Questions tagged [vectors]
Geometric object with magnitude (length) and direction.
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What is the difference between a vector and a representation of a vector in QM?
What does the phrase
The wave function is a representation of the abstract quantum state.
Or more generally,
$A$ is a representation of a vector $\vec V $
mean?
What is the difference between a ...
3
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3
answers
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In this conservation of momentum problem, where is the sign error coming from?
Say I have a particle travelling in the $x$-direction and breaking into two pieces:
Conservation of momentum in the $x$-direction obviously gives:
$$mv = m_1 v_1 \cos(30) + m_2 v_2 \cos(60).\tag{1}$$
...
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Understanding angular velocity $\omega$ as a vector
I would like to validate my understanding of angular velocity as a vector.
Suppose we have a particle $P$ moving around in $3D$ space in some arbitrary way. At any given point in time, we would like ...
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How many null directions are there?
The metric signature of spacetime is usually given as ($3,1$), but spaces can also be ($3,n,1$). Null surfaces include photons and event horizons, which exist, so is $n$ actually $ > 1$ in the ...
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Regarding direction-dependent quantities
We observationally determine whether a quantity can be a vector or not. For example, we chose force and momentum to be vectors to due to the fact that inertia depends on direction.
Then it seems like ...
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2
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In equation of torque and angular momentum what is the position vector exactly
In terms of vectors:
$$
L = r \times p
$$
and torque:
$$
T = r \times F
$$
In both these cases what exactly does the $r$ vector represent? Is it vector from origin of axis or center of mass? How would ...
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Lorentz transformation of basis vectors in The geometry of Minkowski spacetime by Gregory L. Naber
Gregory L. Naber's book introduces the Lorentz transformation like this:
Now let $L :M→M$ be an orthogonal transformation of $M$ and
${e_1, e_2, e_3, e_4}$ an orthonormal basis for M. By Lemma 1.2.3, ...
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Can momentum exist in a null direction?
CONTEXT (skip to "my question is"):
As I understand it, and correct me if I'm wrong, an orbit trades momentum between the X and Y directions. But spacetime can have negative and even null ...
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How does the covariant vector transformation rule come?
As far as I understand, if a contravariant vector transforms in the form:
$$\vec{x}'=A\vec{x}.$$ (Where $A$ is the transformation matrix)
Then the covariant vectors shall transform as
$$\tilde{w}'=(A^{...
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Why do we use the Pythogorean theorem for the net Force in this problem rather than just summing the $x$ and $y$ components of $F$? [duplicate]
My solution was that I would need to sum the $x$ and $y$ components for the net force. However, the solution manual say that the net force should be calculated by using the Pythogorean theorem. I ...
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Derivation of the function for the position of a particle given that a constant force acts on the particle which always points to fixed point [closed]
A particle of mass $m$ is moving with initial velocity v. A constant force F acts on the particle in a direction which always points to a fixed point P. If initially the direction of v was ...
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Angular Components of Polar coordinate vectors
I’m a third year physics student who was relaxing on vacation during spring break, and now am having a crisis because I realized I somehow never came across this problem before.
A vector in polar ...
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Show that the dot product of two basis vectors in special relativity gives the metric
I'm reading Schutz's Introduction to GR and came across an exercise problem. The problem is the following:
Show that the vectors $\{\vec e_{\bar \alpha }\}$ obtained from
$$\vec e_{\bar \beta } = \...
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Orthogonal self-intersection of geodesics
I learnt that geodesics parallel transport their velocity vectors. Does that mean a geodesic cannot intersect itself orthogonally?
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Elliptical orbit, work done by gravity
Consider two points (A & B) on one half of an elliptical orbit. Satellite moves from point A to B. I want to calculate the work done by the gravitational force, but I DO NOT WANT to use energy ...
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Where does the negative sign disappear?
The defining equation for simple harmonic motion is such
$$a=-ω^2x$$
When we find the centripetal acceleration of an object in orbit we use the formula
$$a=ω^2r$$
As a consequence of the accleration ...
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3
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Where to apply $\nabla$ operator when taking curl of a cross product?
In my EM class we went over $$\nabla\times \frac{\vec{d}\times \vec{r}}{r^3}$$ which apparently can be breaken down to $$r(d\cdot \nabla)\frac{1}{r^3}-d(r\cdot\nabla)\frac{1}{r^3}+\frac{\nabla\times(d\...
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Vertical Component of Normal Force on Bank
Consider the above diagram.
Apparantely the vertical component of the normal force should balance $mg$.
However, this cannot be the case. The normal force is equal to the component of $mg$ ...
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Why "time part" represents energy in Four-momentum?
I was going through Spacetime Physics by Taylor and Wheeler and came to a point where they said, and I quote,
In what follows we find that momenergy is indeed a four-dimensional
arrow in spacetime, ...
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How can vertical component of normal force balance the weight?
Consider a bicyle on a bank.
The weight of the bicycle acts downwards, we can resolve this vector to the normal force and a component down the bank. Hence the normal force is less than this weight ...
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2
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Confusion about breaking apart vectors
Hi I've probably got a very basic question but I'm really confused about this. If I have a vector that starts at the origin and points to say (3,-3) so the 4th quadrant, and I am wanting to split ...
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Tangential acceleration and the transverse acceleration?
i'm studying Classical mechanics from Analytical mechanics textbook , and i'm encounter with transverse acceleration in Chapter five The term $\omega \times r'$ is called the transverse acceleration, ...
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Magnitude of Acceleration Vector when Speed is Constant
If I observe a change in direction of velocity, but not in speed: What does the acceleration vector look like?
I am confused! The difference vector between two vectors of equal length A has a ...
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Instantaneous speed x instantaneous velocity
Related to Distinguish between instantaneous speed and instantaneous velocity
I understand that the average velocity is given by the displacement divided by the change in time, and it is a vector ...
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Can we call numbers unidirectional vectors? [duplicate]
I have never thought so deeply about addition and subtraction. But today I noticed something. When adding or subtracting numbers, we actually apply the rules we use for vectors (for example, the ...
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Could you calculate the force between two NON-PARALLEL, straight current carrying wires?
Just like there are ways to solve for the force between two straight parallel wires, what is the way we could find the force between non-parallel wires?
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Comparing vectors on a sphere
Say I have two points on the surface of a sphere $p_1$ and $p_2$. To each point, I have two unitary vectors $v_1$ and $v_2$ (not necessarily tangent). I want to find the alignment between $v_1$ and $...
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Physical significance of $\vec{w}$ $\times$ $($curl $\vec{v})$
I think if curl of a vector field $\vec{v}$ corresponds to an applied rotation, it's cross product with a velocity vector field $\vec{w}$ (say) should give something analogous to the resulting torque. ...
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Calculation of angular frequency and wave vector from time series data using minimum variance method
Suppose, I have 20 data for the velocity components Vx, Vy and Vz with 5 minutes interval of time, how to find the angular frequency and wave vector using minimum variance method for those data? What ...
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Finding radial acceleration from $xy$ vector cordinate [closed]
I know that is a silly question but i cant figure it out.
Suppose we have
$$ \textbf{R} = A i + B j $$
and want to find the radial acceleration.
We know that the radial acceleration is
$$ \ddot{r} -...
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