all right let's go ahead and continue with uh where we left off last time so let's do torqus and moments two so last time we discussed torque and how to calculate torque a couple different ways we spent a good amount of time on practical and anatomical examples of torqus we talked about the internal joint moment and then we talked um quite in depth about the muscle Force component and also about Co contraction and so today we'll talk about external moments and manipulating moment arm length we'll talk about some practical examples of joint moments we'll calculate joint moments in static in static equilibrium and then we might discuss stability and equilibrium or we'll just leave this for next time so one of the prompts that you were given or one of the the directions you were given um at the end of last class was to think about you know why co-contraction could be beneficial or other instances in which co- contraction is harmful um can you remind me did I give you the two examples of the uh the ACL and cartilage did we get there okay perfect so what other instances did you come up with where co-contraction is beneficial um and where it's also potentially harmful right let me know in the chat I'll give everyone a couple minutes to type um someone said ground reaction force and and without the details I I can't necessarily say that's an example or not um but co- contraction is something that occurs at the Joint level um and so it's like your antagonist Contracting when our agonists are Contracting as well and if you think back to linear kinetics uh ground reaction force can only tell us what our whole body is doing it can't necessarily tell us what's happening at a at an individual joint level so I think that's a good thought um and and I do appreciate the answer um but but it's not it's not quite an example but again uh thank you for your for your answer you know I've never thought of childbirth for a positive to help squeeze the baby out um I know very little about the pelvic floor muscles um my initial thought is yes I think that's a very unique example um but it's creative um and my initial thought is yes I'm laughing just because I know very little about that um and so I I can't give a yes or no answer um so just to guide you an example of when co-contraction would be yeah so someone said bicep curl um so let's say you're trying to do a bicep curl right so our elbow flexors have to turn on and let's say we're doing a bicep curl and our elbow flexors turn on but our elbow extensors our triceps turn on too much well they're going to take away from the net joint torque and so you're not going to be as strong in the bicep curl because your antagonists are uh they're producing too much torque so that exercising would be a really good example of when we probably don't want very much co-contraction now an example of when co-contraction could also be beneficial is if you're doing tasks that require really fine motor control so maybe you're writing something or maybe a a doctor is performing surgery well they want really fine precise control so they want a lot of co-contraction so for the exam the only two instances of um co-contraction being beneficial that are acceptable answers are the ACL example and the hamstring example that I gave last time um and for fine control and then for um where where co-contraction is harmful the compressive forces and the cartilage are one acceptable answer and then this exercise example that I gave are is another ex um acceptable answer now again I know we kind of finished uh the content on Monday fairly quickly are there any clarification questions before we get started all right let's go ahead and get started so we don't go around creating internal moments or internal torqus for no reason Reon we create torqus of uh with our muscles our internal moments in response to some type of external load or external demand so there there are external so uh meaning non-muscular external influences create external joint moments and so basically these there's three ways or three things that can create external moments on our joints one is segment mass and weight so if all of us held our arms out like this right at some point we would get tired our muscles are actively holding us in this position so just the mass and weight of our body segments create external torques on our bodies the mass of my arm and my hand they are producing an external shoulder a deduction moment so we have to produce an internal shoulder AB duction moment to deal with that if we hold any external objects maybe like a dumbbell a barbell you know a kettle bell a cell phone anything that we hold those create external torqus as well and then lastly ground reaction forces can create external demands or external moments on our joints so put a big circle or Star by this um I'm going to pretty much guarantee that this is also an exam question um so make sure You' pay a little extra attention to the three contributors to the external moment so let's take a closer look at these first two components so here um we're holding or this individual is holding a position of elbow flexion now our muscles or his muscles or her muscles are actively maintaining flexion if we relaxed our bicep I want you to let me know in the chat I'm looking for about 10 answers if we relaxed our bicep what would happen to the elbow joint what would the joint action be e right we would get elbow extension so the weight of the arm creates an external elbow extension moment it's external because our segment our mass is it's external to us and it's an elbow extension moment because it's going to cause elbow extension so what we have to do is we have to produce an internal elbow flexor moment it has to be the opposite if we want to maintain static equilibrium if there is an external elbow extension moment there's an internal elbow flexor moment if we were to grab a dumbbell this dumbbell would create an additional external elbow extension moment and so our elbow flexors produce a larger internal elbow flexor moment to deal with that demand so on an exam you should know you know what kind of a moment something's going to cause if I give you a diagram and I say you know and I put an arrow one way you should be able to tell me whether that's going to cause you know elbow extension knee extension shoulder adduction whatever it is so you should be able to tell me the external demand and then what we have to create internally to deal with that demand uh let me know when I'm when I'm good to move forward this slide usually takes a bit of time for uh for students to catch up and write down the notes for so just let me know when I'm good to move on e now the question is how can we increase or decrease the external demand so really increase or decrease the external moment on our joints so we go back to this formula of torque equals force time moment arm or lever arm but even more simply torque equals force time distance so this is it's more than just a mathematical equation it has multiple human movement and exercise applications so if we were to take the example again of a bicep curl and I wanted you to increase the torque I want you to find a way to increase the external torque that this dumbbell creates I want you to make the exercise harder a really easy way would be uh just to grab a heavier dumbbell if we grab a heavier dumbbell the force goes up the moment arm or lever arm doesn't change so torque goes up and that's definitely a way to make an exercise easier or sorry harder and to increase the external Demand on our joints but because this is a biomechanics class we need to be able to um make the moment arm or lever arm shorter or longer to increase or decrease Demand on our joints so here's an example so honestly let's just assume that these two people are they're the same people so we're going to assume the arm mass is the same the length of their arm is the same and the mass of these two dumbbells is the same well our shoulder joint in a lateral Rays is our axis of rotation and then the dumbbell force is the force component and then here's the moment arm and what I'm hoping that you notice is this guy on the right or on the sorry the left side his elbows are straight and so his arm is completely locked out and so uh he's maximizing the length of his moment arm but in this case on the right his elbows are bent so uh the moment arm is uh decreased that weight is closer to his shoulder joint axis of rotation and so in these two pictures for the same amount of force because he shortened his moment arm there is less external demand here so the practical application is you know if you don't have that many dumbbells or the dumbbells are in increments that are really large you might be you know you might have a dumbbell that's a little bit too hard or a little bit too easy for you and so if it's too easy you can try to find a way to lengthen the moment arm so that the external Demand on the joint is higher but if that dumbbell is a little bit too heavy for you then potentially you could find a way to shorten the moment arm so that the exercise is a little easier because the external torque is a little lower so uh we have um an activity I'm going to put everyone in breakout rooms what I want you to do is I want you to come up with other examples in exercise sports or daily life where we manipulate the moment arm length to increase or decrease the difficulty of an exercise of a sport or an activity of daily living right so I'm going to pause the uh recording um and then we'll do breakout rooms all the rooms are open so go ahead join those rooms I'm going to be popping by to make sure that everyone is participating so make sure your mics are on or at least you're chatting so that um we get as much participation in an online class as possible e e so again The Prompt was what are some other examples of movement uh where we manipulate moment arm to increase or decrease difficulty and so one example is a push-up when we do a push-up right we have our axis of rotation at our feet our body weight around our belly button is our Force component and the distance is Our Moment arm well if a push-up is too hard one of the ways we make it easier is to do a pushup on an incline right to do it on a box when we do a push-up on a box the axis of rotation doesn't change our body weight doesn't change but the moment arm becomes shorter and because the moment arm is shorter and the force doesn't change external torque goes down so it's easier for us if we do something like an inverted row or like a suspended row TRX row and it's too hard we could shorten the length of this uh of this rope or of this like TRX and start at more of an incline and now the body weight and the axis of rotation don't change but the moment arm or lever arm length does for those of you who uh go grocery shopping fairly often or you have to carry a lot of bags at once how do you carry those bags are you going to make multiple trips or are you going to fit as many bags into your hand as possible my bet is that you're going to go all at once right like unless I'm going to Costco where they don't do bags I'm going to make one trip and it could be a really difficult trip but it's only going to be one and I'm not going to carry my groceries out like this I'm not even going to carry my groceries like this I'm going to carry my groceries as close to my body as possible and so we're going to try to keep our our arms as close to our sides as possible so that we eliminate the moment arm and if there's no moment arm the external torque is very very low the only reason you feel a burn is it's not because of your shoulder joint it's because of the muscles of your shoulder girdle uh that are really active to keep your arm in place and just FYI this is just really really good Photoshop I actually used this slide excuse me for my interview at UNLV and none of the faculty members nor I really realized that this was photoshopped um it actually is it's extremely extremely well photoshopped now if we think back to uh ground reaction forces in linear kinetics the ground reaction force is the force exerted on a body by the ground after contact sorry I'm I'm assuming you need a little bit more time to to write this down I apologize uh take a minute let me know when you're good to go so ground reaction forces are the forces applied to our body by the ground and if you look here her this is Abby Steiner she's one of the best sprinters that America has this ground reaction force Vector it it it's it's posterior to the knee joint and it's anterior to the hip joint so the location of this ground reaction force Vector relative to our joint axis of rotation can create external demand so if I kind of make this bigger and we have our knee and ankle joint we have this ground reaction force and the ground reaction force it's anterior to the ankle and posterior to the knee now if we think about torqus torque is an axis a distance and a force so our joint centers our ankle joint and knee joint centers are the axis of rotation this ground reaction force is the force component and then we have this distance between the knee and the ground reaction force right that's the moment arm now just because we've applied this to an actual joint doesn't mean that the concept of torque changes it would be just like if I gave you this example and I said this was a torque it doesn't change just because we apply it to the knee joint now let me know in the chat is this torque is it causing a clockwise or is it causing a counterclockwise rotation what does it look like it's counterclockwise and so if we apply that to the knee joint right this torque is causing some type of counterclockwise rotation now the knee joint when the knee joint moves it involves the tibia moving and if this tibia were to move counterclockwise what joint action would that be would this be uh knee flexion or would it be knee extension it's flexion so the ground reaction force at the knee is causing our knees to flex so it is causing an external knee flexion moment and in order to counteract that we have to produce an internal knee extension moment so again this ground reaction force is causing an external knee flexion moment it's making our knees flex and and if we don't want to flex our knee and we want to maintain this position we have to create an internal knee extension moment what I want you to do I'll give everyone 90 seconds I want you to determine what type of external moment the ground reaction force is causing at the hip and what we have to do internally to prevent that right I'll give everyone 90 seconds and then we'll move forward you don't have to let me know in the chat e so this is causing a clockwise rotation and if we apply this to the hip joint right that is our thigh moving uh clockwise that's hip flexion so there's an external hip flexion moment and so what we have to do is we have to produce an internal hip extension moment now if we look at this ground reaction force the magnitude of the ground reaction force is the same throughout the entire Vector so so if this ground reaction force is a th000 Newtons it doesn't start from zero and then go to a thousand at the tip it's a thousand no matter where you look so if we look at the concept of torque torque equals force time moment arm if this force is the same if the moment arm is longer then the torque is greater if the moment arm is shorter the torque is less so in the chat let me know which joint has the greater external torque on it the knee or the hip and tell me why which joint has the greater torque appli to it and why how do you know yeah the hip because the moment arm is longer now this ground reaction force Vector will shift in the direction of more mass so if we put our body in a position that there's a lot of anterior Mass this ground reaction force Vector it'll shift a little bit more anterior if we increase our posterior Mass so we find a way to put more mass behind us this ground reaction force Vector it'll move posterior a little bit this influences joint loading and so I'll give everyone a chance to write down the notes but the real question is how can we shift Mass right our mass is the same so if my Mass is 100 kilograms no matter what I do my Mass is going to stay 100 kilograms but there's things I can do to make more of that mass go forward or things I can do to make more of that mass go backwards so for instance if we think about it one thing we can do to make our Mass more forward is to introduce more trunk lean right get our trunk and move it forward so if we put more mass anteriorly this ground reaction force Vector will shift more anteriorly so then now there's a moment arm at the hip and a moment arm at the knee and if we compare these two instances when we shift our Mass more anterior the ground reaction force Vector moves more anterior so the moment arm at the hip lengthens and the moment arm at the knee shortens so when we do exercises like running or squatting with a forward lean that increases the hip joint torque and decreases the knee joint torque so that's a really good example of how we can shift Mass another way we shift mass is to do a squat with our arms forward versus at our sides so go ahead take a minute write down these notes and then we'll uh we'll move forward with a with a practical example of this it would be pretty helpful uh if you just let me know when you're ready for me to move forward I know I've asked a lot of questions out of you but it just helps me pce so that I'm not going too fast right I'll wait for a couple more people to tell me I'm good and then I'll move forward this is a really important concept yeah so uh there's a question if we lean backwards does that cause more ground reaction force at the knee well remember the ground reaction force magnitude is the same but if we were to theoretically lean backwards that ground reaction force Vector the magnitude wouldn't change but the direction of it would be more backward and so the moment arm at the knee would be longer than the moment arm at the hip or it would shift at least so it would increase knee joint torque and decrease hip joint torque does that answer your question Perfect all right before we do the um the next example um I'm going to take roll but I'm going to take roll a slightly different way I have a poll for you um all it does is it asks for you to put in your first and last name so in order for you to get the attendance points today you have to put in your first and last name so I'll give everyone a minute or so to put in their names I'm going to call for last call and then I'm going to move forward if you can't type in this Poll for whatever reason just let me know in the chat that you're here another 30 seconds and then I'm going to close the poll 15 seconds last call Ashley um I'll remember to give you the points if I don't just shoot me an email and then um you can just site this conversation as attendance all right 5 Seconds 3 two one okay that's attendance so when I learned this concept in this class when I was an undergrad um it it really got me thinking of ways we could we could shift this ground reaction force Vector um and it eventually led to uh the first ever research project that I did and then eventually the second project that I did which was my Master's Degree thesis and I wanted to know you know how do different exercises influence joint loading and at the time there was a really hot debate or topic about you know the differences in a squat and a deadlift and I think when a lot of people think about biomechanics they think about like clinical applications or walking and running but there's a big population that does resistance training biomechanics um as well and and I'm part of that group so you don't have to write any of these numbers down I'm not going to ask you on an exam like according to Dr Cho's study what were the findings right like I'm not so full of myself that I would test directly from my research this is just to help you understand the point now what I found that in a squat the knee joint torque was greater than uh the knee joint torque in a deadlift but if we look at the hip the hip joint torque in a deadlift is bigger than that of a squat so basically the squat has a greater knee joint torque than the deadlift and the deadlift has a greater hip joint torque than the back squat now there's no there were no differences in ground reaction force production so the force produced in a squat versus the force produced in a deadlift there were no differences but there's differences in torque and so that got me thinking is there a difference in the moment arm potentially so these are both diagrams um from a program called visual 3D that we use to calculate our variables on the left is a squat on the right is a deadlift well let's take a look at the knee joint moment arms in the squat versus the deadlift the moment arm at the knee right it looks a lot bigger in squat than a deadlift but the moment arm at the hip it looks a lot bigger in a in a deadlift compared to a squat now if we think about the location of the mass in a squat the weight is behind us right the weight the barbell the weights are behind us but in a deadlift the weights and the barbell the actual bar itself are in front of us and so that could shift the ground reaction force uh vector anterior or posterior to influence the moment arm at the hip or the knee so again I'm not going to test you on this but you should definitely know if you shift the ground reaction force more anterior how does that increase the hip or how does that increase or decrease the knee joint torque and the hip joint torque right so this is just an example of how you could think about that now we can look at joint moments in the frontal plane as well so the ground reaction force Vector can be medial to the knee joint so this is a face on view of someone running and if we zoom in on the knee joint the ground reaction force Vector is medial to the knee joint so there's the moment arm there and so what this moment is doing what this torque is doing it's pushing the knee out laterally and it's compressing the medial component so it's basically trying to make your knee bowlegged so if this is the femur and this is the the tibia and we're going to say this way is medial this way is lateral it's making our knees do this so This Moment here it's called the external knee a uction moment the cam the content here is fair game for your exam now this knee a deduction moment it's higher in knees after ACL tears so after an ACL tear this uh the external Nea deduction moment is higher and it contributes to KNE joint pathology so if you think about it right if we look at a knee and it's every time we walk or run the medial component is compressed right then the card Lage on the medial side of the knee gets thinned so the knee a deduction moment is associated with thinner medial cartilage in people with osteoarthritis it is a predictor of the presence the severity and the pain level of osteoarthritis all right so before we do the math we're going to take like a three-minute break so let's take a break we'll reconvene at exactly 9:15 and and then we'll move forward if you have any questions I'll be at my computer so please let me know so let's calculate some joint moments so this is just a fancy way of saying let's calculate torque at a joint right the the concept of you know how to calculate torque doesn't change so early stage ACL rehab includes a single leg knee extension without an external load right so kind of like this so let's say the knee is flexed at 50° relative to the vertical the lower leg and foot have a weight of 57 Newtons and this weight of 57 Newtons acts 32 M from the knee joint Center calculate the magnitude of the external moment caused by the weight of the lower leg and foot all I'm saying is if I give you this diagram I want you to calculate the torque on the knee joint it's still a force times a distance where just applying it to a joint instead of just an arbitrary axis moment arm and force so I'm going to skip ahead to the next slide because it's just a copy paste I will always give you a diagram for the uh for an exam so if this were an exam question this is what I would give you now in this case you're going to have to either solve for the rotary component or find the length of the moment arm it doesn't matter which one you do it's totally up to you I'll give give you a hint and say it's easier to solve for the rotary component that looks like that and now what I want you to do is I want you to solve for the torque at this joint let's take a minute and a half and then we'll go over the answer together e you don't have your calculator out it's okay just set up the equation if you want to message me privately to see if you got the right answer that's totally okay with me as well another 30 seconds so to solve for the rotary component it's either the S of 50 or the cosine of 40 mathematically they're the same and that's going to give you 43.66 Newtons that's the rotary component torque equals rotary component time uh lever arm the lever arm is 32 M and that gives us 13.97 newon M but this is going to cause a clockwise rotation so it has to be negative because we're solving for joint moments we need some anatomical context so we have an external knee flexion moment of .97 newm for the sake of time I am going to uh move forward right now but keep in mind the PDF is available at 945 so you could write down the little details now if the goal is to maintain this joint angle of 50° via quadricep contraction our quadriceps have to produce an internal knee extension moment of 13.97 newm right it's the opposite static equilibrium is where it were completely motionless we per or perfectly balanced and the sum of all the torqus equals zero so clockwise torqus equals counterclockwise torqus and so if you think about it if the external torque is - 13.97 newm and we want to maintain static equilibrium where all of the torqus added together are going to be zero then our internal torque has to be positive 13.97 13.97 + positive 13.97 equal 0 right so let's move on to something that's a little bit more difficult so during the midpoint of a bicep curl the bicep Force angle of pole is 90° the bicep force is applied 03 M from The Joint Center the weight of the dumbbell is 70 Newtons and is applied 3 m from The Joint Center how much force not torque how much force do your biceps need need to produce to maintain joint static equilibrium and I want you to ignore the weight of the arm and the hand so this is the diagram we have a bicep Force the angle of pull is 90° and this is the dumbbell so what I want you to do the first step is to list your knowns and unknowns I don't believe I've given this to you on your version if I'm wrong please let me know but I want you to write down your knowns and unknowns there are four knowns and there is one unknown if I give you a number that is probably one of the knowns so take a minute um and then write down all our knowns and all our unknowns and then we'll move forward again e so I have a Known Unknown table and again this helps you stay organized and what goes into the equation at the end well one of our known is the weight of the dumbbell or the force of the dumbbell remember weight is a force and it's 70 Newtons the distance of the dumbbell is. 3 m the distance of the bicep is 03 M the angle of pole is 90° and our unknown is the bicep Force so again we're going to move forward because this table is right here what I've done for you next is I've label this free body diagram with all of our known variables right weight of the dumbbell is 70 Newtons it's negative because weight is negative the distance of the dumbbell or the lever arm is3 M the distance of the bicep is 03 M and the angle of pull is 90° and what we're trying to do is we're trying to solve for force of the bicep what I want you to do right now is I want you to pair your forces with distances to create torque every Force has to have a corresponding distance so what I want you to do is I want you to determine what the two torqus are take another uh 30 40 seconds and then we're going to move forward well we have weight of the dumbbell and we have distance of the dumbbell so we have Force time a distance so that's one torque torque of the dumbbell equals weight of the dumbbell time distance of the dumbbell the other torque we have is torque of the bicep we have force of the bicep and distance of the bicep so these are the two torqus that we have remember we're in static equilibrium so now we can plug our torqu into this equation with our values so the sum of all torqu equals z so torque of the dumbbell plus torque of the bicep equals zero what I want you to do I want you to find force of the bicep take two minutes and then I want you to send me the answer in a private chat um if you don't want to share it publicly what your answer is right take two minutes e e e I don't expect Perfection so if you if you sent me the wrong answer it's totally okay um I just want you to try so let's do this together so we know that the torque of the dumbbell plus torque of the bicep is going to give us zero and so if we plug in our GES our 70 Newtons is the force of the dumbbell it's weight of the dumbbell and the distance is3 M we don't know force of the bicep but we know the lever arm or moment arm is 03 M that's going to equal zero now this 70 being negative it's not negative because the force is going down it's negative because this force will cause a clockwise rotation and that's a negative torque so -21 new M plus torque of the bicep gives us zero well if we add 21 to both sides we know that torque of the B equals 21 new M but if we go back to the question I underlined Force how much force do your biceps have to produce so what we have to do is we have to take this 21 newton meters and isolate force of the bicep so it's 21 Newton met divided 03 M which would give us 700 Newtons so it seems like a lot of you got 21 you just forgot that last little step now what if we knew the weight and the moment arm of our hand or the arm and hand combined well it wouldn't really change too much but instead of the torque of the dumbbell plus torque of the bicep being zero it would be torque of the dumbbell plus torque of the bicep plus torque of the weight of sorry torque of the arm and hand equals z we would have one more torque and so this is the equation that I or this is our last example during a curl the bicep Force angle of pull is 60° and this bicep force is 02 M from The Joint Center the weight of the dumbbell is 44.5 Newtons and is applied 045 M from The Joint Center the weight of the forearm in hand is point is 13.35 Newtons and is applied .15 M from The Joint Center how much force do your biceps need to produce to maintain static equilibrium so it's very similar to the previous question so now when you do this there is a certain point that I want us all to get to if we can get to that point we are 95% of the way there right so I'm hoping that we can get there um we have a little bit of time so I'll give everyone five minutes exactly to do this problem right let's see how far we can get um if you want send me the answer when you get and then I'll try to give you feedback so remember the first step is to list your knowns and unknowns okay let's go through this step by step and so again I really do recommend listing your knowns and unknowns so we know the weight of the dumbbell is 44.5 Newtons the distance of the dumbbell is 045 Newtons so there's one torque there the weight of the forearm is 13.35 Newtons and the distance of the forearm is .15 M there's another torque we know the distance of the bicep is 02 M the angle of pull is 60° and the force of the bicep is our unknown so then what we have to do is label the free body diagram and make sure all of these are included so it should look like this I'm going to give you this as the free body diagram if you want and I recommend it on an exam I would do this on your own so now that we have this and again I'm not necessarily going to wait for everyone to write this down because you're going to have access to it in about 78 minutes here's our known and unknowns and we have to pair our forces with our distance to create torqus torque of the dumbbell torque of the forearm and torque of the biceps weight of the dumbbell times distance of the dumbbell gives us torque of the dumbbell weight of the forearm and distance of the forearm gives us torque of the forearm and then force of the bicep times distance of the bicep gives us torque of the bicep so now let's plug these equations or those torqu in to static equilibrium all of our t TS equals z dumbbell torque plus forearm torque plus bicep torque will give us zero so let's plug in the numbers 44.5 Newtons * 45 M this is negative because that torque will cause a clockwise rotation forearm uh weight times weight of the dumb or the distance of the forearm is 0.15 M again that's a negative torque and then force of the bicep times 02 M gives us zero if we do the math we get -2.3 newm minus 2 new M plus bicep torque equals 0 so if we add 20.3 and 2 to both sides we get that torque of the bicep torque of the bicep I apologize is 22 2.03 Newton M divide that by 02 M and we get 1,15 uh 1,1 101.5 Newtons if you got like 1,1 1.4 or three that is totally fine it's a rounding error if you got this answer or really close to the answer I am perfectly happy with our progress today this is the point I want students to be comfortable at however we're not done so if we look at this example the angle of pull here is 60° it's not 90° like the last time and remember if our angle of pole is not 90 we have a rotary and non-rotary component now this distance of 02 M that I gave you it's not the moment arm the moment arm would look like this it's not working give me a second the moment arm would look like that but so this is the lever arm so when we use torque or sorry when we calculate torque using the lever arm remember that means we use the rotary component so this 1,1 1.5 Newtons that's not force of the bicep that's the rotary component but what I wanted us to do is I wanted us to find force of the bicep so what we actually have to do let me clear this is we have to make a new triangle we have force of the bicep with the angle of pull of 60° and then the rotary component is here if you drew the rotary component on the other side of 60 like this that is also okay so to find force of the bicep we do SOA TOA six 90 30 so we can use the cosine of 30 or the S of 60 to find the force of the bicep I recognize that I'm going quickly but we do have a chance to finish this lecture today so I'm taking it right so you're going to have to watch this again again watch this again probably on your own uh to cement it the cosine of 30° equals adjacent over hypotenuse but be careful this 1,100 101.5 is the adjacent side it's not the hypotenuse we can't multiply both sides by hypotenuse so we divide both sides by 1,00 or by cosine of 30 and we get 1,271 point9 Newtons as the force of our bicep the other option is to find the moment arm of the bicep so to find that so we have 60 90 that's 90 because a moment arm is perpendicular and 30 so the S of 60 equals opposite divid 2 m multiply both sides by 02 and the moment arm of the bicep is 017 M we could plug that into the equation instead of the point uh 02 so instead of the lever arm we put the moment arm and then you would get 1, 12719 Newtons so as a hint if the angle of pole is 90° you don't have to do this if the angle of pole is 60° you do so I get that that was a lot in a really short amount of time I I do apologize there's just so much that we have to go over and torque that the lectures are pretty packed um so you're going to have to watch this on your own um now on the exam I am leaning towards just making the angle of pull 90 so that I could give um I guess more points uh canvas doesn't have a way of making um points uh partial on math questions so if you don't get this answer you would get a zero out of a six even though on a written exam I would give you a five out of a six for getting here right I want to be able to give partial points so I'll keep you updated um on what I'm going to do as we get closer to the exam but that's it for today so let's wrap up before you leave what are the components of the external moment how can we manipulate lever arm or moment arm length to make exercises easier or harder what are some examples of joint moments in human movement how do we solve for static equilibrium at a joint and how do we solve for static equilibrium if we're given a lever arm if you have questions stick around if not uh I'll see some of you later this week if not have a fantastic spring break