Physics Lesson 8 on moments

追加: 2026-06-03

[00:00:00]hello guys welcome to the physics lesson this is the physics lesson eight in today's lesson we'll be looking at the turning effect of forces on objects or moment so we are looking at the turning effect of forces or moment meaning the turning effect of forces is called a moment all right so we are saying when a force is acted on a reached object and the line of action of the force is not passing through the center of gravity or the pivot of the object the turning effect called the moment of the force is produced so for you to understand this english which is being used here unless i get this object here so what is being said here is this so if this is the object and the center of the object is here code also the center of gravity so if a force is acted at this point here and this force is not passing through the center of gravity or the pivot then they're saying that force acting on an object like here is going to cause what is known as attaining effect or cause this object to turn like this so such a motion like this attaining motion like this is what we call a moment so examples of moments in real life are when we open it doors when you are opening a door you see a door turns in almost a circular path and also other instances of moment is when you are unscrewing a nut or screwing a nut so those are examples of moments all right so what we are saying here is this if we were to act a force here through the center then this object is not going to turn it will simply move like that it will have no moment so now what we are saying here is this that has forces produces a turning effect on objects so forces will produce attaining infected on objects when they are not acting through the center of gravity of the object but they are acting away from the center of gravity of the object so let's look at the definition of a moment now so we are saying a moment of a force represented by m about a pivot is the product of the force which is f and the perpendicular distance d between the pivot and the line of action of the force so what we are saying here guys is this that a moment of a force about a pivot is the product of the force and the perpendicular distance between the line of action of the force and the pivot so for you to understand let me give this situation here so let's say we have the object here and then a force is acting on it like this we are saying this object will cause it to turn like this right that's what we said so it will cause a moment now what we are saying here is this that for us to be able to get a moment unless we get a force acting like this and then we know the pivot meaning the pivot is the turning point at which the object is turning because this is where the object is turning from in the example for a door the hinge represents the pivot when you are turning the door opening or closing the door the door undergoes a rotation moment on a fixed point known as the hinge and that hinge is called the pivot so the fixed point upon which the object undergoes the rotation or the turning is called the pivot so this point here is the pivot so now we are saying if the force is acting here we are calling the line of action of the force then we are saying if we get this force then we multiply it with this distance here the perpendicular distance so the distance here between the line of action of the force and then the pivot so the distance between the pivot and the line of the action of the force times the force itself gives us what we call the moment so this distance here is called the perpendicular distance y because this distance and then the line of action of the force they must be at 90 degrees with each other or perpendicular to each other so that's why we are defining a moment as in uh a moment of a force about a pivot is the product of the force and the perpendicular distance between the pivot and the line of action of the force so in other words if you want you can say attaining effect of a force but however this is the standard definition of a moment because we'll say a moment now is going to be equal to force times c perpendicular distance so moment is represented by m forced by f then distance by d so say equals now or just get to use symbols only we use m is equal to f times d so we are saying where now where m is moment in newton meters so the units for moment are newton meters f is force in a newton so the units for force must be in newton and d is distance in meters so the units for distance must be any meters all right so let's look at this situation here so now we are representing this situation using symbols just so this is the pivot this is the force this is the distance so when you get this force you multiply with the distance here the distance between the line of action of the force and the pivot times the force itself you get a moment or attaining effect so we are saying the turning effect of a force depends on these two factors so a moment depends on these two factors or the turning effect of a force depends on these two factors so number one it depends on the perpendicular distance between the pivot i mean the point of application of the force and the pivot so we are saying it depends on the perpendicular distance between the point of application of the force and the pivot so now what does it mean so they are saying the distance here the perpendicular distance between the point of application of the force and then the pivot actually matters in any aware where a attaining effect is concerned so we are saying the larger or the longer the distance the larger the moment so i'll give an example of this when we are opening i mean when we are screwing or unscrewing nuts maybe you have noticed with the tracks they don't use short spanners because the short spanners will not produce a bigger moment to either unscrew the nut or screw the nut so they would use a spanner with a long handle because the distance is going to matter and it is going to affect it the moment meaning the longer the distance the larger the moment that's what we are saying here that is one of the factors upon which the turning effect depends on is perpendicular distance between the point of application of the force and the pivot so this distance here matters the longer the distance the larger the moment then another factor is here the size of the applied force so the size of the applied force or sum affects what we call the turning effect of a force meaning the larger the applied force the larger the moment of force so you'd find that the people with um that are music line with more muscles they are more powerful and able to open or unscrew the nut of tyres either on a bus or on a track all right so let's look at examples so that we are able to see how to apply moments in answering questions so here we have a example one which says a force of 2.0 newton acts at a distance of 3.0 meters from a pivot find the moment of the force two a force of five point zero newton provides a moment of 15 newton meter about a p vote what is the distance of the force from the pivot three a force provides a moment of 20 newton meter about a a pivot at a distance of 2.0 meters what is the size of the force all right so let's start with the number one here so we are starting with the number one let's say solutions so in number one they're saying a force of 2.0 newton acts at a distance of 3.0 meters from a pivot find the moment of the force so they want us to find the moment of the force so we write the formula which says moment is equal to force times perpendicular distance then i'll get our data which is the information provided in the question that is going to help us answer the question so sam what are we given here a force off so we are given force which is equal to 2.0 newton so acts at a distance of 3.0 meters so we are given also distance which is a 3.0 meters then they're saying find the moment of the force so they want a moment which is m so say equals question mark because we don't know what it is and it is the center of the question so now we'll substitute so get m since it's what we are finding we'll put it as it is then we'll substitute where this f f we are told it's supposed to be 2.0 so 2.0 is the same as 2 then times then d we are told it's supposed to be three point zero so put three here then we'll say m is equal to we'll multiply two times three which would be six and then we'll not forget the units so never forget units in science please never forget units so the units for moment uh we say the newton meters we are done so let's look at example number two so number two says a force of 5.0 newton provides a moment of 50 newton meter about a pivot what is the distance of the force from the pivot so now they want the distance of the force from the pivot maybe the position at which the force is acting away from the pivot so again as usual we need to write our formula which says moment is equal to force times distance perpendicular distance then we'll put our data down so we are told a force of 5.0 newton so we have 5 as a force so say because 5.0 newton uh provides a moment of so we are given moment off so we are already given moment m is equal to five newton meters then the same what is the distance so they want us the perpendicular distance which you we are going to put it equation mark on then o substitute m we are given is supposed to be 15 newton meters so put 15 equals f we are given is supposed to be 5 then times d is what we are going to find and we don't know we put it as it is then we'll say 15 is equal to o multiply 5 times d which will give us 5 v d then since we are looking for d then we are going to swap these so that the variable or the term containing the variable we are trying to find should be on the right side of the equation or the left side of the equation so however now 5d is equal to 15.

[00:14:32]now for us to remain with the d we must divide by 5 then also here by 5.

[00:14:39]then what we are going to do now here is this now we are going to cancel 5 into 5b to go so that to remain with d is equal to 5 into 15 which would be 3 meters because distance should be in meters so this one is the answer so let's move to 3 3 says a force a force provides a moment of 20 newton meters about a pivot at a distance of 2.0 meters what is the size of the force so they want the force so as usual was saying moment is equal to force times distance then i'll put our data where we are going to say we are given a moment the same a force provides a moment of 20 newton meter so we are given a moment of 20 newton meters about a pivot at a distance of 2.0 so that distance that it is giving a moment of this at a distance of two point zero so meters so distance is two pointy uh zero meters then the question says what is it the size of the force so we don't know force so first is the equation that we are trying to find so then we are going to substitute where this m over 20 is equal to where this f will put f because we don't know what f it is then times d which is a 22 then i'll say 20 is equal to multiply f times 2 which will be 2 f then as usual we begin writing this equation or rewrite this equation starting with this side containing the uh variable we are trying to find or the quantity we are trying to find so we start with the two f is equal to 20 then we divide by two to remain with f even here by two so these two and these two cancel so remain with f is equal to two into 220 which will be 10 newton so our force is 10 newtons all right so let's look at now application of moments uh where do moments work that's what we are now looking at where moments are applied and this is what we are calling applications of moments so in real life in which situation do we see ourselves using moments so we are saying in opening a door or window so whenever we are opening a window or a door there's a moment there are some scientists or the people that designs a door hard to really reason that for the door to continue to remain fixed while as it is allowing us to to open it so that we can go out and go in it must be rotating it must undergo a rotation or a moment even a window so also opening a bottle with an opener whenever we are opening a bottom there's a rotation because an opener needs to have what we call a pivot where the rotation is going to start from and the point where the force is going to be applied then also see so when people are swinging on a seesaw that's where we see also a moment being applied one person goes up another one goes down andy the rotation happens on a pivot then also on a tightening a night with a spanner so when we are also tightening nuts with spanners so these are the ways in which moments are applied so now let's look at the principle of moments so you have also to know what the principle of moments is so we are saying the principle of moments states that an object will attain equilibrium when the clockwise moment equals the anti-clockwise moment so what is it uh this principle of moment is same so let me explain this equilibrium here so equilibrium is is the state of balance if an object is in equilibrium meaning all the forces acting on it at zero so it is either not accelerating as well so an object in equilibrium is also not accelerating meaning all the forces acting on it when they are summed up or they're added the resultant force is zero so whenever the resultant force is zero then the acceleration is zero and then the object is said to be in equilibrium so the principle of them of moment states that an object will attain equilibrium when the clockwise moment equals the ant clockwise moment so these terms here these terms that have been borrowed so these terms are borrowed from a clock so you know a clock has got two arms there's one ammo for minutes and then one um if i mean it has three one arm four we need another arm for seconds another arm for hours so now let's say these are the arms of a watch we always see that these arms they they go in that rotation so they also undergo a moment so they rotate like this so a rotation in the direction of these arms is what we call the clockwise moment then the rotation which is opposite to the direction of the clock is what we call anti-clockwise moment so what is being said here is this an object will attain equilibrium when the clockwise moment equals the anti-clockwise moment so they're saying if this clockwise moment and this ant clockwise moment are equal then the object will be in equilibria that's what the principle of momenty is trying to say here so let's move a bit so we are saying this means that there is no moment of the force produced and the object is in the state of balance or equilibrium so the state of balance or equilibrium so meaning when the clockwise moment is equal to the ant clockwise moment then the object will have no resultant moment and then it will be in a state of balance or equilibrium all right so now what we are saying here is this this principle of moment can be expressed in form of an equation as follows so this principle here can be now written in form of an equation as follows so we can say m m c is equal to m a we are saying where m c is clockwise moment so clockwise moment we have nicknamed it as mc and ma is ant clockwise moment so this one is actually same the clockwise moment is equal to the and clockwise moment at what at equilibrium that's what the principle of moment is so if you cannot remember the definition in an exam you can even write it in form of an equation as long as you're able to explain what is in the equation using the symbols like i've done here so this is still the principle of moment but i've now given a description where i'm saying m c is clockwise moment and m a is a clockwise moment so whenever i give a definition in form of the formula i should explain what those symbols in the formula ah so clockwise moment is equal to and clockwise moment this is still the principle of moment all right so now let's demonstrate this so that you understand better so let's say we have an object here and it is pivoted here if this object is to remain balanced like this it means there must be a force pulling it up which is a force in the clockwise moment because this is how the clock moves now if there's no another force pushing it here this one should rotate now if it is to remain here it means there's another force acting downward and that force is in the opposite of what of clockwise so then that force is called ant-clockwise moment so this is what we mean so this object will be in balance or in equilibrium because this force which may try to get it rotate like that is equal to the other force which can cause it to rotate like this so these forces whenever these moments when they are equal then the object will stay in equilibrium or balance so now if we also change this situation from here like that it is also the same if this is to balance like this then it means this force which is trying to take it this way is equal to another force which is trying to make it this other way so hence this object will not turn any other way it will remain in a equilibrium or in state of balance so let's push this here let's drive the formula that we are going to be using when calculating questions involving the principle of moment so we are saying let's say the force that is taking it in the clockwise moment here we call it fc which is the clockwise force then the force that can take it in the opposite direction or in that clockwise moment let's call it f a which is the ant clockwise force then let's say we draw the pivot here the demarcation of the pivot here then the distance of this force here we will label it as d c which means the distance of the clockwise force the distance of this force from the pivot and then let's label this also as d a which is the distance of the force air from the pivot then the moment being caused by this which can cause this to go here like this this force if it were to cause this one to go like this we are saying each moment can be found the moment going in the clockwise can be found as m is equal to this force then times this distance similarly the moment which can cause this one to go in the ant clockwise which is m a can be found by this f a times this distance of f a from the pivot all right but now you know that we said here that this is equal to this that's what we have said here right i've said this is equal to this as a principle of moment so if this is one is equal to this then the two think these are also equal this and this are also equal definitely they are so we are going to pick this one fc times dc we are saying it is also equal to fa times da this becomes another principle of moment from here now this one becomes the general formula for calculating questions to do within the principle of moments so we are saying this equation is used to calculate forces and the distances that are needed to keep an object in equilibrium as in the diagram above so we are we use this formula i took i create forces that need to keep to keep this object that is in equilibrium like this one so let's look at the example number one all right so example number one says the figure below shows a device designed to compress crushed materials for a school project by the way this example i'm giving you here happened to come in a certain exam i cannot remember so we are told that this figure below here this figure below here shows a device designed to compress crushed materials for exclusions project then the same state one condition is necessary for a body to maintain equilibrium so we should state one condition necessary for this object to remain in a state of balance or equilibrium then two calculate the moment of the fifth newton force above the hinge so the moment of this 50 newton force about the hinge there's a hinge here so the hinge here becomes the pivot then we have c calculate the upward force f this force here which the crushed materials exerts on the position i mean on the piston to keep the beam in equilibrium all right before we answer this let's study and see how it behaves so we are told this is a hinge which means it's a pivot like a door where something is fixed so this one is fixed here it's about to rotate here then here there is a metal support here and inside here now it is attached to something here so this one is a piston and inside here there are crushed materials then here we are told this is a beam and here there's a force meaning if someone pushes this one downward like this force is pushing it downward then it is causing this one to go downward well as this one is rotating around this pivot so this one also goes here to crush the stones here now remember according to newton's third law of motion to every action force there's an equal and opposite reaction force so whenever this one pushes this one down there will be another reaction force that will be in echo in magnitude battery opposite that will be acting upwards so now what we are trying to see here is that the saying number one state one condition is necessary for a body to maintain equilibria so for this body to maintain equilibrium the clockwise moment must be equal to the anti-clockwise moment so let's try to squeeze here and have solutions so we are saying for this to be in equilibrium the sum of the clockwise moment is equal to sum of the clockwise moment or sum of all the forces acting on the object equals to zero or must equal to zero so for this one state one condition necessary for a body to maintain equilibrium saying some of the clockwise moment is equal to sum of the clockwise moment all right so state one condition necessary for a body to maintain equilibrium so we are saying some of the clockwise moment here i should have said the must nasty be equal to some of the clockwise moment or some of all the forces acting on the object must equal to zero so this answer i gave it i thought this question was like state the principle of moment that's how i gave it in this way however now i understand the question says state one condition necessary for a body to maintain equilibrium so the answer should be in this way that is some of the clockwise moment must be equal to some of the clockwise moment so if the sum of the clockwise moment the force taking it this way and the force that is trying to push it this way if the equal then this object or this arrangement here will be in equilibria or we maintain equilibrium so this answer if you want you can say it in this way you can say some of all the forces acting on the object must equal to zero also here you put the mast here here must equal to zero so for this object to be automating equilibrium we are saying sum of all the forces acting on the object must equal to zero all right so let's move to another question so question b says calculate the moment of the fifth newton force above the hinge so we have this fifth neutron force here so let's say solutions so now for us to answer this question very well we must understand they're asking us to calculate the moment and we know the formula for calculating the moment already it's not the principle of moment formula here it's the first formula we were using for calculating the moment so before we do that we need to uh simplify this diagram so write it in this way or break it into the forces acting on it excuse me so all right this as the beam as a line then this hinge is where the rotation or the turning takes place so we indicate it as a pivot then we have this force acting here downwards as the 15 newton then they want the moment the rotation which this one can cause if this one is pushed like this this one can start rotating like this it can either go like this because since the forces are facing downward they need to go like this in the clockwise moment so it's the one they're causing they're asking us to find the clockwise moment into cause and then we said that the clockwise moment is the moment is equal to the force itself and the distance of this force from the pivot that's what we said some will draw here the line and they'll say the distance from the force here to the pivot is what is calculated from here so we have this one here which is 55 and this one here which is 10 so from here to here it should be from the point of action of the force or the line of action of the force to the pivot so add 10 plus 55 which would be 60 5 centimeters so now this one is going to become now our distance if you want you can convert it into what now we can convert it to from 65 centimeters to meters which is going to be 0.65 so just divide by 100 for changing from centimeters to ammeters you just divide the number in centimeters by 100 for it to go to centimeters so this one divided by hundred you're getting 0.65 meters now because distance is supposed to be in meters and that yeah so now we'll get our formula which says moment is equal to force times c distance then on say data then we are given force is equal to 50 newton then the distance is equal to 0.65 meters then the same calculate the moment which we don't know then no substitute to say moment is equal to force which is a 50 times distance which is 0.265 then the moment is equal to when we multiply this one we're getting 32.5 and the unit units must be newton meter all right so we have answered so let's move a bit and here answer question number c which says calculate the upward force f which the crushed materials exist on the piston to keep the beam in equilibrium so they want this force here which is acting which the crushed material are exerting on this piston here so this is the force that can keep this object in equilibrium since if this force is acting downward if it is no other force trying to oppose it then it can cause this one to rotate like that now there's another force so for it to remain in equilibrium here then there must be another force in the opposite under telling us it is this one here checking it so this one is acting upward so now what we are going to do here is to make sure that uh we say solutions then we need to indicate this force on this diagram here to simplify things since we already simplified this one as the pivot this one as this one the distance of this one from the pivot we already found it at 65 or 0.65 then also we need to indicate the force since it is acting upward we can also indicate it here as this is the force going in that direction here then what we are going to do now it is now to show that this is the force f for the want then i'll draw now the distance of this from the pivot here so its distance is this which is 10 centimeters so this force here from the pivot is 10 centimeters then from there now we have everything we need so we will use now what we call the principle of moment so because we have this force which is trying to take it down and this force which is trying to take it up now since this one is not too draw big and it's not going they're telling us it is any equilibrium so meaning it is balanced it's not going this way it's not going this way it means this first taking it that way which is acting like this and this force taking it uh downward they are both equal so now we use the principle of moment which says force which is the force taking it this way which is the clockwise force which is this one times the distance which is also of that force trying to take it this way dc is equal to then we have the force trying to take it that way which is the f a force in the ant clockwise direction times then distance also of this force then i'll say data what we have now is fc which is 50 here clockwise then equals this we have also dc this distance here which is um which is the 65 yeah so now here we are not going to change i want you to understand one thing here when i'm finding the using the principle of moment sometimes you cannot use you cannot change the units because the units cancel each other at the end of the calculation so they really don't matter at this point but when doing the moment where you are using moment is equal to force times distance you need to convert because units don't cast over here but here don't you can't convert if you want you can convert and the answer will still be the same so now what we are saying now here is this so now we don't know if f is what we are looking for or distance here of this one we don't know it i mean we know which is 10 centimeters then this f which we are calling f a because it is facing that direction is what we don't know then we'll substitute f c which is 50 times dc which is 65 is equal to fa is what we are looking for we don't know 8 times then da which is 10 then here i didn't show the units to indicate how they are going to cancel but another question will show that so then what we are going to do we multiply this times this we're getting 3250 is equal to we multiply this by that we get 10 f of a then let's push it here so we are going to say we'll start with this one 10 f a is equal to 3250 then to remain with the f hero divided by 10 even here by 10 so 10 10 or castle then i'll say equals f a is going to be equal to 10 into that which will be 325 newtons as the force which is trying to go that way to balance this one in equilibrium so now let's look at example two example two is like this one here again this is an exam question it says figure b three point one is a diagram showing a uniform meter rule freer is pivoted at its center a newton meter is hung 20 centimeters from the pivot while a 4 newton weight is suspended four centimeters from the pivot so this is the situation where we have this one they're calling it it is a meter rule then this meter rule now uh freely be voted at its center which is not really true they have not been voted at its center or uniformity freely voted yeah it's not before that is not true because it is not undergoing a rotation here it's prevented somewhere where uh where is the pivot all right yeah it's oh they're telling us that's where the pivot is they haven't drawn it or sure all right that is true so the pivot is supposed to be here like this one okay is it true so the question is saying the meta rule is in equilibrium then the question says calculate the reading on the newton meter then two state with a reason whether the newton meter reading would increase or decrease when the 4.0 newton weight is moved to distance of 430 centimeters away from the pivot so let's try to answer here so i want to simplify this one so here they're saying it is pivoted here right so then there's if it is pivoted here on the center that's where the p40 is so now we are trying to do here is to write this one in a simple way so we have this position here showing where this thing is because this newton meter here this is actually spring balance which measures the force so it is also called the neutron meter this meter is not for meters no it has readings here so it can be called a steel beta and electric uh meter box it measures actually electricity but this one it is a newton meter meaning it measures force so now there's also a mass or a force here so this force when you check if this is pivoted here like that then this other one is tied so this force cannot stand on its own they never indicated anything here which they should have indicated here that this one is also fixed somewhere that's how they're supposed to indicate so if um this one is a pivot here like this they need to mean that there's this force which is acting because if this one is hung this mass or this 4.0 newton then this is trying to push it this way now if as this one tries to push it this way now this thing is tied to what to a new tony meter which is also fixed so if this moth if if this one has more force then it will cause this one to stretch and it will show some reading here now if this one cannot uh move further meaning it will be any equilibrium because they have told us that the meta rule is in equilibrium in fact so since it is in equilibrium meaning this force which is taking it here and another force which is here because this is the only thing on the meter rule fixed here it is where the rotation happens so meaning there's a force acting that way here so that's what i'm saying we now draw it in this way now where now we have a pivot here which is the center then this same newton meter now will have a force facing upward all right then or call it f that is the force that this one is going to read then or find the distance of this one from here they're saying it is what it is 20 centimeters then now we have this other force here which is 4.0 newton and this one from the pivot it is that distance which is 40 centimeters now the question says we calculate the reading on the newton meter so the reading on the newton meter here is equal to this force here so if we are able to calculate this force here then we are able to know the reading so now let's squeeze now so this diagram now is no longer useless because we have picked every information put it here so push it here to have a space so now say calculate the reading on the new don't meet so use the principle of moment because this thing is in equilibrium meaning the principle of momentum will come when i was saying fc is equal times f if d c is equal to f a times c and d a where i will say data now we have uh f this one now is going in there and clockwise like this opposite with the arms of the clock so call it f a this one which is this one this f a is the codon which is the four neutrons then d a is a distance of the phone newton from the pivot which is 40 centimeters then and next you will look at dc which is this one which would be 10 20 centimeters then this one is f c which we don't know because this one is the first trying to take it this way this one is trying to take it this way now here i want to show you that these ones don't matter so what we are going to do is this so we are going to put f c which is this one we don't know times c uh 20 centimeters this dc where is dc here dc 20 centimeters equals then f a f s this one 4 times d a 40 centimeters so i've put the units here so multiply this times this which will get us at 20 centimeters f fc so this times this is 20 centimeter fc equals then this times this or getting 16 newton then this one centimeter here then or divide by 20 even here by 20 so you realize that 20 and 20 will go and this centimeter and this centimeter will go then will remain with it f4 c equals then here this centimeter and this centimeter will go so you see the units are cancelling out each these ones the distances units for distances are cancelling each other out so you divide 120 160 by 20 which will give you eight newtons so now this will be the reading so the reading now calculate the reading on the new 20 meter it will be now 18 newton so here it will read 20 newtons so now let's look at another question so question b says state with a reason whether the pivot i mean the newton meter reading would increase or decrease when the 4.0 newton weight is moved to distance of 30 centimeters away from the pivot so the same uh we gave a reason whether the reading here on the newton meter here would increase meaning since we found the previously uh eight newton so they're saying we we now investigate whether it will increase maybe to nine or ten or decrease maybe to 76 uh wendy this force here when this force is pushed this way instead of being at 40 centimeters away from the pivot now they push it maybe at 30 centimeters that's what they're saying at 8 centimeters away from the pivot so we you think this one will increase so i said this i said and it will decrease since the clockwise moment i mean that clockwise moment will decrease to keep the meter row in equilibrium so what i'm saying here is this i'm saying this uh reading of a new newton meter here it will decrease since the clockwise moment wheel and decrease to keep the metal row in equilibrium so since when you move this one here remember when we looked at in the factors that affect the moment on the factors that affect the moment we said the distance or the perpendicular distance between the line or the point of application of the force and the pivot affect the uh the turning effect of a force remember where i said if you are opening uh or unscrewing the nuts offering a truck people use long handles because long handles now they'll give a more force to tororate rotate or m yeah a more force to provide more rotation so that the mat can either come out or tighten all right so now here imagine if they are bringing this down here so you expect also the distance to start decreasing so you expect that the distance times this to to give you a small moment now if this one will have a small moment then this one will have oh start is supposed to push it here meaning if the downward is small then this one must start pushing it here now since this one should remain in equilibrium it should remain in equilibrium meaning if this one starts decreasing in order to avoid this one taking it in this way this one also must decrease so that this one remains just in equilibrium like that so that's the point here so that's why i said it will decrease since the ant clockwise moment will decrease to keep the rule and the meter row in a equilibrium the meter ruler in a equilibria so we can also prove this mathematically by calculating also using the principle moment where we are saying fc times dc is equal to f a times da so we are saying if we are to use this data here f a we know that it is this one here for newton then its distance here has been now decreased to 30 because they say it is moved to 30 then now we want to find out this d it is still 20 centimeters now we want to find out this how it is going to be uh when this one is moved to 30 so say this one question mark then substitute equals then here we'll put 20 then here put it for three times see 30 then here we multiply could be 20 fc equals this one will multiply to the 120 newton centimeter then here divided by 20 here by 20 then here will remain with fc equals 120 divided by 20 it will be 6 newton so for real it has decreased previously this one was in eight newton winning we used the fort now when using 30 it has decreased just as we said here that it will decrease since the ant clockwise moment will decrease to keep the meter rule in a equilibrium so let's look at the other example here so here we are saying the diagram below shows a metal row devoted of its center but kept in equilibrium by a suspended mass of 240 grams so this question actually was sent to you when my student one of you my students send these questions i wanted to solve it here so everyone here can benefit so we have this meta room which is perverted of its center meaning and when the center is supposed to to be here so emitter row is actually 100 centimeters so please just memorize that one a meter rule one meter is equal to 100 centimeters so if you have a meter rule just know that in length in total length it is 100 centimeters so now since it has been voted off its center we have been given here the mark here meaning if we are at 50 centimeters then this is the middle of the meter room so from here 50 from here 1500 all together which makes one meter so now here we have a pivot then here we have an object of mass 240 grams so here we have zero then here we have five centimeters 20 centimeters 50 centimeters now [Music] let's uh read a bit yeah okay so they're saying the diagram below shows a meter row diverted off its center but kept in equilibrium by a suspended mass of 240 so this meter rule guys if this mass is not there it's not here but you put a pivot here where do you think it will go it will go this way because this side is longer and it is heavy than this but now to keep it from going this way they have put another mass here trying to provide another force this side so that this thing remains in equilibria meaning the moment this side and the moment this side are equal so the anti-clockwise moment and the clockwise moment are equal that's why it remains in equilibrium now let's see the question says uh the center of mass of the meter row is at 50 centimeters so there's a center of mass so what is the center of mass it's a point through which the mass of the object appears to be concentrated so for a metal room the mass of it is supposed to be concentrated where on the center here that's where its mass is so yeah so they're saying what is the mass of the object so what is the mass of the roller i mean what is the mass of the ruler so the mass of the ruler is concentrated where uh at its center so what we are going to do here um now we are going to start now are laboring everything properly so here we have a mass of this one here which we are going to change like this so this mass i'm changing it like this to show that it's a something which is pointing downward causing this thing to face downward then now if this is balanced then here is another mass of the meter rule balancing with this one because the mass of the meter rule is acting through its center trying to balance this one here so this one will call it m which is the mass of the meter rule then we are going to say um [Music] the distances here that are going to work so here we are going to say the whole of this is a 100 centimeters but we need to know from here to here what is it from this mass from the pivot what is the distance so we have been guided so from here to here it's supposed to be five centimeters then from here to here it's supposed to be 20 centimeters so now how about from here to here so we are just going to say since from here to here it's 20 from here to here's five so we're going to say 20 minus 5 which would be 15 so in here we have 15 centimeters so that we know the distance of this uh mass from the pivot then also we will have to know this one here so this one here so we are told from here to here it's 50.

[01:05:11]now from here to here it's 20 so say 50 minus 22 remaining 30 centimeters all right so now we'll drop this other information here so remain with this information which is very important so say now we use the clockwise uh i mean the principal moment because we are dealing with an object in equilibrium so we are going to send fc which is the clockwise force the one taking it this way times its distance is equal to then that clockwise moment the one taking it this way f a times d a they know uh this one taking it this way actually it is this mass here so coity instead of f we'll call it m c then times the knee d then equals then f uh f which is taking it this way it's actually m this mass here so call it m a mass then times d then i'll say our data now we are going to say m a mass which is actually taking it this way and clockwise is actually um 240 then its distance here structure 15 centimeters the knee will shift to this other part where we say distance of this mass which is mc taking it in the clockwise direction is 30 centimeters then m which we are calling mc we don't know it is the mass of the ruler so substitute then we are going to say mc which is this one we don't know it to the main mc times distance dc which is 30 is equal to then m [Music] a m a which is 240 times then d a d a which is 15 centimeters so here we're going to multiply this times this which will be 30 centimeters m c equals this times that which will give us 3 600 grams centimeters then to remain with the uh mc or divide by 30 centimeters even here 30 centimeters then these up to there after they will go they know remain with mc is equal to when we divide this as again this and this will go then remain with that so when we divide this into that it will be actually 120 grams so this will be the mass now that's the mass in grams but usually mass is supposed to be in cage so you can convert it you divide this one by 1000 which will give you a mass in cage at zero point one two zero kilogram so we are done with the hot topic on moments so next we'll be looking at the simple machines thank you for watching see you in the next lesson as for now bye you