Geometric object with magnitude (length) and direction.

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Is it possible to prove that the curl of a gradient equals zero in this way?

If $(\nabla\times\nabla\Phi)_i = \epsilon_{ijk}\partial_j\partial_k\Phi$, where Einstein summation is being used to find the $i$th component... Using Clairaut's theorem $\partial_{i}\partial_{j}\Phi =...
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797 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
1k views

What is the physical meaning of a dot product and a cross product of vectors? [duplicate]

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 &...
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266 views

Why does something on an inclined plane move forward at all?

We just started studying about the inclined plane and vectors in motion, but i don't understand one thing: Why on earth does the object on the inclined plane move forward (I.e in the direction where ...
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55 views

Why is the spatial term for contravariant 4-gradient negative, whereas for other 4-vectors it is the covariant part that is negative spatially?

The contravariant 4-displacement is: $${x}^{\alpha} = (ct,\mathbf{r})$$ And the contravariant 4-gradient is: $${\partial}^{\alpha} = (\frac{1}{c}\frac{\partial}{\partial{t}},-\nabla)$$ From what I ...
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49 views

Vector Navigation and equations [closed]

So I am taking a grade 12 physics online course and I am getting stuck on the Vector Navigation equations as there isn't much explanation in my course. The following text is found in my online course....
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132 views

What is total acceleration?

I'm currently taking a Physics class and we are studying motion in a circular path. and i'm kind of fuzzy on what the total acceleration actually is. take this problem for example An automobile ...
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28 views

Why use vectors to describe velocity/force/etc instead of treating magnitude and direction as separate values?

I'm only 4 weeks into my first college-level physics course, so this is a very elementary question. Also, in asking this question, I'm just playing devil's advocate in order to better understand the ...
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58 views

Time dependent ODE involving cross product

Let $\vec{A}$ be any time dependent vector quantity, and $\vec{\alpha}$ any constant vector. I was told that a solution to the differential equation $$ \dot{\vec{A}} = \vec{\alpha}\times\vec{A} $$ is ...
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1answer
114 views

Dropping objects on a rotating disc: angular momentum?

I'm designing a very simplistic particle simulator. Particles are dropped on a spinning disc and then bounce back (although lose some momentum due to the friction of the disc). I'm working with an ...
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244 views

Is the displacement vector tangent to the circular path?

My book says that when a mass travels in a curved path, like a circle for example, the instantaneous velocity and displacement vectors are both tangent to the path. I agree that velocity vector is....
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406 views

Finding the magnitude of Two Vectors [closed]

Vector C has a magnitude 23.4 m and is in the direction of the negative y-axis. Vectors A and B are at angles α = 44.4° and β = 27.7° up from the x-axis respectively. If the vector sum A+B+C = 0, what ...
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139 views

Why are $2\pi$ factors included in the definition of the reciprocal lattice?

I would like to know where the $2\pi$ factors are coming from in the formula for reciprocal vectors in reciprocal lattices. For example, in a simple cubic lattice the primitive vectors are given by $$...
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1answer
45 views

Acceleration in a system equal for every body — why?

A 1 kg cart can slide frictionlessly on the table. The black weights each weigh 1 kg. The pulleys are frictionless. The task is to determine the acceleration of the cart. For the left-most weight we ...
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2answers
103 views

Do components of force have direction when doing work?

When we get angle > 0, the x-component of force is along the direction of displacement and so their product is called Work. So the x-component of force is said to have direction of the respective ...
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1answer
543 views

What is the work done said when angle between force and displacement>90 and <180?

If the angle between $Force$ and $Displacement$ is obtuse then by using the formula of $Work$ we get negative quantity so is it said then that the system is losing energy or it is merely for the case ...
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1answer
42 views

Computing the Initial Velocity of an orbiting body

I'm working on a simulation program that replicates the movement of planets around a large celestial body (the sun). This is a three dimensional simulation that uses vectors. At present, I'm ...
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1answer
46 views

How to expand this equation considering acceleration due to gravity into 3D vector space?

How can we expand this following equation into 3D vector space? I learned this equation from this answer: Don't heavier objects actually fall faster because they exert their own gravity? The ...
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1answer
55 views

What does it mean by $t=-1$?

if the position vector of a particle is $\hat{r}=\left(4+3t\right)\hat{\imath}+\left(t^3\right)\hat{\jmath}+\left(-5t\right)\hat{k}$, i want to find at what time this particle passes through the point ...
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1answer
348 views

How to show that the force and velocity are perpendicular and that both have constant magnitude? [closed]

The force acting on a moving charged particle in a magnetic field $\hat{B}$ is $\hat{F}=q\left(\hat{v}\times \hat{B}\right)$ where $q$ is the electric charge of the particle, and $\hat{v}$ is its ...
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1answer
550 views

What does “projection of a vector” really mean?

Let $\vec{a}$ & $\vec{b}$ be two non-collinear, non-zero co-initial vectors having angle $\theta$ between them. The projection of $\vec{b}$ on $\vec{a}$ is given by the dot product of $\vec{b}$ &...
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1answer
3k views

How can I calculate the speed of an object knowing its horizontal and vertical velocity components?

Let's say a ball is thrown and it experiences typical projectile motion (moves in a parabolic arc etc.) and the only information we know are the equations for the horizontal and vertical components of ...
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1answer
1k views

Vectors-Can anyone explain me the concept of sense in vectors?

Is it same as the direction?Then , why another term "sense"is used ,instead of direction? Can anyone illustrate it?
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117 views

Integral ambiguity

I'm a bit confused with some notation I encounter in physics calculus. Consider this: Taken from here. Integration operates on functions, correct? What does it mean to integrate $\frac{d{\bf p}}{dt}...
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485 views

How do I find the perpendicular velocity of a particle to a varying magnetic field?

I am trying to find the component of velocity perpendicular to a magnetic field. This was easy when the magnetic field was static and pointing in only one direction (the $z$ axis), but now I need to ...
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1answer
225 views

Plane Polar coordinates for simple pendulum in moving lift(elevator) [closed]

Can any one help me with the following. A simple pendulum is suspended from the ceiling of a lift. It is moving upward with acceleration $a$. The string of the effective length of the pendulum makes ...
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1answer
594 views

Finding angular momentum about the center of mass?

If we have a couple of particles of an equal, unknown mass: $$r_{+} = (c + e^{-Bt} \cos({\theta}))\textbf{x} + (d + e^{-Bt} \sin({\theta}))\textbf{y}$$ $$r_{-} = (c - e^{-Bt} \cos({\theta}))\textbf{...
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1answer
87 views

Some subtleties in direction of drag force

Consider a body released from a height $h$ and assume a drag force is linearly proportional to the velocity. Then by Newton's Second Law, $$m\mathbf{\dot{v}} = \mathbf{F_g} + \mathbf{F_{drag}} = m\...
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505 views

Need clearing up on vector decomposition in motion physics

I've been pursuing physics on my own, and I need something cleared up. Say I have two arbitrary objects, I have their velocities, I know when the collide, I have their normal vectors, etc. I know ...
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2answers
3k views

How to find the resultant of two forces? [closed]

I got this question in a assignment and haven't been able to figure out how to get to the correct result. A force of 6 newtons and a force of 10 newtons can be combine to form a resultant of ...
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1answer
166 views

Interchaning a position between two reference frames?

$\vec{r}_a$ is a positional vector from reference frame $a$. What is the position of same point from reference frame $b$ ? If required, assume position of origin of frame $a$ is $\vec{m}$ and unit ...
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385 views

Navier-Stokes equations: conservation of momentum

The first Navier-Stokes equation (conservation of mass) says: $\vec \nabla \cdot \vec v=0$ For a stationary flow, the l.h.s of the second equation is (conservation of momentum): $\rho \frac{D\vec v}{...
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925 views

Induced voltage of a conductor in a magnetic field

A book which I referenced for Electrical Machinery states that the voltage induced in a conductor inside a magnetic field is given by $$ \mathcal{E}=(\mathbf{v} \times \mathbf{B})\cdot \mathbf{l}$$ ...
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1k views

Utilizing maximum acceleration $a$ for displacement $d$ with initial velocity $v_0$ and final velocity $v_1$

Problem My goal is to move an object from point a to b (displacement $d$) as fast as possible utilizing the maximum available acceleration $a_{max}$, taking into account the initial velocity $v_0$ ...
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2answers
304 views

Resolution of vectors

What is the fundamental basis of resolution of vector. Suppose we have a vector $\vec{mg}$, now we resolve it into two components, horizontal and vertical. My question is what is the basis for telling ...
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1answer
1k views

Hydrostatic pressure at lateral directions

I just read that, with respect to a stationary tiny cube, suspended in a fluid, that has a negligible weight and dimensions: Pressure is the same in every direction in a fluid at a given depth, ...
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328 views

Rotating a reference system on a vector

Assume you have a vector $\vec{x}=(\sin(\vartheta)\cos(\varphi),\sin(\vartheta)\sin(\varphi),\cos(\vartheta))$ given in spherical coordinates in a reference System "R". I want to rotate the reference ...
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1answer
92 views

How to express answers where inequalities are involved?

Part of the floor of a workshop is inclined at 10 degrees to the horizontal. This is to allow the safe storage of steel cylinders. A cylinder of mass 7000 kg is stored as shown in the diagram (c the ...
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3answers
218 views

Mechanics Problem

I'm trying to follow Feynman's lecture. Unfortunately I'm a bit stuck on a small piece, so if you could show me what I'm doing wrong then I'd greatly appreciate your help. I want to exactly know how ...
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1answer
196 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 ...
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1answer
413 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 $m$, ...
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2answers
317 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....
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1answer
20 views

How can I calculate the torque on a body resulting from a spinning propeller?

If a quadcopter has all of its propellers spinning on the same direction, the body of the quad will obviously start spinning in the another direction. I know how to calculate the torque acting on a ...
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1answer
44 views

Notations used to express direction [closed]

We express direction relative to a reference point and call a certain direction positive and it's direct opposite direction negative, by convention. But, what notation should we use to express a ...
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2answers
54 views

Finding if two objects collide

The question that I'm trying to understand is this: This is the part of the solution I don't understand: From my knowledge, if $v_p-v_q$ is due south, this means $r_p-r_q$ is also due south, ...
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1answer
37 views

Calculating relative velocity in three dimensional space

Given two points $\mathcal{A}$ and $\mathcal{B}$ in $\mathbb{R^3}$ whose position and velocity vectors are, respectively: $$\mathbf{r_A}=\begin{pmatrix}r_{A_{x}}\\r_{A_{y}}\\r_{A_{z}}\end{pmatrix}$$ $$...
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1answer
30 views

Differences in notation of momentum 4 vector

I have noticed three ways to write the 4 momentum vectors: $P = (E/c, \vec{p})$ $P = (E, \vec{p})$ $P = (E, c\vec{p})$ I know how to derive equation 1, and as far as I know, one can use the ...
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0answers
45 views

Centripetal acceleration [closed]

I know if a particle is accelerating around the earth it has $$a= \omega*v$$ My question is how do I express this in terms of the unit vector. Would it go something like this. $$|a| = |\omega*v| $$ $...
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24 views

Wire with current in magnetic field $\vec{B}$has force $\vec{F_1}$. When rotated, $\vec{F_2}$. Find $B$ [closed]

I have the following question: In a wire with $10cm$ there is a current $4A$ going 'upwards' in the $z$ axis. The force over this field, under a constant magnetic field $\vec{B}$ is $F = -0.2\vec{i} +...
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69 views

Zeroth component of 4-momentum and relativistic energy-momentum relation

As I understand it one is forced to use 4-vectors since we require objects that transform as vectors under application of Lorentz transformations and 3-vectors do not (technically they do under ...