I liked the explanation at the start of component forces but, the dot product using this car analogy leads to a couple issues I feel. The dot product outputs 50 (N...) for the first two scenarios, for the "overall force we are pushing on the car" but, this is physically speaking incorrect for the car, the result is 15N newton in the positive x direction, In this scenario the dot product moreso would find how similar(+) or different(-) the two forces are (like when you say how much your friend is helping you) BUT while using an abstract SCALAR metric, like how you knew to remove the N sign from your different dot product examples. It doesn't work in Newtons, but if you did want to then you would: 1. compare the forces in Newtons, by subtracting each force's x & y component from the other's to see the difference 2. find the "overall force we are pushing on the car" in Newtons, by adding each force's x & y component together and use Pythagoras to summarise the information into an amount of Newtons and resulting direction I'm sure this isn't news to you considering you have a maths UA-cam channel, but in this example it just happens that physics denies that the result is how the dot product processes two forces... Mechanical work is an example that is more fitting in physics for the dot product! Good interesting video Irish brother
Yeah you’re definitely right about that. My aim with this video was to give a better intuition as to what the dot product means, not necessarily rigorous uses of it. When I learned about the dot product, I was told it’s a measure of “how parallel two vectors are,” which has even more issues than the force analogy. And you’re also right that I should’ve said that it is indeed an “arbitrary scalar metric” - some people might think, due to my explanation, that the dot product can be used to find the resultant force in a direction, which of course isn’t true. Thanks for pointing all of that out. It was very insightful and interesting! 😄
Thank you so much...! 😊
Yh the car analogy rlly helped when i heard of it i think it was from eddie woo who told it to me
I liked the explanation at the start of component forces but, the dot product using this car analogy leads to a couple issues I feel.
The dot product outputs 50 (N...) for the first two scenarios, for the "overall force we are pushing on the car" but, this is physically speaking incorrect for the car, the result is 15N newton in the positive x direction,
In this scenario the dot product moreso would find how similar(+) or different(-) the two forces are (like when you say how much your friend is helping you) BUT while using an abstract SCALAR metric, like how you knew to remove the N sign from your different dot product examples.
It doesn't work in Newtons, but if you did want to then you would:
1. compare the forces in Newtons, by subtracting each force's x & y component from the other's to see the difference
2. find the "overall force we are pushing on the car" in Newtons, by adding each force's x & y component together and use Pythagoras to summarise the information into an amount of Newtons and resulting direction
I'm sure this isn't news to you considering you have a maths UA-cam channel, but in this example it just happens that physics denies that the result is how the dot product processes two forces... Mechanical work is an example that is more fitting in physics for the dot product!
Good interesting video Irish brother
Yeah you’re definitely right about that. My aim with this video was to give a better intuition as to what the dot product means, not necessarily rigorous uses of it.
When I learned about the dot product, I was told it’s a measure of “how parallel two vectors are,” which has even more issues than the force analogy. And you’re also right that I should’ve said that it is indeed an “arbitrary scalar metric” - some people might think, due to my explanation, that the dot product can be used to find the resultant force in a direction, which of course isn’t true.
Thanks for pointing all of that out. It was very insightful and interesting! 😄
I love the analogy and no background music that too straight tot the point. Immediately subbed