Questions tagged [vectors]

Geometric object with magnitude (length) and direction.

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3answers
70 views

Can one of the component of a vector have the same magnitude of the vector? [closed]

In vectors, if a vector is broken down into its components then can one of the components of the vector have the same magnitude of the vector itself??
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5answers
288 views

Why do we use vectors in quantum mechanics?

I've been trying to make my understanding of quantum mechanics more mathematically rigorous, but I'm struggling a bit with the lack of intuition behind the fact that we represent quantum states with ...
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2answers
2k views

Is the right hand rule a trick to avoid tensors?

I have read in this answer that "to represent angular momentum as a vector you need to use a right hand rule. This is annoying, because physics at ordinary scales is reflection invariant but ...
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3answers
34 views

How is velocity defined in circular motion in central force field?

In my view the velocity is change of displacement in the increasing direction of displacement. Now in circular motion in central force field the particle is changing its direction then how is the ...
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3answers
350 views

Direction of Coriolis force [closed]

My doubt is all about finding the direction of coriolis force by using the direction of the moving object. I really find it difficult to determine the direction of coriolis force through direction of ...
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1answer
38 views

Would a $y$ axis affect the $x$ axis in a free body diagram? [closed]

Would a $y$ axis affect the $x$ axis in a free body diagram? like forces and all that can you add them or use them together. Or they do not interfere each other?
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2answers
177 views

What does the spherical-harmonic notation $Y^{m}_l(\hat{\textbf{r}})$ mean, and how does it relate to the usual $Y^m_l(\theta, \varphi)$?

By using the plane wave expansion, the decomposition of stationary harmonic plane wave into partial waves can be given by $$ e^{i\textbf{k}\cdot\textbf{r}} = e^{ikz} = e^{ikr\cos\theta} = \sum^{\infty}...
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1answer
39 views

Defining the change in direction due to wind

My question: Which force vector (A, B, C, or D) represents the APPROXIMATE direction in which the boat is travelling as a consequence of the wind? My approach: I looked for which vector combination ...
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7answers
4k views

Why isn't average speed defined as the magnitude of average velocity?

Speed is usually defined as the magnitude of (instantaneous) velocity. So one could assume that average speed would be defined as the magnitude of average velocity. But instead it is defined as $$s_{...
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1answer
90 views

What does parity operation mean on a vector represented in polar form

Recently i studied vector's mathematical meaning (i.e the vectors transforms the same way as co- ordinate system) and our teacher introduced us to parity operation and how vectors transforms under it. ...
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1answer
238 views

Triangle of Forces - 4 forces

If 3 vectors can be rearranged in a triangle in which only the head and tails of the vectors make contact, i.e. there is no head to head or tail to tail contact, then equilibrium seems to be the case, ...
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1answer
46 views

Torque acting on car trailers

My question: "Which car trailer below will be moved in a straight forward line?" Relevant info: All forces (represented by the arrows) in the diagram are equal in magnitude. The car trailer diagrams ...
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1answer
130 views

Basic vector calculus: Show that $\nabla \vec{r} = \vec{1}$ [closed]

Show that $\nabla \vec{r} = \vec{1}$ My instructor in my E & M class put the $r$ and $1$ in bold. I am not sure what a bold one means. From my work I get $1ii + 1jj + 1zz$.
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1answer
184 views

Why torque and force between two electric dipoles are not equal and opposite, is it violation of newton's 3rd law?

so, here are two dipoles distance $r$ apart i have calculated following: (i)$\vec {F_{p_{1}}} $ (force on $p_{1}$ due to $p_{2}$)$=0$ (ii)$\vec {F_{p_{2}}}$(force on $p_{2}$ due to $p_{1}= -\dfrac{...
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2answers
234 views

Why can work done by friction be negative if work is a scalar?

Work done by an object can be defined as the force times the distance traveled in the direction of the force. I've read from the internet that the frictional force acting on an object sliding over a ...
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2answers
186 views

Tension between two/three ropes using vectors

Say there are three points, $a$, $b$, and $c$, with associated vectors $\vec{r_a}$, $\vec{r_b}$, and $\vec{r_c}$. $a$ and $b$ are both attached to firm surfaces, and each are connected to $c$ by ideal ...
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2answers
61 views

What does it mean to find the component of 2 vectors in the direction of another vector?

I understand how to take the cross-product of 2 vectors ($\vec{a}\times\vec{b}$), but what does it mean to find the component of $\vec{a}\times\vec{b}$ along the direction of another vector (for ...
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0answers
54 views

The Field $\mathbb{F}$ of A Hilbert Space [duplicate]

Is it always necessary for the field of some arbitrary Hilbert space I define to describe a system be a field of complex numbers only? Is it possible to have a field of naturals, or reals? Since the ...
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1answer
75 views

Dimensional analysis of vectors, possible?

Usually we use dimensional analysis to find the dimension of acceleration or force, but can we do the same thing to find the dimension of the vector acceleration, and the vector force, or we can't ...
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0answers
48 views

Visualizing a scenario where wave vector's direction is different from Poynting vector's one

Can someone help me visualize how the direction of the wave vector can be different from the one of the poynting vector in a scenario like a lossy medium? I'm not seeing it.
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2answers
128 views

How can I show that the acceleration vector for uniform circular motion undergoes uniform rotation?

Does it suffice to show that the dot product between the acceleration vector and the derivative of the acceleration vector = 0?
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5answers
3k views

Does the magnitude of a physical quantity have units or is it just a plain number?

Does the magnitude of a physical quantity have units? For example, if a velocity vector is $36\ \mathrm{m\,s^{-1}}\ \hat{u}$, is its magnitude $36\ \mathrm{m\,s^{-1}}$ or just $36$? Also why?
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2answers
113 views

Velocity of a ring tied to an inextensible rope

In the diagram, the pulley is weightless and friction less and the thread connecting the pulley with the ring is inextensible. The thread is attached to the ring which in turn can move only ...
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2answers
73 views

Four-vectors in relativity

I have a question about specifically whether the components of a 4-vector could depend on the position $x \in \mathcal{R}^4$, where I denote Minkowski space with $\mathcal{R}^4$. I know that the ...
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1answer
134 views

Rotation matrix help [closed]

So I am doing some exercises in Susan Lea's book Mathematics for Physicists, currently question 7 chapter 1: Find the matrix that represents the transformation obtained by (a) rotating about the x-...
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2answers
185 views

The acceleration of circulation motion

We know that in circular motion the position vector is $r\hat{r}$. Then the velocity is the time derivative of it. So it gives $$dv/dt = r d\hat{r}/dt + \frac{dr}{dt} .\hat{r}.$$ now I can't ...
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2answers
1k views

Unit vectors in the cylindrical coordinate system as functions of position

What is meant by the statement that 'The unit vectors in the cylindrical coordinate system are functions of position'. And, comparatively, how are unit vectors of rectangular coordinate system are ...
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3answers
765 views

Change of basis vs. change of coordinate system

I'm trying to understand how the translation of coordinate system works in physics, (for example in the Galilean transformations). When I talk about vectors, I usually mean quantities that can be ...
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3answers
391 views

How do we know that the motion of the particle in an central force field lies on a plane?

If I take r as the radial vector of the moving object and v as the velocity vector of the moving object in central force field. Then r should be perpendicular to r×v . So that depicts that r.(r×v) = ...
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3answers
383 views

When a car's non-driving wheels are turned, what is the frictional force vector that actually causes the vehicle to turn in that direction? [duplicate]

I am almost a little embarrassed to be asking this question since my education and experience is in mechanical engineering. However, I've drawn a few diagrams, but am still a little puzzled by this ...
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1answer
78 views

Which relation is correct for resultant instantaneous velocity in 2d?

Please forgive me if the following question sounds silly and I can't exactly pin point where exactly the problem is but there is some problem with my understanding of vectors. In Cartesian ...
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3answers
179 views

Why are we able to use Components of Vectors?

Last year, I took physics and over the summer I have started to wonder about why many phenomena work the way they do (such as why is $\mathrm{KE} =\frac{1}{2}mv^2$, etc.). I have found answers to all ...
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2answers
55 views

Point of application when the force is the up thrust?

We have been taught that the point of application is the point at which the force is applied. In contact forces, the point of application is the point of contact and in forces acting from a distance, ...
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4answers
613 views

does tension in the string affect its equilibrium?

In my textbook (Sears and Zemansky's University Physics), it is written that the vector sum of the forces on the rope is zero, however the tension is 50 N. Then is tension different than the force? ...
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1answer
37 views

Scalar Flow Across a Small Area Element

I've just started reading the text "Vectors, Tensors, and the Basic Equations of Fluid Mechanics" by Rutherford Aris and I came across the following problem. If $\rho$ is any scalar property per unit ...
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1answer
37 views

Are angles for vectors always measured from the horizontal?

I have a vector which has been stated to have a force of: 96.0 N at $51.3^\circ$. I had a different answer because I was measuring my angles from the north. By default if an angle is given by itself ...
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1answer
120 views

Can acceleration be both the “rate of increase of velocity” and the “rate of increase of speed” in Physics?

A Dictionary of Physics (Oxford University Press) defines acceleration as: The rate of increase of speed or velocity However, from reading many other definitions it seems to me that acceleration ...
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0answers
48 views

Quick clarification of what Feyman meant here, talking about symmetry in physical law under reflection

When Feynman says "Now if the law of reflection symmetry is right in physics, then it must be true that the equations must be so designed that if we change the sign of each axial vector and each cross-...
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1answer
160 views

Time derivative of vector in rotating frame with angular velocity about a rotating axis

In general, I know that if you have a vector $\vec{F}$ in a rotating frame, and the frame has an angular velocity $\vec{\Omega}$ that the time derivative of $\vec{F}$ in a fixed frame would be $$\frac{...
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5answers
196 views

What does it mean if the dot product of two vectors is negative?

If the dot product gives only magnitude, then how can it be negative? For example, in this calculation: $$W = \vec{F}\cdot\vec{r} = Fr\cos\theta = (12\ \mathrm{N})(2.0\ \mathrm{m})(\cos 180^\circ) = ...
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0answers
42 views

Can you take the derivative of the normal unit vector in n-t coordinate system? [closed]

In class we are looking at rotation about a fixed axis. Using the n-t coordinate system, the notes derive the acceleration like: (1) $a= \frac{dv}{dt} = \frac{d\omega}{dt}{\bf{r_p}} + \omega\frac{d{\...
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3answers
1k views

A block on inclined plane

A block of mass $m$ is placed on an inclined plane (a ramp). If a constant force $f$ is applied to the ramp so that it is accelerating horizontally at a proper rate, the block will remain at the same ...
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2answers
84 views

Vector rotations and quantum mechanics [closed]

Quantum mechanics deals with wave function and complex numbers that can be seen as vectors in 2D plane. I am interested in vector rotations and there use in quantum mechanics. What is the role that ...
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1answer
57 views

Does it make sense to multiply a unit by a negative number?

I was thinking about the way our system of units of work, and I realized that we have been multiplying units (such as for lengths) by negative numbers, when dealing with vector quantities; positive ...
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3answers
118 views

Elements of vector algebra and particle physics

What does scalar, vector, pseudovector and pseudoscalar particles have to do with the concept of scalar, polar vectors and axial vectors in vector algebra?
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1answer
2k views

Why is work scalar and the dot product of force and displacement?

I asked many people why work is scalar. But the questions and the answers just cycles. My question : Why is work a scalar quantity? Their answer : Because it is the dot product of Force and ...
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3answers
302 views

Are contravariant basis vectors and basis 1-forms identical?

The reason I'm asking this is because I am trying to develop a set of notes from my reading of MTW (and Wrede, Menzel, Bergman, etc.). I represent covariant basis vectors with $\mathfrak{e}_{i}$, ...
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1answer
85 views

What is the actual meaning of dot product of 2 vectors? [duplicate]

I couldn't get the physical significance of dot product
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2answers
752 views

When will velocity and acceleration vectors be perpendicular? [closed]

Suppose a particle is moving in the $xy$ plane with $$x=at, \quad y=at(1-bt),$$ where $a$ and $b$ are positive constants. When will the velocity vector and acceleration vector be perpendicular? I ...
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3answers
237 views

Feynman's Four Gradient in Special Relativity

I am having trouble understanding Feynman's explanation of four gradient. In section 25-3 of Vol. 2 of the Feynman lectures, he explains why the four gradient is not $(\frac{\partial}{\partial t},\...