 Today we are going to start talk. Heard of talk before? All right, heard of talk before? Yes sir. So you have heard talk before, what is? Talk is something which will? Causes rotation. Causes rotation, simple. All right, force is something which causes translation and the torque is something which causes rotation. Write it down. All right, so torque is something which will rotate an object. Now just like force, you know, torque also exists in this one. All right, we need to just identify it, what it is and we need to quantify it like best possible way to quantify it. And the way you should quantify it should be consistent with the observation. Getting it? But exact quantification, whether you call this length as 1 meter or not, this length is definitely less than that length. It should be consistent. Nobody is going to ask you why force equal to mass and acceleration. But it should be consistent that if velocity is increasing quickly, the force has to be more. That's all. You could say why not force equal to m into a square. That also, you know, you can take it as force. But people have taken the simplest possible expression combined with mass and acceleration. So similarly, let's try to see the observation related to the rotation and then we can quantify what the torque should be. Fine. Now in order to have translation, we need a force. Now if a rigid body is at rest, do I need force for it to translate? Any object needs a force, right? And is the force required for it to rotate? If the object is initially at rest, I want that object to start rotating. Do I need a force, yes or no? I need a force, right? And larger the force, faster the rotation, yes or no? Logical, right? So torque should be proportional to the force. Is there any doubt in this? So torque in physics is represented by letter tau. Have you seen tau before? Tau should be proportional to force. You will see that, have you ever any object like for example, seesaw? You might have played, no? Yes. Rotational rotation, it need not be complete circle. So this is the fulcrum. You apply some amount of force over here. This is the force. It will rotate, yes or no? Yes. Now if you apply the same amount of force over here, will it rotate faster or slower? Slower. The force is same. So torque is not just proportional to the force. It has to do its distance as well. So the greater the distance from the axis of rotation, greater is the effect of its rotation. Simple? Yes. So this is let us say distance d. So the torque should be proportional to the distance. Always find an axis of rotation. Right now there is a fixed axis of rotation. So you can easily see that there is an axis which is visible very clearly. Now if I throw this chalk in the air, it rotates and then comes back. Do you see any axis of rotation? Not exactly, right? So basically, I mean this is a convenient way of writing. In your textbook it is written that torque is proportional to distance from the axis of rotation. But in reality, you can find torque about different different points. Fine? You can say torque with respect to a particular point is proportional to distance of that point from the force. Now with respect to this point, this force with respect to that point, the torque will be zero because distance is zero. So the torque is proportional to perpendicular distance from the point about which you are finding the torque. And when you see a fixed axis, you naturally tend to find a torque about that fixed axis. But there need not be fixed axis all the time. Fine? Now what if I am applying force like this? So if I apply like this, what will happen? It will rotate but not as well as this like this. So if this is angle theta, only the F sin theta component helps it to rotate. So it not just depends on force and perpendicular distance, it also depends on angle. And we have found out that if angle is 90 degree, the torque is maximum. And if angle is zero, the torque is zero. So that is why we need to bring that angle also in the picture. So then I have agreed that let us call the torque as distance from the point into the force into sin of angle. Now what is this angle, how do you determine this angle theta? This is the maximum angle. Theta is what? It is the angle between the force and the distance from the axis. It is the angle between the, suppose from this point you are finding torque. So you draw a line from this to the force. This is your one vector and this is your another vector. So it is the angle between this vector and that vector. Your distance vector starts from the point about which you are finding the torque. So it is R F sin theta. Can this torque be negative? Depending on which direction you consider to be positive. It can be negative. And this force is the torque negative? What do you want to be negative and positive? R F sin theta. Tell me whether it is negative or positive. R is a magnitude of distance, F is a magnitude of force. Yeah, no, because it is positive. Positive or negative? Positive. No, because if you see length to be positive, F will assume it to be positive and theta here will not give you a negative sign. Okay, sure, yeah, but why does F have to be positive? Why? Oh, you keep quiet then. Okay, keep quiet. Others, what do you think? Negative or positive? Then positive. Theta is greater than, what is greater? Are you sure? Yeah. That is the theta. This is one vector. There is another vector. So this is the angle actually. This theta is not that theta actually. This is the tail and here is the tail for the force. This is the angle. Tail to tail or head to head? Both will give you the same thing. Fine? How do you find angle between the two vectors? You are not there. You have not watched the video also. This is R, F into sine of angle between R and F. Why it should be angle between? I want to represent it. So I want to write, if this is the definition, right now the torque is what? Negative or positive? Sine of obvious is still positive. Sine of obvious is still positive. Yeah exactly. It tries to rotate like this. It tries to rotate it in this way. Fine? And then if it is like this, then it will try to rotate it in that way. Yeah but if you have this one force, it will never be negative. The definition is anti-clockwise positive. Okay so there should be some sine convention right down. We usually take anti-clockwise to be positive. The sense of rotation in anti-clockwise to be positive and sense of rotation in clockwise to be negative. Okay? So over here R cross F is in which direction? So this is R cross F I have to find out. R is like this and F is in my right hand in the direction of the first vector and then curl in the direction of second vector. R cross F is in two. So this is clockwise or negative torque. Curl in the direction of the second vector. See if suppose this is vector A and this is vector B. How do you find A cross B and then curl in the direction of second vector? So thumb is A cross B. B cross A go towards A. Okay? It depends on perpendicular distance. Sorry it depends on the distance. The force, distance and the force. Is it clear? S and theta. Comparable distance. Are you getting it? So I can write this as F perpendicular. And in this chapter to determine this sign of the torque we just use our sense of rotation or just look at it. If you take that as to be positive this will be negative so likewise one sense of rotation will be positive other sense of rotation will be negative. Okay? Along the single axis only two sense of rotations are possible. Okay? So R cross perpendicular distance perpendicular component of force and then torque can also be written as R sin theta into F. What it is? R sin theta is what? Propenticular component of distance. Propenticular component of the distance from the force. This is the torque. So physically if you look at method. Okay? Propenticular distance of the force that causes the rotation. So basically if the force in the distance from the axis then the torque will be zero. It will not rotate at all. For example this force, this line of force was passing through the axis. Its top angle distance from the axis is zero. So there will not be any rotation. Are you getting it? Similarly if, let's say this is a door. If I apply a force like that, this force if I extend will cross the axis. It will cut the axis. What is this perpendicular distance from the axis? Propenticular distance of this force from the axis. Tell me. How much is this perpendicular distance from the axis? It's bad. So the breadth of this. You are saying this? No, that's. Then? What it is? How much? It's less. What is the force? The answer is zero. Okay? It is passing through the axis. This line of force cuts the axis. There is no distance from the axis. Are you getting it? So it will not cause any rotation. We will write down a force, a line of force, if passes through the axis. The line of force, if passes through the axis, creates zero torque about that axis. Creates zero torque about that axis. Okay? Any doubts? Still no? If you have to find out the torque, take the line of force and extend it. Okay? Extend it and drop a perpendicular about which you are finding the torque. That is the perpendicular distance. That into the force is your torque. And suppose you know the perpendicular component of force, take the perpendicular component of force and multiply with the distance. That again will give you the same torque. Okay?