Geometric object with magnitude (length) and direction.

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309 views

Angle needed for object A to intercept with object B

Object B is 15 degrees East of North at a distance of 20km/h. Object B is moving at an average speed of 30km/h in the direction 40 degrees East of North. If object A is capable of moving at 100km/h, ...
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1answer
85 views

How to add magnitude data in an ENU coordiante system

I have water velocity data taken in an ENU (East, North, UP) or XYZ coordinate system. The data is contained in 3 columns like this: ...
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1answer
524 views

Resultant vector problem

$\newcommand{\v}[1]{\vec #1}\newcommand{\i}{\hat i}\newcommand{\j}{\hat j}$ Problem statement (1,2) A shopper at the supermarket follows the path indicated by vectors $\v A, \v B, \v C, \v D$ in ...
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1answer
744 views

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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1answer
289 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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1answer
625 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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3answers
32 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
23 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
50 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
68 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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2answers
83 views

Why is force a localized vector and not a free vector?

A vector which is drawn parallel to a given vector through a specified point unlike free vector in space is called a localised vector. The effect of a force acting on a body depends not only on the ...
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1answer
73 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
45 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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3answers
105 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 ...
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2answers
102 views

Free vs bound vectors and torque

When considering basic Newtonian mechanics, we can treat vector as free and move their point of application at will. This is consistent with the affine nature of Euclidean space. However, when ...
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2answers
88 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
199 views

Rate of change of a vector

I'm studying the book "Classical Mechanics" by Goldstein together with a coursebook my professor provided. I'm having trouble grasping how to intuitively determine what the rate of change of a vector ...
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1answer
109 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
223 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} ...
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2answers
256 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
286 views

Angular position vector?

I'm a mathematician, so I like my angular velocities to be vectors. It makes my angular momenta and torques vectors as well, and so they have nice operations I can do on them. Because of that, I pick ...
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2answers
821 views

I don't understand the idea of perpendicular vectors being independent of each other?

So problem 71-75 is about vectors. The problem says: A river has a current flowing with a velocity of 2.0 meters per second due east. A boat is 75 meters from the north riverbank. It travels at ...
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2answers
1k 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
91 views

Commutation of abstract $O(3)$ generators and vectors

I've been given the following problem, and I'm quite lost with it. Let $L_1$, $L_2$, and $L_3$ denote the abstract o(3) algebras. You are given that $\vec{A} = (A_1, A_2, A_3)$ and $\vec{B} = (B_1, ...
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1answer
125 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 ...
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1answer
261 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 ...
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1answer
448 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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2answers
637 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
244 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
589 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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2answers
236 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
77 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
196 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
160 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
304 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
274 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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944 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 ...
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3answers
31 views

Find time-parametrization given path and speed of a particle

Consider a particle in two dimensions with position vector $r(t)=<x(t),y(t)>$ and the shape of the path is described by a function $y(t)=f(x(t))$ (Thus $r(t)$ is a parametrization of $f$ with ...
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0answers
25 views

Suspended mass in motion free-body diagram [closed]

A 20kg mass is held by two ropes which span 90 from each other. The mass is being accelerated at 1m/s^2 to the right. Draw a free body diagram for the mass and find the numerical values for each ...
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1answer
18 views

Laboratory fixed-vector components

What are laboratory fixed-vector components? I have an effective Hamiltonian derived from a 40-something year-old Chemical Physics paper. The article mentions the term laboratory fixed-vector ...
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4answers
136 views

How to find total force on an object?

If there are a multitude of forces acting on an object in different directions, how do we find the TOTAL force? I know we add up the $ x $- and $ y $-components of the forces individually, but how do ...
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0answers
52 views

At time $t=0$, what are the magnitude and direction of the perpendicular component of dp/dt? [closed]

In the dark in outer space, you observe a glowing ball of known mass 4.6 kg moving in the xy plane at constant speed in a circle of radius 7 m, with the center of the circle at the origin (< 0, 0, ...
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0answers
52 views

Four-momentum, four-velocity, energy

If given the four-momentum of any particle monitored by an observer as: p = $p^\hat{α}e_\hat{α}$ using unit vectors in observer’s reference frame and u = $e_\hat{0}$ then I get I'm just ...
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1answer
28 views

Speed with wind resistance

This is probably a basic question, but it has been a while since I did anything like this. If a boat is sailing forward at speed $x$ and the direction of the wind, with magnitude $y$, is either equal, ...
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1answer
169 views

Relative wind velocity explanation - understanding Irodov problem 1.6

I am having trouble understanding the reasoning behind the solution in this Irodov General Physics problem. The problem is 1.6: 1.6. A ship moves along the equator to the east with velocity vo = ...
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1answer
115 views

Kinematics simple question [closed]

Question: In order to protect himself from the rain, a person is standing holding an umbrella at right angle to the horizontal surface. The rain is falling at 10m/s when the velocity of the wind is ...
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1answer
56 views

Angular velocity vector in terms of motion of an object

May be it is small question in this forum but I'm trying to get the feel of the understanding about the angular velocity. If this question is getting rejected please kindly refer me to appropriate ...
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3answers
256 views

Why does the moment of force (aka. torque) depend on the perpendicular distance?

Couyld anyone explain how the lecturer concluded that $$(\underline{r_2} - \underline{r_1}) \times \underline{H} = \underline{p} \times \underline{H}$$
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1answer
218 views

Where do these formulas for an object being pushed up an incline come from? [closed]

An object on an incline with an angle $\theta$ is being pushed at constant speed. Constant speed implies $a = 0$. Because $F=ma$ and the object must have mass greater than 0. If I want to find the ...
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2answers
70 views

Position with respect to time with friction

I'm interested in equations of motion when friction is present for a little graphical side project I am working on. I'm really rusty with physics, so I apologize if this is a basic question or doesn't ...