Geometric object with magnitude (length) and direction.

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1answer
141 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 ...
2
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3answers
188 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
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2answers
876 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 ...
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2answers
111 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
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1answer
1k 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
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1answer
437 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 ...
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1answer
250 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 $m$, ...
3
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1answer
241 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 ...
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3answers
288 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
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2answers
459 views

2D - Kinematics - Linkage System using Vector Algebra [closed]

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 ...
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2answers
407 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 ...
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2answers
279 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 ...
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0answers
107 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 ...
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2answers
263 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} ...
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2answers
444 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 ...
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1answer
825 views

How to find acceleration given position and velocity? [closed]

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
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2answers
75 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
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1answer
213 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: ...
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2answers
237 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 "$a\left|V\right>$" . ...
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2answers
530 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 ...
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1answer
535 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 ...
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2answers
250 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 ...
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4answers
237 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 ...
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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 $f(T)$ ...
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1answer
277 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?
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2answers
2k 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 ...
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2answers
2k 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
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2answers
2k 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
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2answers
671 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
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1answer
13k 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. ...
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2answers
487 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
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0answers
90 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 ...
3
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3answers
47k 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
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1answer
310 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
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1answer
206 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 ...
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3answers
10k 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 ...
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2answers
386 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 = ...
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2answers
456 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) ...
14
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5answers
8k 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 ...
13
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6answers
20k 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 ...
5
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1answer
256 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 ...
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1answer
233 views

What is a simple physics application of the reciprocal of a square root? [closed]

I learned yesterday that the inverse of square roots is used to calculate the vectors of surface normals in 3d graphics. It seems like such a mind-bogglingly simple idea, and it leads me to wonder if ...
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2answers
523 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 ...
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2answers
3k views

The resultant of two forces acting at any angle?

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 $c^2 = a^2 + b^2$ ...
4
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1answer
1k 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 $$\pmb{H}=\pmb{\nabla} \phi +\pmb{\nabla} \times \pmb{G},$$ ...
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3answers
1k 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? ...
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6answers
1k 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 ...
0
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2answers
302 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 ...
0
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2answers
587 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 ...
0
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3answers
3k 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?