue that we talked about with the credit memo with the sales returns and allowances instead of hitting the sales. I won't go into that in detail here. Look at the other credit memo one for that. If you don't want to reverse sales exactly.


Good afternoon. My name is Samo Maena. I'm the Managing Director of Kenya Broadcasts Incorporation. Kali Booni Nyumbani. Hapa ni Nyumbani. I think it's important to say that we are derited as Kenya Broadcasts Incorporation because of this new show that we are starting. It's a partnership between KBC and Chip Kizi. And I'm very happy to see young people back to our screen. All the people you have come with are young people. The future of this country belongs to young people. And one of the things that we are aspiring to do is giving young people an opportunity. You will never challenge anyone that he or she has not done this or that if you don't give them an opportunity. And so we have been discussing this matter with Chip Kizi for the last close to two months. And I'm very happy that the speed we have moved with Chip Kizi to see the flotation of this idea is very commendable. I like the speed he works with and that is how the world should move. That is how we should do our own things. The new show we are starting is a comedy show. He will be the main person in the comedy show. But what we are looking for in this show is to try and get the talent up there. Because KBC is a national TV station. And so we will be trying to get talent across Kenya, across our 47 counties, and giving them a platform. Even Chip Kizi himself, if he was never given a platform, he would still be probably somewhere in the village. And so this opportunity of this show is trying to market and monetize talent. Because many people have talent but they don't have a platform to demonstrate or display their talent. Together with people like Benahia, let us support young people. And the ribaditry KBC we have decided. The biggest operation of this country are young people. And if they are young people, why don't you give them a platform to push forward their talent? We will start in Nairobi but after we stabilize properly, we will move the show across Kenya. So that we take the show to the people. So that we take the show to the people. Other than people coming to Nairobi to record the show. So we know in every county in this country, they are very low talent. That has not been seen on screen. We are going to promote this show 360. We have 14 full radio stations. We have 8 subservices. We have another TV called Y254. Did you know there is Y254? Yes. It's for young people. So we are discussing with the team to see whether the show will be going to on both television stations concurrently at the same time. Because that TV station is for young people. Even the way they do their news is for young people. We try to promote young talent. And the content in that TV is for young people. So Chikizi, I am very happy that now anytime now we are going on air on Monday. We are going on air on Monday. And we have put the show at prime time 8pm to 9pm. It's one hour of serious comedy. So we would request all of you here to support this show. It is for young people. It is for exposing talents. And we are moving it from Nairobi. We will move it after it stabilizes. We will move it to the counties. After going to counties, if it does well, we can go to Kosti 20s. Because in every village in this country, there is a talent that has not been exposed. Let's expose young people. Let's support young people. This is the future and the foundation of this country. Asante Nisana, Nakalibuni Ten, Nyumbani. Chikizi. Thank you so much. Nafkiri hangu kwanza ni niyanze na kukushkuru MD. You know, mimi nime kuwako industry for 10 years now. And one thing you do when you are in the industry as a talent is that you look for platforms. You really look for them. You look for broadcasters. You look for TV stations. You look for MDs to pitch your idea. But most of them, they really, it's hard to get them. So me na kushkuru sana for opening your doors to us, listening to me, giving me an opportunity. When I came here, I didn't know that the way you swiftly acted and the way you adapted into the idea, I thought that nime kuji kukuletria storizajaba, lakini wukani skiza na wukani akumodeti. So excited. I had taken a break from TV for at least 3 years now. And I am happy to come back home. Like I had said, this is home. This is a home of comedy. This is where Churchill started. This is where Nyambane started. This is where Ojuang started and finished. So for me, and having been in the industry for 10 years, I am happy at this point of my career to be back here. Where the legends started. But even me maybe in 20 years, what do I call it in Tajiakama Ojuang? No 20, no 100 years, not 20. And so Chibukizi show is back. We are going to be live on KBC. Like MDR said, it's going to be a serious comedy talk show. But also it's a comedy show that is, it has a reputation of giving a chance to the people who don't have a chance. We have a reputation of giving now itanga Chibukizi. Chibukizi is a swear word that means upcoming. So it's very fair for the name to accommodate the upcoming talents. Whether it's singing, whether it's comedy, whether it's whatever your talent is that you believe that.  Nakama bile emilewa what's life. So tutokwana katelo, tutokwana we are also trying to pick from the online community one young female host that is going to help us engage in the social media space. But generally this is it. We are back home. We want to entertain. We want to go to each and every village like you said, look for the other Chibukizi. So that maybe by the time Mwaka inaisha, tukwe sasa eitunom leteya vijanawengine mulabda onafanya launching the other TV station with new programs. So mimi MD from deep down my heart I'm grateful. I'm grateful to all of you for finding time to be here with us. I can promise one thing. That he may enda he. He may enda I say, tutapiga show, tunadaka kupiga kelele, tunadaka kurudisha to position KBC malina ko ina o small way. Natu nomba support. Wale watua kanyumbani, join us. Social media. Ata wale watua mba wana jihisi waka natalanta. This is home. We are going to be a live recording. We are going to have audience members this time. For the longest time when I started doing the show, I used to do it in studio. But now we are going to have more than 200 people join us for our live recordings. So that now even this talent that we are looking for. Our goal is to, MD was telling me that chibukizi wajako niyambia mambo yaatumi yambili. Mimi nataka utagenese, shuambai opia ita tagenesa revenue ya kulipa hao asa neweni onataka tutafute. So goal is that in six months the way we had calculated we will be able to hold chibukizi shuad KCC not with 200 people but with a thousand of more people. Ya. Tu merudi kufanyamboka kuchikesha na labda nimpati e bena ase metu jambo merudi dionerudi shi MD. Bena. Hello guys. Aka. Aka. Aka. Aka. Aka. Aka. Yes. Uki pata chansia kudresa. Uki pata chansia gwenda kwa ewa. Enda to the police, Indio. Men. Acha chantumia itu e na serious niyata kakostimusina jwa kakopia na kapaise na hupani na hitu mani. So opia mimi. Niko grateful sana kukoko ispes. Nis kuma. Nema niyaji. E ni bute. Niku bute to butane. Baikesha otu jitu nezakotumia fkapi, Indio. E na ni chenye ni konacho chenye chipua konacho chenye piu konacho tikiunga nisha pamoja ndoina create one big thing. Indio. Nezakoni kum small. Mbibi easy mic zotea pivi nezakoni kitu small likiwa mic apa but mbibi tomorrow it might be a bigger media house ama kitu ingi na kubash itatoko kosapotia kuna yango natu lenge kitu moja. So lenge kwa itu kama kawa biletumia sema. Niku cha pua was up easy. Was up easy. Aslandi man. So I think mbibi Mr. Zungumza sana I'll take it back to but before I take it back to MD allow me to introduce one of the group members that are going to be working with us. This is wachani shkejina vizuri. Deeper connections. Deeper connections it's a group and this is a whole idea kuna MD. How I say nipakashonist how kaziwa niku chepa mziki lakini mzikiya wana ichapo ekiwa na some test of our traditional yetawatia your your flavor afrika yo. How ndu guzangu na kwa mbia kama huyu nmepatananae leo huyu nmepatananae two days ago we met on social media huyu alintumi a DM akani ambia ho mambo mingi ni kama mbimi na mambo ashizu zaakomina kujatu pigei and that's the old point that we live in a world where as young people we must come together and intentionally support each other. So that we can grow. These platforms mimi ni kiku jani jpge kifuwa pa ni anza kusema ho mimi nmepawashuwa pa sasa ni tawale niku se kutafutaspesia kuakumodej hawa hama wale ungini wakupale inje wa ni aku kwa DM ama labda aku kwa simu ama labda aku kwen unini nmukenda kwa interview wana urizawata wama kaji. Guys we are open. We are open for business. Most of you you've interviewed katello and I've seen you ask so many questions kulianda je kuna kua je kuko api ni uko ki ukenda kaiole kuna mizani kwa mbiana kaku omoka kule te uom zani tumu omoe bro kama kuna talent yani ziti omoe njimki omoe yosai ziti na omo kbc kuna watu wana kuangana manenu ome punguki wana manenu wizidom mutuana rusha manenu utuana wizidom akuna nyumba haina kbc kwa ii Kenya ukwe turukana ukwe mombasa ukwe lamu every house as a kbc ni remote too so ujuwe atutengenezi platform tu e nyeiko Nairobi nimsani tukuna chansia tu toe staapa na tumtoe kwa na juli kana the whole country with your support online and plus kbc we are going to do wonders before I take it back to MD allow me to introduce Karo Karo Asha we work together she can make a few points and then we take it back to MD but also kindly poly before that maybe to skia how wasa new it kwanza nyei nyei siitina give shukram sana kwa chifu na kbc na piya kwa nii nyei manzei tumilekus kumana sisi vitalen our music is fused with urban and traditional we call it banter so ii wotu venei bename seima tukuna nii nyei na sisi together you can make wonders we give thanks for doing it here asante asante sana my name is Karo Asha I work with an organization called Asha Skanya so for me I am grateful that kbc and basically this entertainment industry has created a platform for all of us and of course I look forward to working with everybody to talk about Shopia asante asante sana we actually have a whole segment for youth we have a whole segment where she will be helping moderate so to say me tuna at 10 one of the main reasons we wanted to sign these contracts so that misi anze kwenawuko mi anze kusumbu wa mdina ulini promise na sasa na sasa nikama kime ni rampa so we wanted to sign these contracts so that everybody can see that mboka imelu dimen na chya ase me puretuna say na umeski ya watua legal kapa kapa e nasi mama kapa kapa to nbihaka ma ni roman ni pala pala tuna say plea msi iqa this one here is this one here is my kuduub my small brother but he ran he is my manager he also runs a production company That is called Falm Entertainment. We will be talking more about that. I don't know whether Mr. Mike you want to say anything. That's why he was signing because he is our boss for this one. And that's the old point guys. If you look at this team, it's a youthful team. We don't know whether we will be talking about this or not. We don't know whether we will be talking about this or not. We don't know what will be happening. We are not going to organize it. We are not going to give it to the music. We are not going to say that we will interview with Deputy President or President. Or whoever. We don't want them to help us have a youthful conversation. We do not have anything for us without us. So thank you so much M.D. Thank you. One of the things I want to request to you young people, please support one another. It's important. Provide some stairs for someone to grow. If you want to grow, please support one another. If you hand it together, you're going to get more. But if you think you are the best thing that ever happened to the world, then you lose. You need other people and do not be a terminator of talent. Some people in this country, because I am a talent, but I support that talent, you are part of the people who kills talent. Please don't kill talent. Provide. Support. Come where you can't see, support those who can't see. If you cannot do poem, support those who can do poem. But don't be a terminator of talent. Count on KBC to support you. Count on this partnership we have entered with Chip Kizi to support young people grow. Finally, let's monetize talent. It cannot be a talent if it is not giving you some tunes. Let's support talent when people make money, they become better citizens. Because even that talent, if it's not bringing some coins to the parcel, it's just useless. It's not helping. And people have misused talent in this country. We are not going to be part of that. We are going to monetize talent. We are going to look for supporters in government, outside government, private sector, so that the talent we are going to work with, they are taking something home. It's not in our side to utilize talent without paying. And I have had this discussion with Chip Kizi, that talent must earn something. Not only just come in kuchakeshawatu, they must earn money. Because they must start getting some basics from that talent. How much money do you earn? $1,000. $1,000. Anything? Let's give it a few questions. Utaziuliza Mutransana MB. How much money do you have? $1,000. Let's go. We have so many comedians here in Kenya. We have so many comedians here in Kenya, but you can say if you work with Chip Kizi, maybe why? And also maybe what are some of your expectations, you expect them? Of course we can come to Mahale. We don't know what we expect, maybe benefits we expect from Chip Kizi. So that is my question for you. Any other? My name is Wayne Smody. Wayne Smody, M-O-D-I. My question to Chip Kizi, you are coming after 2-3 years out of the screens. What new are you going to bring in to the comedy world? And are you in idea of supporting even the fewer or the lesser people, although you have spoken about it, but to what extent are you going to go so that you can support the upcoming comedians? I'm Pizenta Makina from Nikolas Kiafot, and my question actually goes to both of you. You say that you're trying to discover new talents and from what you said that for the two of them they reached out to you. My question is because if you say you're going out to different counties in the country, how exactly are those people going to find out about it? Maybe someone who's watching and they want to reach out to you, they want to be part of the group. How do you expect those people to get to you? To add on the same question for Makina, like which criteria will you be using to make sure that you select those? Because we know when you look at TikTok and there's so many things again, you have a good thing you can say here to get those comedians, so we just think that you're going to make sure that you get those kind of work. My question to Mr. Pizenta, you say that you will be supporting talent. Of course we understand talents and need each other. So are you going to work with the people you've been, I want you to take care of maybe also other countries? Mr. Pizenta, I have to concentrate on the work. With the good work you've been doing, we know you've been touching with the second most person and I can say that I've seen support talent. What changes are you going to make to make sure that every foot seven county is represented within the talent that you're bringing on board? And number two, why TBC? Why not MTV or any other TV stations? And maybe lastly, apart from these kind of comedians and the percussion, who are we expecting to this in on the show? I think we can really pleasure that first. My name is Sharon Therreq for Badarang TV. Actually Pukizi, I wanted to ask a question. Will you only be dealing with the comedians or will you also be dealing with other activities that you'll be bringing on board? I've been working on TV for a long time. In the business station, I've been working on issues and I've been working on TV for a long time. I've been working on TV for a long time and I've been working on TV for a long time. But I've been working on TV for a long time and I've been working on issues and I've been working on issues and I've been working on TV for a long time. Any question? What inspired you to come back after three years out? It was, you have mentioned that you guys want to have one person from the kina industry under media. Let me tell us why have you decided to have one kina person from the kina industry? Why not really be two or three kina people? Okay. Okay. Let me tell you why we chose Chibikizi. Number one, he approached us with the idea. Okay. So it is him who approached KBC with the idea. And what we have done is discuss the idea, how we are going to improve it. It is his idea. It is not our idea. It's always good to give it where it is due. We don't say it's us. It is him who approached me with the idea. Number two, why him? I think he is the best. He is the best in town. Number three, would you struggle to look for a comedian better than Chibikizi? And because he has done it before, what I know he and we have agreed with him on this, he has to apply creative and innovative ways of improving the show. What do I expect? I expect young people to troop back to KBC and watch KBC. That viewership increase, that is what we are looking for. We are looking for more eyeballs on our TV. And the eyeballs we have been hunting for many years are for the young people. And what better way of attracting young people but rather than having them on screen doing their thing. So I expect high viewership on KBC, not only on Chibikizi show but on other shows. So and with that it means money will fall and we will follow. That is it. I get viewership and I get resources. This was in Guinness hotel. I think he is a manbo. I think he is a manbo. I think he is a manbo. I think he is a manbo. He is a manbo. I think he is a manbo. I think he is a manbo. I think he is a manbo. I think he is a manbo. I think he is a manbo. I think he is a manbo. I think he is a manbo. I think the best way to answer that question and everybody who has asked what new are we going to do. Itabidi towards the first episode I believe in content. And let me explain but before there was Chibikizi there was just a normal Mololongo boy roaming around the streets of Mololongo. But I had written down a creative plan. I had envisioned myself cracking jokes. So the best way because I the best way to hype a show the best way to answer your question is for us to watch the first episode on Monday and then we will be able to see who is the manbo. So how are we going to make a manbo. So we are going to make a manbo. So on Monday we will watch the first episode what we are going to make. I need to be clear. How I do the reason why I remain I use the same name Chibikizi Chibikizi show and how and if I explain how I met with Catello for context. Last month I was using the same name Chibikizi Chibikizi show and I said to Kuma Kuma and he said we are going to do things that we need. Now we are going to use the same name Chibikizi Chibikizi show and the next step is to utilize your platform. I will open my doors and my team has a brief that if you see anybody So, Band Fuel Ia Greetings, We are going to give you a platform, We are going to give you a platform, We are going to give you a platform, hafizn ch deserti na kumubu kwezi Ngakata ia muhia nene kataka kwa kwa atu�ina kwa youth nareinu hwumbretu nrata Kwa hia chisha hwumbretu nene hwumbetu jika wama hwumbetu hwumbetu hwumbetu kwa kwa kwa kwa kwa hwumbetu nyeni kwa gafimu kwa na kutu naihini jitu me, mebi kwa KBC, tu tokot na peyana, communicate, tell us. Una jua talent, I say that everybody has a story to tell. Everybody, doesn't matter how talented you are, but kuna za kwa kuna jamatu wa pa inja ni taxi driver, lakini ewe imbambahe. So hu ondo umtuna ta futa. Mi na taftam tu, wanda wa zimu, manya siwa zimu, ani pehistoria ke ya kwa ni niye ni wanda wa zimu, siwa zimu. Na tafta ule soja, mwenye ni security guard, mwenye anayaza chekesha, lakini ewe anakwa kwa fomzingine. Hakuna kriteria. Then also who we are going to be seeing, we are going to see everybody, you know. Na eza unsurprise, labda neotu kuna truth for man, labda keksha tu kuna kibe, maweeps, hapa dunha pewa maweeps, the next day maybe tu kuna evu mongai, the next day maybe tu kuna MD, maybe one time we have the president, maybe the next time to kuna dereva wata aksiza usiku. Ata wale dada zetu apa MD haki kubali, siji kama siya kwa wata kubali, lakini kuna dada zetu wako apa kwa istuti kua, numa kbc mania pomwenye lewa. How dada zetu wako kwa giza usiku na monspitu. They have a story to tell. So really who you are going to expect is everyone. This is Kenya. This is a Kenyan show. Koma diaza wei of bringing everybody together. You bring together the kids, the parents, the teenagers, the teachers, the professional, the lawyers. So that's it. That's the whole structure of the show. Is the show going to be Nairobi alone? No. I am happy that for the first time I think I am working with a TV station that is intentional about young people and they listen. I talk to MD, Ali, he gets it. He told me no chipu isho, asma we find a way and even promise that he's going to help me even now mobilize funds from our supporters, from partners. So really we are not going to be Nairobi show. We are going to move from Nairobi and go on the road, go to all the counties like he has said and then also as time goes by we trickle down. We want a situation where tutafania chipu ishi live show kariobangi. Nairobi is a county but it's upangu. Upangu iskona isakachini wa tupe episode na tutokia boka matukona. Matukuna wad. We do an episode in Kibera, we do an episode in Tala, we do an episode in Nyale Enda, we do another one in Mololongo. This show is a show that is flexible and it's flexible. It's a show that is going to be in this town. Tukikuja wad jia, tutapigakelele wad jia. Tukiendaga risa, nanaju anikiwa na supportian yundu gusango online. We are going to reach everyone that we need to reach. So in terms of is it a Nairobi show? No. Are we looking for Nairobi talents? No. Are we only looking for comedians? We are looking for everybody. We have enough comedians. Not sure. Tukuna Bena, Niko, Katelondio Hujo and even already as you can see we have a band here. We have Karo here. Karo is going to maybe help us moderate the youth panel. The youth panel, we are going to be engaging young people in different sectors to have a conversation about young people. We've set aside a segment where we can have young people talk about religion, we can have young people talk about government. And these young people niwatu to random, niwatu nikijana wa kibera, nikijana wa Karen, nikijana wa Shaka Hola, nikijana wa Izie Heriazote. So really it's not a Nairobi show. Umuuliza what's new nakuomba mande, tafadali, blada. Blada, da tuonane mande nikunyeshim blada zalakasi. Mambo mupia ni mingi. Nakipisti ni mingi sana. Umuuliza one female. Why one female? Eh... It's not really about... I did not think about it that way. But this particular one, she's doing very well in that space. And the reason why maybe you don't want to announce is because we are yet to agree on terms of how we will engage her. But in the online space, I think even as we create our own platforms, I think the outside world in atuonavingine. So ulemtukunavile kuna sisi wengine to meji position better. So there is a particular young lady that I feel like she's done well for herself and her age. And whatever she do will fit in with what I do in this show. And now as we move forward, maybe we'll be able to accommodate more, a man maybe, bro maybe niza kupia job, na onani kazi na da futa. So... And maybe even you guys, I need to have a meeting with you, you agree to want to do MDU, mezi kia masima to monitor his talent. I need to agree with you guys, we say now, wiktukianza mande, how do you want us to engage as ufaluma entertainment, as jibukizi with online media? What can we craft together that permanently and every week that we are engaging and we are pushing our show together? And I think niha yotu kwa wale wa meuliza maswadi nihizotu ni mezibu hafia, but just haomtu maybe ma... to asiku wuzi o wao. Kapisa. The previous president used to say something and he used to address young people, used to say and I used to listen to him, used to say, young people, power is not given, it is taken. Shumilu kwa nafkriyanga nihizi kuu, pan kerealize ni, ni mimi coming to MD, MD yama kwa mbiyapa ali omkeleshwa na I came to boss, so mitu atu paka kuku o mzewe woga, diyo, and even if I was close to the president or the deputy and they gave me a chance, then nip nip tume isi tukiju wa wuki kwa, watu, kama sasa ni miku omtanda watu semana tumi wa, wuki tumi wa iva unatumika vizuhurin dugu yango. There is no problem whatsoever. Kama dugu yako, kama un dugu yango, nidugu yango minim sani. Sasa ni kwa se kumpe a chance na anayaza deliver what I want him to deliver just because he is my brother. It is unipeti politics. We are young Africans, we are focused in, we are the future leaders of tomorrow. Yuki tumitu wa nasemanga iva. Sisi ni fiyungozi wa keshu. Lasima tuwanze leo. Wewe kama unafikiri yati tumasa idiwa jyutu najuana, wekana yuana rati wewe utaona vile tuki deliver. As politics affected. Mambo ni matatu tafarani. Politics is not affected. Politics is a way of life. Maisha enye ni siyasandu kusango. Iituna piga apa ni siyasapia. Unadua. Siyasa is a way of life. It has not affected me. If anything, it made me aware of the system and country that I live in. And also encourage everybody. Let's be involved in our governance. Usikai inje wu ambi wangwe, ukujange kuwambi wahu ukudihenda. Be involved. My brothers and sisters, no one is an iron of knowledge. All of you, watch the show, criticize the show, improve the show. Just take a phone and tell, tell jibu hiyu ni upuzi, kumgeza rada hapa. Watch the show, criticize the show and tell him where to improve. Let's not... I have told you do not be terminator of currents. Wambi e where he is going wrong or where he can improve. Usikue partiya kuwuharibu, ukue partiya kuwumgeza. Nakujenga. Tujenga ni. It is to the benefit of many of us if the show succeeds. If it succeeds, Kenya succeeds. Thank you, sir. Mungo ambariki na fanyemema. Amen, God bless you.


At the only jungle warfare training facility in the Department of Defense, service members can expect to encounter some of the harshest jungle environment on Earth. Marines with Combat Assault Battalion completed the culminating event to the basic jungle survival course, the E-Course, April 17th at the Jungle Warfare Training Center. The course spans multiple miles and teams were required to navigate an array of obstacles designed to push the mind and body to its limits. The strenuous course is made more difficult when teams are required to remember a group of items from the beginning of the trail. What the Kim's game is, they come through at the covert. It's a box. We open it up, we give them two minutes. There's 13 items in that box, what they do, they remember that item, those items. Once they get here to the pit in Pine where we are now, they have two minutes to discuss amongst themselves all the items in the box, and they'll hesitate to get one Marine to come up and give all those items to the Chief over here. Three, two, one. The purpose of the Kim's game is to keep their mind strong in those stressful environments.  You just want to see if they can retain the information they picked up on their mission or whatnot.  The course includes a tactical combat casualty care assessment involving first aid and casualty transportation. After stabilizing the victim, teams create stretchers on the fly and traverse more than a mile navigating steep hills and harsh terrain. We knew when we were going to UDP that we were going to have the opportunity to come up to G8 Jungle Warfare Training Center, so I wanted to have an opportunity for at least some of the Marines of the company to come up here and experience, you know, one of the only jungle warfare training centers that the U.S. military has. And while we're here in Okinawa, that opportunity arose to send at least one platoon of AAV Marines through here, give them something different to do, a little flavor of what it's like to patrol through a dense jungle. The Marines ended the day panting and covered in mud, but are better prepared to deploy to any climb in place at any moment's notice. Reporting from the Jungle Warfare Training Center, Camp Gonzalez, Okinawa, Japan, I'm Marine Corporal Stephen Hines.