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Questions tagged [vectors]

Geometric object with magnitude (length) and direction.

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Is spinor the sum of scalar, vector, bi-vector, …, pseudo-scalar?

Is spinor $\psi$ actually the sum of scalar, vector, bi-vector, ..., pseudo-scalar? Before talking about spinors, we have to differentiate two kinds of spacetime, demonstrated with the example of ...
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2answers
28 views

Why does tangential acceleration change in value?

I don’t understand why tangential acceleration changes in value in a parabolic movement with constant acceleration (gravitational acceleration). Since acceleration is constant, tangential and ...
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1answer
12 views

About the EKG and why it's waves are positive or negative.e

So, I understand that the EKG is a way of measuring the electroactivity that happens in the heart through the vectors that are created by it. Every cardiomyocyte has the ability to change its ...
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0answers
36 views

Solid rotates about $n$ axes

A solid rotates about $n$ axes intersecting at one point. The absolute value of angular velocities of each rotation $|\boldsymbol{\omega}_k|\,(k=1,..,n)$ are constant. Find the angular velocity vector ...
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1answer
22 views

How to determined the angle of force weight in an incline force vector problem?

today in class I was introduced to some basic incline problems. I know that Force weight can be resolved into 2 components-the parallel and the perpendicular. I was given the angle of the ramp to be $...
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0answers
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Ship vector problem [on hold]

Ship A travels east at a rate of 30km/hr and sees ship B 30° in relation to the north. Ship B is travelling at a constant speed. After 20 minutes ship A sees ship B 45° in releation to the north and ...
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2answers
60 views

Snell's law in vector form

Snell's law of refraction at the interface between 2 isotropic media is given by the equation: \begin{equation} n_1 \,\text{sin} \,\theta_1 = n_2 \, \text{sin}\,\theta_2 \end{equation} where $\theta_1$...
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Consider two vectors $A=4i+6i-3k$ and $B=-2i-5j+7k$ [closed]

Consider two vectors $A=4i+6i-3k$ and $B=-2i-5j+7k$ Find the angle between vectors $A$ and $B$ Find $A\cdot B$ and $A\wedge B$ Find a unit vector $C$ that defines the direction of $A\wedge ...
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What's the magnitude of the resultant force? Vectors and scalars [closed]

What is the formula required to calculate the magnitude of the resultant force. Here is an example question: Two forces, each of $10\text{ N}$, act at a point $P$ as shown in the diagram. The ...
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1answer
26 views

Inclined plane vector

I have a question, I need to find $P$ in the following situation. A box of mass 5kg is in equilibrium on a slope at $pi/6$ from the horizontal. I need to find the magnitude of the force in the ...
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3answers
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Why is $\langle c \cdot f|g\rangle=c^*\langle f|g\rangle$?

Why is $\langle c \cdot f|g\rangle=c^*\langle f|g\rangle$? $c$ is a complex number and $c^*$ is the conjugate. I think that $\langle c \cdot f|g\rangle=c\langle f|g\rangle$ because that's how scalar ...
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2answers
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Can you anti-dot? (9-22 from Marion Thorton)

I'm solving a question out of the textbook and it reduces to the following. a particle of mass 2m with velocity $v_0$ collides with a particle of mass m at rest. The collision is elastic. So using ...
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1answer
57 views

Difference between quadrivector and 4-vector

Why is the square of a 4-vector equal to $t^2+x^2+y^2+z^2$ while the square of a quadrivector is equal to $t^2-x^2-y^2-z^2$? Aren't they the same mathematical object?
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1answer
36 views

Dot product in cylidrical coordinates

I'm given the vector: $$\vec{V}{(r,θ,z)}=\frac{1}{r}\hat{e_r} + (r\cosθ)\hat{e_θ}+\frac{z^2}{r^2}\hat{e_z}$$ I want the scalar product ${\vec{\nabla}}\cdot{\vec{V}}$ We know that in cylindrical ...
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1answer
44 views

$mg\cos\theta=N$ or $N\cos\theta=mg$ [duplicate]

I was reading up of centripetal motion when I saw the relation that $mg=N\cos\theta$, as can be seen from http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/carbank.html, in the case of a ...
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4answers
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Is a unit vector really unitless and dimensionless?

According to my textbooks, a unit vector has no units and no dimensions, but is only used to specify direction. It only shows the orientation of a corresponding vector in space. I think it's true, or ...
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2answers
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Why Gravity doesn't affect Horizontal acceleration/motion?

It is still hard for me to grasp on why gravity doesn't affect horizontal motion, doesnt gravity causes a change in resultant force and thus cause a change in acceleration $F=m.a$
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1answer
34 views

Prove Von Neumann entropy is invariant under coordinate transformation

https://en.wikipedia.org/wiki/Von_Neumann_entropy#Properties How to show that von Neumann entropy for $p_k$ with basis $|\psi_i\rangle$ is the same for $p_n$ with basis $|\phi_i\rangle$? That is, to ...
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6answers
688 views

Definition of inner product as in the case of work

According to the mathematical definition of "vectors", vectors are simply the elements of a set $V$ which forms a vector space structure $(V,F,+,*)$. The definition of inner product states that it is ...
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1answer
52 views

Resolving forces on inclined circular motion

When resolving forces vertically and horizontally in a problem where a car is going around a banked bend, why do you consider the components of the normal force? Shouldn’t the normal force just cancel ...
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2answers
56 views

Definition of velocity in classical mechanics

Let $(r_1,r_2,r_3)$ be the coordinates of a particle $r$ in the coordinate system $\phi$. Let $\{\hat{e_1},\hat{e_2},\hat{e_3}\}$ be the coordinate basis of $\phi$. Why do we define the velocity $v$ ...
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1answer
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How to distinguish a spinor from a 4-vector?

Lets say we are given a four components object. To be explicit lets consider that these components are $ x^\mu = \mu $ with $\mu\in{0,1,2,3}$, i.e. $$ x^\mu \sim \left[ \begin{matrix} 0\\ 1\\ 2\\ 3 \...
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3answers
49 views

How to determine the direction of instantaneous acceleration in a 2D motion? [duplicate]

How do we determine the direction of instantaneous acceleration when the body is moving in a plane (or a 3D space)? This question has been truly bothering me for nearly two weeks. I looked it up, ...
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0answers
50 views

Pendulum in Polar Coordinates

The net force acting on the bob is equal to the sum of the gravitational and tension forces, $$ \begin{align*} \mathbf{F}_\text{net}&=\mathbf{F}_g+\mathbf{F}_T\\ &=(-mg\cos\theta\,\hat{\mathbf{...
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3answers
63 views

Can velocity in $y$-axis be equal with velocity in $x$-axis?

So if $u_y=30 m/s$ and $u_x=30 m/s$ can we say that $u_y=u_x$? my confusion is because velocity is vector they are not equal ( equal in magnitude but not dimension). But can we say that they are ...
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2answers
35 views

Best way to use a pulley

Which is easiest way to pull a pulley? I have posted a diagram in which there are three cases. In all three cases force and mass of body are same and pulley is frictionless. My understanding is that ...
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1answer
70 views

What is the difference between a state vector and a basis vector in Quantum mechanics?

I searched about the difference between state vector and basis vector in Quantum mechanics but couldn't find any clear explanation. Can someone please give a simple and clear explanation of this?
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5answers
105 views

Instantaneous velocity

So here’s a question I’ve been thinking of for a while. Suppose we say, “an object is having an instantaneous velocity along a particular direction ( say 10 m/s along the $x$-direction)” . Is it fair ...
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2answers
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Why, when calculating work done when a person climbs stairs, the distance is the height of the stairs but not the distance the person travels?

I was thinking, since Work Done = Force * Distance moved in the direction of the force , the distance moved in the direction of the force would be the distance of the slanted stairs instead of the ...
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1answer
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Basic question about a point mass and the geometry of a general trajectory

Just to ruin the punchline upfront: With this question, I'm trying to do a sanity check about the logic of insisting on a trajectory and only then thinking about forces. I took Classical Mechanics ...
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2answers
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Acceleration in a non-inertial reference frome - derevation

The general velocity equation for a point B in on body rotating and translating about point A with respect to the inertial reference frame say 'xyzo' can be expressed as, $\vec{r_{B/o}} = \vec{r_{A/o}...
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2answers
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How can I show the negative gradient of centrifugal potential equals centrifugal force?

Given, the centrifugal potential is $$V = -m\frac{1}{2} \left\lVert\ \vec w\ \times \vec r\ \right\rVert^2 $$ I simplified, $$V = -m\frac{1}{2} (w^2 + r^2) $$ ,converted to Cartesian $$V = -m\...
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5answers
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If force is a vector, then why is pressure a scalar? [duplicate]

By definition pressure is the perpendicular force applied to a unit area. So it has a direction which is perpendicular to the area. So it should be a vector. But I did sone googling and found out that ...
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3answers
59 views

What does this equation regarding Kepler's laws of planetary motion actually mean?

I'm doing a project in multivariable analysis regarding Kepler's laws of planetary motions and the following equation was a recommended equality to use, but none of the variables were actually defined:...
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1answer
45 views

The commutator of position and momentum operators in three-dimensional Cartesian coordinates

I'm to calculate the commutator of the following operators : $\mathbf{\widehat{r}}=\mathbf{e}_{x}x+\mathbf{e}_{y}y+\mathbf{e}_{z}z$ and $\mathbf{\widehat{p}}=-i\hbar\left ( \mathbf{e}_{x}\frac{\...
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1answer
41 views

States created by translation operator

Quantum Mechanics Volume One page 188 by Claude Cohen Tannoudji. In $q$ and $p$ state vectov formalism. $QS(\lambda) |q\rangle=(q+\lambda)S(\lambda)|q\rangle$, where $S(\lambda)=e^{-i\lambda P/\hbar}...
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1answer
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According to newton's laws, why do the two different masses of an Atwood machine move in opposite directions?

Consider an Atwood machine with two different masses $M$ and $m$ such that $M > m$. When trying to find the acceleration of that system, all solutions I've found go like this: There are 2 forces ...
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1answer
69 views

Is torque always equal to the derivative of potential energy with respect to rotation angle?

For any three-dimensional rigid body, the applied torque on that body is defined as: $\vec{\tau} = \vec{r} \times \vec{F}$ where $\vec{F}$ is the applied force on the object (i.e. $-\vec{\nabla} U$) ...
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3answers
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components magnitude is same to the magnitude of vector and its not parallel or perpendicular to it, how?

In this picture if R is the component of P which is the reactionary force of mg, then according to the picture R is balancing mg in equilibrium. So my question is how can a component of a vector have ...
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3answers
65 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
140 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
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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
78 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
36 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
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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
24 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
28 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
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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, ...