Geometric object with magnitude (length) and direction.
2
votes
2answers
183 views
Coordinate transformation from earth to solar
I am building a 3d model of the solar system and need to figure out the position of the pole stars of each planet in order to tilt the planets in the correct direction the correct amount. I've already ...
0
votes
0answers
63 views
How to find the directional cosines?
l+m+n=0 where l,m,n are the directional cosines of a point P in the x,y,z plane. How do I find the angles the radius vector makes with the axes. I get two equations l+m+n=0 and l^2+m^2+n^2=1. But how ...
1
vote
3answers
86 views
Currents and magnets
I've watched this video on YouTube by Sixty Symbols entitled "Currents and Magnets". In the video, the professor demonstrates the expansion of a wire due to current heating it up and he also ...
0
votes
0answers
250 views
(beginner) Position Vector [closed]
I don't understand how vector GP was found. In the solution, they described GP as being equals to vector : \begin{pmatrix} -Rsin[\theta(t)] \\ -Rcos[\theta(t)] \end{pmatrix}
How to think ?
Then I ...
0
votes
1answer
84 views
Showing $ \textbf{F} \cdot d\textbf{s} = -dV$ is equivalent to $ F_s = -\frac{\partial V}{\partial s}$
Can someone please explain how the following
$$ \textbf{F} \cdot d\textbf{s} = -dV$$
is equivalent to
$$ F_s = -\frac{\partial V}{\partial s}$$
using some intermediate steps. I don't follow this ...
0
votes
2answers
100 views
Showing $ m\int \frac{d\textbf{v}}{dt} \dot \normalsize \textbf{v}dt = \frac{m}{2}\int \frac{d(v^2)}{dt}{}dt$
Can someone please explain how this equation is valid, using intermediate steps if available?
$$ m\int \frac{d\textbf{v}}{dt} \dot \normalsize \textbf{v}dt = \frac{m}{2}\int \frac{d(v^2)}{dt}{}dt$$
...
1
vote
1answer
113 views
Determine the flow and amplitude equation for thermal energy (with Del operator)
It is a question vector calculus and Maxwell's laws. I put it this way. Let's say, we are working in a $3$-Dimensional space ( e.g $x\cdot y\cdot z = 4\cdot3\cdot2$, a certain room/class of that size ...
0
votes
3answers
120 views
Dimension of vector resulting from tensorial product
I'm quoting what I found in a book about quantum computation:
Individual state spaces of $n$ particles combine quantum mechanically through the tensor product. If $X$ and $Y$ are vectors, then ...
2
votes
2answers
456 views
Meaning of angular velocity in a rotating system
When you study the motion of a rigid body you have $\vec\omega$, the vector associated to angular velocity. In the case you are using Euler angles and want a quick formula for the rotational kinetic ...
0
votes
2answers
99 views
Precessional motion of active galactic nuclei
I want to set a simulation for jet which has a precessional motion. The symmetry axis of jet is $z$ axis, i.e. jet is propagating along $z$ direction making angle $\theta$. I set the velocity ...
2
votes
1answer
471 views
Which are other anomalies like Divergence of 1/r^2?
As one might have learned in the basic science (ex. Electrodynamic
theory), when we apply the divergence theorem to the vector function
like 1/r^2 with it pointing in the radial direction (like ...
2
votes
1answer
287 views
Combined Gravitational Force Vectors in a Spherical Coordinate System
Asking a question here is quite intimidating for me -- while I love Physics, my high-school understanding only allows me to go so far... I've been trying to solve this problem for the last couple of ...
0
votes
0answers
65 views
Consider the rectangle ABCD with the following Dimensions abs(BC)=3 and abs(CD)=4, so, abs(AB+BC+CD)=5 [closed]
[Consider, the, rectangle, ABCD, where \left \| \widehat{BC} \right \|=3 , and, \left \| \widehat{CD} \right \|=4, then, \left \| \overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD} \right ...
1
vote
1answer
165 views
How to determine n equidistant vectors from point P in three dimensions
As an assignment for uni I need to figure out an algorithm that explodes a particle of mass $m$, velocity $v$, into $n$ pieces.
For the first part of the assignment, the particle has mass $m$, ...
2
votes
1answer
142 views
Why can we use just one angular velocity vector to describe the rotation of a whole non-inertial reference frame?
The other day in class the professor was explaining non-inertial reference frames. We were working out how to find the acceleration of a point as measured from the non-inertial reference frame, and ...
2
votes
3answers
235 views
How to distinguish 4D and 3D vectors in handwriting?
Usually vectors are denoted with bold font in printbooks and with arrows above in handwriting.
In Thorn's e al. Gravitation, 4D vectors are denoted with bold and 3D vectors with bold italic. How to ...
2
votes
2answers
302 views
2D - Kinematics - Linkage System using Vector Algebra
I have this question that I dont know how to solve correctly :
My question is, how do I find $V_B$ ? I will find the angular velocities myself, but I want to know the method to get $V_B$ ?
I know ...
0
votes
2answers
189 views
Find vector position in time give this graph?
Graph is position x position. There are 3 points, $A$, $B$ and $C$.
$A(0,2)$
$B(4,2)$
$C(6,0)$
Particle travels from $A$ to $B$ and from $B$ to $C$ at constant $v = 2 ~m/s$.
Find vector ...
0
votes
2answers
183 views
So where is mistake in the formula of wave number (magnitude of wave vector)?
I have following form for wave vector $k_2=n_2 \omega/c_0$. Now because $\omega=2 \pi c/ \lambda$, then $k_2=n_2 \omega/c_0=\frac{n_2 2 \pi c_0}{c_0 \lambda}=\frac{n_2 2 \pi}{\lambda}$. But problem is ...
1
vote
0answers
80 views
Phonon vectors and characteristic length interpretation
Basically I have a set of vectors of unit length, $\{\nu_i\}$, describing the movement of phonons (all orthogonal to each other), $\{\omega_i\}$. Lets say I only have two atoms, $m_1$ and $m_2$. In ...
1
vote
2answers
210 views
Kinematics Problem
The question asks me to find the angular velocity.
Now I do not want you to solve my homework, I want explanation please.
It states that the acceleration of point P is $\vec{a}= -3.02 \vec{i} ...
1
vote
2answers
220 views
Potential of surface charge
I have a question about the $ \hat{n} $ in this formula $\sigma = P \dot{}\hat{n}$.
Why do sometime in my book they get $\sigma = P \cos{\theta}$ for a sphere. Isn't $\hat{n} = r$ ?
And then in ...
1
vote
1answer
607 views
How to find acceleration given position and velocity?
Sorry for this very simple question but I am still very new to the laws of motion.
I am dealing with 2-dimensional vectors in my programming environment and I'm following these slides to learn about ...
2
votes
2answers
60 views
Another question about Shankar's notation
I have another question on the notation in Shankar. I think it's sloppy, but I also may just be misunderstanding it. Again, this is at the very beginning of the math intro.
He has:
$$a\left| V ...
1
vote
1answer
141 views
Is there a more clever way to apply the cross product of two vectors to magnetism?
I am just beginning to learn magnetism and my book used two ways to define the force caused by the magnetic field, brushing over the latter.
The first:
$$F = q v B \sin (\theta).$$
And:
...
1
vote
2answers
209 views
Question on notation in Shankar's Quantum Mechanics - math intro on vector spaces
I'm just beginning Shankar's 2nd edition Quantum Mechanics and having some trouble with notation. He defines his vectors as "$\left|V\right>$" . And with a scalar multiplier as "$a\left|V\right>$" . ...
0
votes
2answers
345 views
Question involving Vectors and Forces
This is a question I found in Mechanics for Engineers by Beer & Johnston.
A 600-lb crate is supported by the rope and pulley arrangement as shown below.
Write a computer program which can be ...
1
vote
1answer
302 views
Bra space and adjoint vectors
If I'm not wrong, a bra, $ \langle \phi_n | $, can be thought as a linear functional that when applied to a ket vector, $| \phi_m \rangle$, returns a complex number; that is, the inner product it's a ...
-1
votes
1answer
370 views
The acceleration of a particle moving only on a horizontal plane is given by a= 3ti +4tj, [closed]
The acceleration of a particle moving only on a horizontal plane is given by a= 3ti +4tj, where a is in meters per second-squared and t is in seconds.
At t = 0s, the position vector r= (20.0 m)i + ...
1
vote
2answers
160 views
Why no basis vector in Newtonian gravitational vector field?
In my textbook, the gravitational field is given by$$\mathbf{g}\left(\mathbf{r}\right)=-G\frac{M}{\left|\mathbf{r}\right|^{2}}e_{r}$$
which is a vector field. On the same page, it is also given as a ...
3
votes
4answers
200 views
How to apply an algebraic operator expression to a ket found in Dirac's QM book?
I've been trying to learn quantum mechanics from a formal point of view, so I picked up Dirac's book. In the fourth edition, 33rd page, starting from this:$$\xi|\xi'\rangle=\xi'|\xi'\rangle$$
(Where ...
5
votes
6answers
2k views
How is gradient the maximum rate of change of a function?
Recently I read a book which described about gradient. It says
$${\rm d}T~=~ \nabla T \cdot {\rm d}{\bf r},$$
and suddenly they concluded that $\nabla T$ is the maximum rate of change of $f(T)$ ...
0
votes
1answer
227 views
Finding The Resultant Vector [closed]
A plane is flying southeast at 215 km/h. Suddenly there is a wind from the north at 75 km/h. What is the plane's new velocity with respect to the ground in standard position?
0
votes
2answers
1k views
Find the Unit Vector of a Three Dimensional Vector
How can I find the unit vector of a three dimensional vector? For example, I have a problem that I am working on that tells me that I have a vector $\hat{r}$ that is a unit vector, and I am told to ...
0
votes
0answers
70 views
Vector Calculus - Mass of a block (I'm being dense) [closed]
I'm currently revising for some exams, and as part of one of my practice questions am finding the mass of a block by use of it's mass density function. It involves a triple integration as seen below. ...
0
votes
1answer
794 views
Vertical component of moving weight at a 45 degree angle
Here's an easier one.
I use the leg press machine at the gym so I don't have to worrying about hurting myself while lifting heavier weight.
The weight glides on a track that looks to be 45 degrees.
...
2
votes
2answers
1k views
split gravitational force into x, y, and z componenets
I am writing a program for a computer science class in which I am doing an n-body simulation in 3-dimensional space. Currently, I have figured out the gravitational force along the hypotenuse between ...
1
vote
2answers
393 views
What is the physical meaning of a product of vectors?
My teacher told me that Vectors are quantities that behave like Displacements. Seen this way, the triangle law of vector addition simply means that to reach point C from point A, going from A to B ...
2
votes
1answer
1k views
How Does force relate to velocity
I had originally asked this question on math overflow and it was suggested that I ask it here.
So I know that a force will change the magnitude of velocity if it is at an angle other that 90 degrees. ...
3
votes
2answers
322 views
Is (0,0,0) an undefined vector?
I'm not sure what to make of the direction of a vector with components (0,0,0). Is it an undefined vector?
2
votes
0answers
75 views
Surface normal on the earth to the sun at a given point in time
How complicated is it to calculate a surface normal on the spherical approximation of the earths surface pointing towards the sun at a given point in time?
What I try do is to highlight a small area ...
2
votes
3answers
21k views
Linear acceleration vs angular acceleration equation
I'm learning about angular velocity, momentum, etc. and how all the equations are parallel to linear equations such as velocity or momentum. However, I'm having trouble comparing angular acceleration ...
0
votes
1answer
199 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 ...
0
votes
1answer
159 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 ...
1
vote
3answers
6k views
Uses of Vectors In Real Life
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 ...
0
votes
0answers
112 views
Vectors and finding lines on a point [closed]
Long John Silver, a pirate, has buried his treasure on an island with five trees located at the following points: A (30.0m, -20.0m), B(60.0 m, 80.0m), C (-10.0m, -10.0m), D (40.0m, -30.0m), and ...
0
votes
2answers
283 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)
...
9
votes
4answers
3k 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 ...
7
votes
6answers
9k 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 ...
-1
votes
1answer
1k views
how to calculate the angle in the x-y, y-z, x-z plane given only 3D vector direction and magnitude? [closed]
Please help me solve this. I have been thinking of all sorts of ways to solve this but can't figure out how :(. Ok here's the problem:
I am given a three dimensional velocity vector (i know the ...
