Hell Yeah! Appreciate the guessing perspective shown here. Gives a broader view of the same thing you have to normally look very closely at. Another way to learn!
Very cool. Simple yet very effective approach! By the way I like the long videos better because it gives the brain room for deeper thinking. If you decide to do something under x minutes, your brain has to focus on that time frame and creative thinking can be less effective. What do you think about that?
Yes! if I do short videos I will make sure I do long videos. Some students just want the solution. But after talking to my bother today. I gave him a book of logic riddles and puzzles and he gave me pre-college math and physics riddles. And we both agreed that problem solving is way more important than just recalling a known answer. So on top of long format videos I might even make them extra long showing the first attempts and errors. I don't think anyone is making videos like that. Showing the pure madness, brute force, creativity, and dead ends that happen while problem solving. And then that problem you sent. Now that I went through all that. I want to make 3 more videos showing the most concise method to sum moments about two the intercection of two vectors. Finding the perpendicular distance from dot product of a unit vector and how to intuit the unit vector fast given geometry. BIG THANKS! for that 3 vectors with a cross product that cancels. I understood the logic but will try it for myself. Dotting the cross product back in should give a single number scalar. I get how dotting the two cross vectors will be a scalar of zero but I don't logically know why the third vector stills stays a vector. I will play around with that! I understood that will work for any 3 none planar vectors. If planer the dotting the cross product vector would be zero all around. So I understood when it would be useful. Way Cool!
@holdmybipolar First of all, letting the errors and struggles in the video make you a strong character. Many simply do not want to show how "vulnerable" they are. But the funny thing is, THAT is what makes the difference! Very strong, very cool. As you said, this format is not common, because poeple are simply afraid of failure and what others think or say. Only strong caracters have the gut to let errors and struggles in. For students it is a gold mine, because a student WILL make those mistakes for sure. And if one can see what the exact error is, he/she will learn faster. As for the "clever trick". I guess it works because of vector algebra characteristics. If you cross product 2 Vectors ( for example S1,S3), then you make a vector "V" perpendicular to S1 and S3. That is cross product. So now you have "V" perpendicular to S1 and S3, but not S2 and F. Now if you dot product the whole equation with "V", S1 and S3 will be eliminated, because "V" is perpenducular to them (90° ), and the dot product says : AB cos phi. In our case ( S1 S3 cos phi.) Now cos90 becomes 0. So those S1 and S3 become 0. Because "V" is NOT perpendicular to S2 and F, so dot product wont give 0, bacause the angle between "V" & S2 and "V" & F is not 90° . That is how this elimination works I guess. And why you are allowed to do this approach? Because if I add to every element +1 in the equation then it wont change the value of that equation. Here I add to every element a dot product.(It is just a deliberate coincidence that I mutiply everything with a special vector V (S1 cross S3) that will cancel S1 and S3.) So neither S2 nor F wont change its original value, becuase of equillibrium. I add the same value to those. And also you said that you do not logically see how S2 and F remain vectors after a scalar multiplication. I am not sure but I guess they won't. We make scalars from vectors in this case. So the unknown S2 (vector) after scalar multiplication becomes a S2 scalar. We simply handle it as a scalar unknown. But again, it is only my guess, to understand it deeper I should dive into Vector Algebra deeper. Again, this method is brilliant, because you do not need a calculator to solve for 3 unknowns with System Of Equtions function. You can do it by hand. After some google research, it turns out that this method works outside of Concurrent 3D Systems as well. But the use of it requires a careful investigation, where, when, how! For systems with Moments it is also usable somehow but I need more knowlede on that...
Hell Yeah! Appreciate the guessing perspective shown here. Gives a broader view of the same thing you have to normally look very closely at. Another way to learn!
Make a video on chimney mechanics
I sent you the "clever solution" via Email. There are 2 Mails, because I forgot to attache the PDF in the first one. But read it anyway.😅
Very cool. Simple yet very effective approach! By the way I like the long videos better because it gives the brain room for deeper thinking. If you decide to do something under x minutes, your brain has to focus on that time frame and creative thinking can be less effective. What do you think about that?
Yes! if I do short videos I will make sure I do long videos. Some students just want the solution. But after talking to my bother today. I gave him a book of logic riddles and puzzles and he gave me pre-college math and physics riddles. And we both agreed that problem solving is way more important than just recalling a known answer. So on top of long format videos I might even make them extra long showing the first attempts and errors. I don't think anyone is making videos like that. Showing the pure madness, brute force, creativity, and dead ends that happen while problem solving. And then that problem you sent. Now that I went through all that. I want to make 3 more videos showing the most concise method to sum moments about two the intercection of two vectors. Finding the perpendicular distance from dot product of a unit vector and how to intuit the unit vector fast given geometry. BIG THANKS! for that 3 vectors with a cross product that cancels. I understood the logic but will try it for myself. Dotting the cross product back in should give a single number scalar. I get how dotting the two cross vectors will be a scalar of zero but I don't logically know why the third vector stills stays a vector. I will play around with that! I understood that will work for any 3 none planar vectors. If planer the dotting the cross product vector would be zero all around. So I understood when it would be useful. Way Cool!
@holdmybipolar First of all, letting the errors and struggles in the video make you a strong character. Many simply do not want to show how "vulnerable" they are. But the funny thing is, THAT is what makes the difference! Very strong, very cool. As you said, this format is not common, because poeple are simply afraid of failure and what others think or say. Only strong caracters have the gut to let errors and struggles in. For students it is a gold mine, because a student WILL make those mistakes for sure. And if one can see what the exact error is, he/she will learn faster. As for the "clever trick". I guess it works because of vector algebra characteristics. If you cross product 2 Vectors ( for example S1,S3), then you make a vector "V" perpendicular to S1 and S3. That is cross product. So now you have "V" perpendicular to S1 and S3, but not S2 and F. Now if you dot product the whole equation with "V", S1 and S3 will be eliminated, because "V" is perpenducular to them (90° ), and the dot product says : AB cos phi. In our case ( S1 S3 cos phi.) Now cos90 becomes 0. So those S1 and S3 become 0. Because "V" is NOT perpendicular to S2 and F, so dot product wont give 0, bacause the angle between "V" & S2 and "V" & F is not 90° . That is how this elimination works I guess. And why you are allowed to do this approach? Because if I add to every element +1 in the equation then it wont change the value of that equation. Here I add to every element a dot product.(It is just a deliberate coincidence that I mutiply everything with a special vector V (S1 cross S3) that will cancel S1 and S3.) So neither S2 nor F wont change its original value, becuase of equillibrium. I add the same value to those. And also you said that you do not logically see how S2 and F remain vectors after a scalar multiplication. I am not sure but I guess they won't. We make scalars from vectors in this case. So the unknown S2 (vector) after scalar multiplication becomes a S2 scalar. We simply handle it as a scalar unknown. But again, it is only my guess, to understand it deeper I should dive into Vector Algebra deeper. Again, this method is brilliant, because you do not need a calculator to solve for 3 unknowns with System Of Equtions function. You can do it by hand. After some google research, it turns out that this method works outside of Concurrent 3D Systems as well. But the use of it requires a careful investigation, where, when, how! For systems with Moments it is also usable somehow but I need more knowlede on that...
Take lectures on civil engineering topics please