Questions tagged [vectors]
Geometric object with magnitude (length) and direction.
2,604
questions
0
votes
1
answer
1k
views
Calculating vector of plane resulting from tailwind
In some basic physics homework I have, it asks what the resulting vector would be for a plane traveling at x m/s in y direction that is affected by a tailwind going in z direction at w m/s. How would ...
- 103
0
votes
1
answer
661
views
What causes a gyroscope to eventually rotate/fall over?
Hey so I've just learned about angular velocity and momentum and how torque changes it.
Looking at a wheel spinning around an axis, with one end being held up by a rope, what causes the wheel to ...
- 227
0
votes
3
answers
45k
views
Uses of vectors in real life [closed]
I always wonder how vectors are used in real life.Vectors and decomposition of vectors,dot and cross products are taught in the early stage in every undergraduate physics course and in every ...
- 472
1
vote
2
answers
3k
views
Vectors, Component Addition, and Significant Figures
I have two vectors $\vec{A}$ and $\vec{B}$ and I need to find the x- and y-components of $\vec{C} = \vec{A} + \vec{B}$. Here's what I have so far:
$$|\vec{A}| = 50.0 \mathrm{m}, \theta = -20.0^\circ$$...
- 113
1
vote
2
answers
3k
views
Acceleration vector - deceleration vs direction
If acceleration of something $= - 10 \text{ m s}^{-2}$
And forwards is define as north.
Does that mean the object is getting slower (decelerating) or accelerating in the reverse direction (south)
...
- 6,927
36
votes
4
answers
67k
views
How can area be a vector?
My professor told me recently that Area is a vector. A Google search gave me the following definition for a vector:
Noun: A quantity having direction as well as magnitude, esp. as
determining the ...
- 1,035
87
votes
9
answers
140k
views
What is the physical significance of dot & cross product of vectors? Why is division not defined for vectors?
I get the physical significance of vector addition & subtraction. But I don't understand what do dot & cross products mean?
More specifically,
Why is it that dot product of vectors $\vec{A}...
- 7,335
5
votes
3
answers
3k
views
Does the phase space (configuration and momentum space) of particles have a Euclidean norm? Does it have a useful meaning of "distance"?
Often in engineering physics, different vector spaces are used to visualize the trajectories (evolution) of systems. An example being the $6n$ dimensional phase space of $n$ particles. It is not very ...
- 1,672
5
votes
1
answer
758
views
What does scalar phi represent in spacetime?
Trying to understand one-forms and vectors via Schutz's A First Course In General Relativity.
His example uses a spacetime diagram, a scalar field phi, a curve (worldline) parametrized using proper ...
- 3,059
8
votes
2
answers
2k
views
Nature of spacetime 4-vector and tangent space?
An entry level confusion about spacetime. I understand that a 4-vector describes a point or event in spacetime. But I've also read (Bertschinger, 1999) that re spacetime "we are discussing tangent ...
- 3,059
-2
votes
2
answers
40k
views
The resultant of two forces acting at any angle? [closed]
I am studying about forces as vectors. And they give me this equation:
$c^2 = a^2 + b^2 - 2ab \cos C$
Can anybody explain me the second part of the equation? I perfectly understand $c^2 = a^2 + b^2$ ...
- 312
11
votes
1
answer
6k
views
Uniqueness of Helmholtz decomposition?
Helmholtz theorem states that given a smooth vector field $\pmb{H}$, there are a scalar field $\phi$ and a vector field $\pmb{G}$ such that
$$\pmb{H}=\pmb{\nabla} \phi +\pmb{\nabla} \times \pmb{G},$$
...
- 3,732
35
votes
1
answer
10k
views
How to define orbital angular momentum in other than three dimensions?
In classical mechanics with 3 space dimensions the orbital angular momentum is defined as
$$\mathbf{L} = \mathbf{r} \times \mathbf{p}.$$
In relativistic mechanics we have the 4-vectors $x^{\mu}$ and ...
- 9,890
0
votes
3
answers
3k
views
Direction of Magnetic force from a current running through a coil of wire
What is the direction is the magnetic force vectors pointing from a coil of wire that has current running through it?
http://www.ndt-ed.org/EducationResources/CommunityCollege/MagParticle/Graphics/...
- 3,871
19
votes
9
answers
6k
views
Quaternions and 4-vectors
I recently realised that quaternions could be used to write intervals or norms of vectors in special relativity:
$$(t,ix,jy,kz)^2 = t^2 + (ix)^2 + (jy)^2 + (kz)^2 = t^2 - x^2 - y^2 - z^2$$
Is it ...
- 2,890
0
votes
2
answers
519
views
vector cross products
Lets say you have a free particle in a rotating frame of reference with constant angular velocity $\mathbf{\omega}$. By free, I mean there are no real forces on it. Lets call the moving system "primed"...
- 307
2
votes
3
answers
2k
views
Understanding weight on an inclined plane
I'm trying to solve a problem where I have an object resting on an inclined plane, with the angle of the plan being alpha, and the weight being w. I'm having trouble figuring out how I can calculate ...
user1766
-1
votes
3
answers
14k
views
Vector product in 2 dimensions [closed]
If I have a vector A=4i+3j and B=5i-2j, how can I find the vector product AxB? I know that given the angle, its C=AB sin theta, but how can I solve this without the angle?
user1763
13
votes
3
answers
17k
views
Physics of a skateboard ollie
Does anyone have a good explanation of the physics and vectors of force involved in the skateboarding trick the ollie (where the skater jumps and causes the skateboard to rise off the ground with him)...
- 281
4
votes
2
answers
4k
views
Can vectors in physics be represented by complex numbers and can they be divided? [closed]
Below is attached for reference, but the question is simply about whether vectors used in physics in a vector space can be represented by complex numbers and whether they can be divided.
In abstract ...
- 2,204
3
votes
3
answers
2k
views
Negative vectors (e.g. velocity)
If you said someone had a velocity of $-12\,{\rm mph}$ and they were traveling north? Wouldn't it mean that they were traveling $12\,{\rm mph}$ south?
This is a quote from here:
if something [...
- 6,927
1
vote
4
answers
2k
views
How to correctly show units with a vector?
Supposed I have an position vector $$\vec{r}=\begin{pmatrix}
10.0 & -30.0 & 25.0\end{pmatrix}$$ expressed in $\mathrm{millimeters}$.
What is the correct notation to display $\vec{r}$
$\begin{...
- 38.7k
26
votes
7
answers
9k
views
How is it that angular velocities are vectors, while rotations aren't?
Does anyone have an intuitive explanation of why this is the case?
- 2,784
0
votes
3
answers
2k
views
A force's magnitude
In this question I asked about gravity and in the answers it came up that the magnitude is equal (of the gravity acting on the Sun and the of the gravity acting on the Earth)
Does magnitude simply ...
- 6,927