so let's say if you have a door and if you apply a force at these three locations let's say at point a b and c is it easier to push the door at a b or c what would you say you'll find that it's a lot easier to push the door at position a but it's very very difficult to push it at position c and even though the forces are the same there is a quantity that's different and that quantity is known as the torque torque is the force times the moment arm or lever arm in the case of position a the moment arm is greater than that of position b and so it's easier to move the door at position a than that position b because you can produce a greater torque at point a at point b to generate the same torque requires about twice the force as in position a so it's a lot harder to move the door at the middle or even at the edge of the door on the left side now let's talk about the different ways in which you could calculate the torque so we're going to apply a force that's perpendicular to the door and let's say l is the distance between where you apply the force and the axis of rotation and i want to distinguish that with r the moment arm the moment arm is the perpendicular distance from the axis of rotation to the line of action the line of action is a line that's parallel to the force it extends from the force so that perpendicular distance is known as the moment arm so the torque is the force times the moment arm it's also any perpendicular force times l but now what if there's an angle how does the situation change if we put an angle between the force and the door so let's say if we apply a force at this position let's say this is parallel to the door so we have an angle theta how can we calculate the torque now so first let's draw the line of action of the force so that's the line of action and then draw a line that's perpendicular to the line of action from the axis of rotation so this line right here is the moment arm now we said that l is the distance between where we apply the force and the axis of rotation so what i'm going to do is turn this into a right triangle i'm going to draw it separately so this is r this is l and notice that these two they form vertical angles so this must be theta as well so theta is right here so l is the hypotenuse and if we want to calculate r from l notice that r is opposite to the angle theta so we can say that r is equal to l sine theta using sohcahtoa if you're not sure how to get this start with the sine theta is equal to the opposite side which is r divided by the hypotenuse which is across the box that's l and if you multiply both sides by l then you can see that r is l sine theta so we know that the torque is the product of the force times the moment arm and in this example the moment arm is l sine theta so the torque is the force times l which is the distance between where you apply the force and the axis of rotation and then times sine theta where theta is the acute angle between where the force is applied and basically the door so that's one way in which you can calculate it another way is to view the problem differently so that same force has a parallel component and a perpendicular component and here's the angle theta notice that theta is opposite to the perpendicular component of the force here's the right angle so the perpendicular component is f sine theta now even though we're applying the force in this direction this is the component of the force that actually does the work to turn the object in this direction so therefore we can focus on just the perpendicular component of the force and then this is l which is the same as r in this problem so the torque is equal to the perpendicular component of the force times l and the perpendicular component of the force is f sine theta so in the end the torque is just f times l times sine theta so you get the same equation as this one so now you have all the equations that you need to calculate the torque acting on an object now there are some other things that we need to talk about so whenever a force causes an object to rotate in a counterclockwise direction that force will create a positive torque and if you have another force that causes an object to rotate in the clockwise direction then the torque generated will be a negative torque so keep that in mind so here's a question for you so let's say this is the axis of rotation and we're going to apply a 200 newton force 3 meters away from the axis of rotation and at the same time we're going to apply a 400 newton force at a distance of 1.5 meters from the axis of rotation calculate the net torque acting on this object feel free to pause the video first let's calculate the individual torques so torque 1 is going to be f1 times r1 where f1 is 200 newtons and r1 is 3 meters so this is going to create a positive torque of 600 newtons times meters so that's torque 1. it's going in the positive counterclockwise direction now what about torque2 torque 2 has a tendency to cause the object to rotate clockwise which means that it's going to be a negative torque so let's call this f2 so torque 2 is going to be f2 multiplied by r2 and so that's going to be 400 newtons times 1.5 meters we're going to say it's negative 400 because it creates a negative torque so 400 times 1.5 is 600. so torque 2 is negative 600 newtons times meters the net torque is basically the sum of the two torques so the first one is positive 600 the second one is negative 600 so the net torque is zero which means that the object is in equilibrium so it's not going to rotate clockwise or counterclockwise let's try another example so here we have a propeller that can spin in this direction or that direction or this direction it could spin different ways so first we're going to apply a force of 300 newtons at a distance of let's say 4 meters and then we're going to apply another force of 600 newtons at a distance of 3 meters and at an angle of 60 degrees and then there's going to be another force which is directed here and that's going to be a 500 newton force and it's at an angle of 50 degrees so calculate the net torque of the system and the distance let's say it's 5 meters from the axis of rotation so i'm going to call this f1 f2 and let's say this is f3 so the net torque is the sum of all three torques t1 t2 and t3 so t1 is going to be f1 times r1 t2 is f2 times r2 and t3 is f3 times r3 now torque 1 is going to cause the object to rotate in the clockwise direction so that's going to be a negative torque so it's going to be negative 300 times four torque two will cause the object to rotate in the counterclockwise direction so it's gonna be a positive torque so it's 600 times three and times sine of thirty i mean sixty not thirty now keep in mind r two is l two times sine theta so l is 3 and theta is 60. so now let's multiply by f3 times r3 now f3 will cause the object to rotate in the counterclockwise direction so it's going to be a positive torque f3 is 500 newtons and r3 we're going to use l3 sine theta where l3 is 5 and theta is 50. so it's going to be 5 times sine of 50. so the net torque is going to be t1 which is negative 300 times 4 so that's negative 1200 plus t2 which is 600 times 3 times sine of 60 which is 15 58.8 and then plus 500 times 5 times sine of 50 which is 19 15.1 so the net torque is about positive 2274 newtons times meters so that's the net torque of the system because it's positive the object will rotate in the counterclockwise direction the concept of torque is very useful for leverage you can use a torque to multiply a force by adjusting the lever arm of a simple machine so the simple machine we're going to focus on is basically the seesaw so let's say if you apply a downward force of 300 newtons at a distance of six meters from the fulcrum so this is the axis of rotation and let's say this part is three meters long what is the output force that will be generated on the right side if you push the left side down with a force of 300 newtons at this location so what you need to understand is that the torque that's generated on this side this is a positive torque that's going to create another positive torque on the right side so the torques will be the same so let's call this t1 and let's call this t2 but keep in mind in this example t1 is equal to t2 the force that you exert on this side will continue to travel on that side so t1 is going to be f1 times l1 where f1 is 300 and the level arm in this example is 6 meters you can say r1 instead of l1 the result will be the same so t1 is 1800 newtons times meters now t2 is going to be the same it's going to be f2 which is basically the output force multiplied by the lever arm so i'm going to write it as f2 times l2 so t2 is still going to be 1800 newtons times meters and l2 is now 3 meters so 1800 divided by 3 is 600 so the output force will be 600 newtons so notice that the output force it doubled compared to the input force that you applied to the machine so you put in 300 newtons and you got an output of 600 units so therefore the mechanical advantage of this system is two because the machine it doubled your force mechanical advantage is the ratio between the output force and the input force now granted this is an ideal situation an actual machine might produce a force of 580 590 it may not exactly be 600 but theoretically that's what it should be the ideal mechanical advantage of a machine is equal to the input lever arm divided by the output level arm the input level arm is the level arm of the input force which is f1 so that's 6 meters the output level arm is associated with the output force which is three meters so six divided by three will still give you a mechanical advantage of two so this is the ideal mechanical advantage and this is the actual mechanical advantage of the machine now another simple machine that can use leverage to multiply forces is the shovel so let's say if you're digging up a pile of dirt and you want to lift it up and move it somewhere else so you're going to use a shovel to get the job done so let's say this is the shovel you're using and let's say this is the axis of rotation so you're going to apply a force in this direction and an output force will be generated in that direction now let's say that the distance between the axis of rotation and where you apply the force is one meter and let's say the output level arm is 0.1 meters so if you apply a force of 200 newtons what output force will be generated so in the last example we saw that t1 is equal to t2 the torque that you create in this direction will be equal to the torque that's created in that direction around the axis of rotation now t1 is equal to f1 times l1 the input force times the input level arm and t2 is f2 times l2 which is the output force times the output lever so the input force is 200 newtons the input lever arm is 1 meter we're looking for the output force and the output level arm is 0.1 meters so it's 200 times 1 which is 200 divided by 0.1 so the output force is going to be 2 000 newtons so notice that the smaller force is associated with the longer side and the stronger force is associated with the shorter side now it works out this way so that the torques are balanced the torques have to be equal so now that we have the output force what is the mechanical advantage of this simple machine so the mechanical advantage is equal to the output force divided by the input force so that's going to be 2 000 newtons divided by 200 newtons which is 10. so that's the mechanical advantage of this particular shovel it increases your force by a factor of 10 that is of course if you apply the force at the edge of the shovel if you apply it at the middle of the shovel your mechanical advantage will be reduced by two it's going to be half of its current value so it's gonna be five so your output force at this position will be 200 times 5 or a thousand newtons but if you apply your input force at the edge then the mechanical advantage will remain 10 and so your output force will be 2000 units so therefore if you're lifting something with a shovel you don't want to put your hands here because you're not going to create enough leverage to increase the force so you're going to be working harder to lift up stuff but if you want to lift up something heavy with less effort you want to place your hand at the edge of the shovel now granted you may have to push down a longer distance but still you can lift up something with a smaller amount of force the force that you have to apply will be small relative to the force that the machine will generate for you which will be large you