Questions tagged [vectors]

Geometric object with magnitude (length) and direction.

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1answer
108 views

Using $v_f = v_0 +at$ for objects in free fall [closed]

I have a question about the difference of using $v_f = v_0 +at$ and $s = v_0t + \frac{1}{2}at^2$ for objects in free fall. I'm trying to solve a problem where there's a ball rolling along an inclined ...
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3answers
87 views

How to specify the orientation of an area vector?

We all know that the area of a triangle having consecutive sides as $\vec { a }$ and $\vec { b }$ is $\frac { 1 } { 2 } | \vec { a } \times \vec { b } |$, but what is the direction of that area vector?...
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214 views

Angular momentum of a system about the center of mass

Let $\mathbf{R}$ be the center of mass of a system of particles. Then the angular momentum of the system is $$\begin{align} \mathbf{L} &= \sum \mathbf{r}_i \times \mathbf{p}_i\\\\ &= \sum \...
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6answers
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How can static friction depend on the normal force, but be directed orthogonal to it?

According to my understanding: two orthogonal forces aren't related and two orthogonal vectors don't affect each other the force of static friction $F_s$ depends on the normal force $F_n$, so $$F_s = ...
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2answers
101 views

Positive work along path [closed]

Consider I have a simple formula for the work along some path (in 1 dimension): $$W~=~\int_{x_0}^{x_1}\vec{F}\cdot d\vec{x}.$$ If I now move from left to right ($x_1 > x_0$) along the axis (...
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4answers
151 views

Angular Momentum Derivation without Vector products - is it possible? [closed]

I am trying to prove myself the formula for angular momentum: $$L = mvr = pr$$ without use of any vectors. I started by considering the comparison between $E = \frac{1}{2}mv^2$ and $E = \frac{1}{2}...
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3answers
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if a vector has a magnitude equal to zero, can that thing exist? Can that thing be measured? [closed]

consider a vector (a vector is a physical quantity ) having magnitude equal to zero.Now, if something has a magnitude equal to zero, can that thing exist? Can that thing be measured? if net force on a ...
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2answers
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Proof that $\vec {r(t)}=\vec r_0 + \vec v_0 t + \dfrac{1}{2} \vec a t^2$ for uniformly accelerated motion

Displacement of a particle moving through $ x $ axis is given by $$ x(t)= x_0 + v_0 t + \dfrac{1}{2} at^2 $$ Can we deduce from it that $$ \vec r(t)=\vec r_0 + \vec v_0 t + \dfrac{1}{2} \vec a t^2$$ ...
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1answer
81 views

Unit vector in displacement

When we use vectors in physics why does the unit vector (for displacement) equals magnitude of 1 or magnitude of 1m?
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5answers
184 views

Why we use vectors?

When we say that the position of an object is +5m on x axis why we need to use vectors? I mean could we don't use vectors and just say +5m on x or y or z axis instead of writing 5*unit vector either $...
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0answers
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Expressing Fresnel Equations in terms of $\mathbf k$-vectors

Write the Fresnel Equations in terms of the k-vectors (or the propagation constants $\gamma$). Assume that the x-direction is normal to the interface, and the z-direction is parallel to the interface, ...
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3answers
62 views

Coriolis force decomposition of angular velocity [closed]

I can’t for the life of me understand how the $\omega$ in this is decomposed to $$\vec{\omega}= \omega (-\sin(\theta),0, \cos(\theta))$$ Any help would be greatly appreciated!
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1answer
146 views

Is this Question correct? Newtonian Motion - Relative Motion of Rain

There is a question in a textbook which states: "A cyclist is riding north at 12km/h when it starts to rain. The rain appears to be falling towards her at an angle of 10 degrees relative to the ...
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3answers
113 views

What is the real notion/feel of a tensor quantity? [duplicate]

I have been just introduced to the term tensor while studying Rotational Dynamics, particularly about Inertia. But I just don't get a clear line separating vector from a tensor. What does someone mean ...
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1answer
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Isn't the velocity in an orbit always tangential, not radial and tangential?

In this video the person resolves the momentum vector into two components, tangential and radial. But isn't the velocity at every point on the orbit tangential?
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1answer
106 views

The action of Lorentz transformations on 4-vectors in special relativity

So I am studying special relativity and have been introduced to basic tensor calculus used in the theory. Recently, I came across a statement that is confusing me: $$\Lambda^\mu_{\,\,\nu} x^\nu = x^\...
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1answer
119 views

Is $\nabla=\nabla'$? Nabla operator acting on $r^n$

I have been taught that $$\nabla r^n =\text{gradient of }r^n =n r^{n-1}\ \hat{\boldsymbol r}$$ but in introduction to electrodynamics by Griffith (4th edition) on page 173, $\nabla' r^n$ is given by $-...
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3answers
405 views

Is spinor the sum of scalar, vector, bi-vector, pseudo-vector, and 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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1answer
175 views

Banking of road

If a car is moving on a banked frictionless road one of the component of normal reaction force acts as the centripetal force required for the turn. But normal reaction force is a reaction force. ...
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2answers
416 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
21 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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1answer
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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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2answers
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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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1answer
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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) [closed]

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
86 views

What is the difference between a quadrivector and a 4-vector? [closed]

What is the difference between a quadrivector and a 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 ...
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1answer
55 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
357 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
2k views

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
102 views

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
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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
724 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
81 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
73 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
181 views

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
252 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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3answers
72 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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1answer
257 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
152 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
109 views

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
31 views

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
69 views

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
9k views

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
88 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
244 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
55 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
200 views

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
203 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. $-\vec{\nabla} U$) ...