New answers tagged vectors
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Connection between contra-/covariant vectors in SR and complex numbers?
I think the thing you're looking for here is the Wick rotation. You start with a real vector space with coordinates $(t,x) \in \mathbb{R}^2$ and replace the real $t$-coordinate with a purely complex ...
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Why the normal vector addition does not seem to work in centripetal acceleration?
If the curve is given in parametric polar coordinates (r(t),θ(t))
, the velocity and acceleration vectors can be calculated in the moving base . (We denote by a point the derivation with respect to ...
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Why the normal vector addition does not seem to work in centripetal acceleration?
You cannot add acceleration and velocity by vector addition because they are quantities of different dimension. You cannot add m/s and m/s$^2$.
What you can add is velocity and the product of ...
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Why the normal vector addition does not seem to work in centripetal acceleration?
The concern raised in this question, as I understand it, is that we start with a tangential velocity:
But then, the acceleration, being perpendicular to the velocity, causes the increment $\mathbf{a} ...
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Why the normal vector addition does not seem to work in centripetal acceleration?
Its important to note that the velocity is infact not constant,as it is changing its direction.
But,I'm going to show you why the speed is constant if we have the fact that the angle between the force ...
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Why the normal vector addition does not seem to work in centripetal acceleration?
Speed but not velocity is constant. The velocity vector changes all the time exactly due to the acceleration component.
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Accepted
Derivative of the product of a scalar function and a vector valued function
The author's point here is that one can treat a vector function like a scalar function when it comes to differentiation. This may be obvious but the book is meant for students with a limited ...
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Counter example for 2D rotation not being vector?
The constraint "without complex math" is highly subjective. I'll take it to mean "without Geometric Algebra / Clifford Algebra" (which clarifies what is and what isn't a vector, ...
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I have confusion between the concept of distance and displacement
The reason is that is how the two quantities are defined. They are defined that way because we have situations - both in and out of physics as a scientific practice - where we want to either have or ...
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I have confusion between the concept of distance and displacement
See friend you are not wrong anywhere you just have confusion between vector and scalar quantities. let me clear it to you,
See displacement is just the direct path from 'New Delhi' to 'Mumbai'. In ...
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I have confusion between the concept of distance and displacement
But I want to know that why distance doesn't have direction ?
Consider a ruler. It is a device that measures spatial separation or distance. The length of the ruler does not change no matter what ...
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I have confusion between the concept of distance and displacement
Before getting into an answer, I shall first address a question in one of the comments. The question was `But can you explain to me that if displacement is $0$
then how displacement can have direction?...
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I have confusion between the concept of distance and displacement
Using your own example, let's say that you're planning to fly from Delhi to Ludhiana (284km), and then from Ludhiana to Mumbai (1350km).
How far did you fly?
$$284+1350 = 1634\text{km}$$
That number ...
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I have confusion between the concept of distance and displacement
We define distance to be a "directionless" quantity and displacement to be a vector quantity because its useful to define them this way. Consider a round trip on a line between two points. ...
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I have confusion between the concept of distance and displacement
Shyam is travelling from New Delhi to Mumbai. Now according to this example we can say that distance and displacement are same.
If you look up New Delhi to Mumbai on the Internet you get two values:
...
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How can I formalize better this proof that angular momentum is conserved for a small impulse?
This is a comment that got too long. OP's question is very good. The quoted paragraph of infinitesimal estimates on p. 188 in Ref. 1 seems like an anticlimax after introducing a rigorous Def. 4.6 of ...
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How can I formalize better this proof that angular momentum is conserved for a small impulse?
I'll attempt to sum up here my understanding in a "community wiki" fashion. Anyone who reads this and thinks it can be improved please edit / comment.
The definition of Lagrange stability (...
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How can I formalize better this proof that angular momentum is conserved for a small impulse?
Overview
If total momentum is conserved between two bodies due to Newton's 3rd law, then angular momentum will also be conserved as the impulse will act and react on the same line of action.
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How can I formalize better this proof that angular momentum is conserved for a small impulse?
Summary of the changes in $\delta L$ for a decomposed $\delta p$
To be a bit more complete, here is a mathematical overview how $\delta p$ concretely changes the $L$.
Parallel to $\mathbf{L}$: $\...
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Accepted
How can I formalize better this proof that angular momentum is conserved for a small impulse?
In general, $\delta \mathbf{L} = \delta \mathbf{r} \times \mathbf{p} + \mathbf{r} \times \delta \mathbf{p}$, which in this case becomes $\delta \mathbf{L} = \mathbf{r} \times \delta \mathbf{p} = \...
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Pauli matrix relation of dot and cross products with complex numbers
This is a confusing form of the Clifford-algebraic identity $ab = a\cdot b + a\wedge b$, where $a$ and $b$ are vectors. It's confusing because it mixes Clifford-algebraic and 3D-vector-algebraic ...
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