Questions tagged [vectors]

Geometric object with magnitude (length) and direction.

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1answer
24 views

Why is the tension $\vec T$ downwards in the system?

Link to video Doubt: At pulley $A$, consider the free-body diagram. Why is the tension, $\vec{T}$, in both hands downwards? I know $\vec{T}_2$ is upwards since it is the force acting upwards in ...
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2answers
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Flight time of spherical bullet fired horizontally versus dropped vertically / effect of crosswind on spherical car

Would a spherical bullet fired horizontally from a musket stay aloft longer than a spherical bullet dropped from the same height? I know two similar questions have been asked (Will a bullet dropped ...
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1answer
22 views

The sign of $d\mathbf{r}$ when integrating the universal gravitational force in order to define gravitational potential energy [duplicate]

I am trying to find gravitational potential energy by integrating the gravitational force: $$\mathbf{F}(\mathbf{r}) = - \ G \frac{Mm}{|\mathbf{r}|^2} \ \hat{\mathbf{r}}$$ where $\mathbf{r}$ is the ...
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If the vector $\vec{A} = 2\hat{i}+4\hat{j}$ and $\vec{B} = 5\hat{i}+p\hat{j}$ are parallel to each other, the magnitude of $\vec{B}$ is? [on hold]

If the vector $\vec{A} = 2\hat{i}+4\hat{j}$ and $\vec{B} = 5\hat{i}+p\hat{j}$ are parallel to each other, the magnitude of $\vec{B}$ is____________ how to solve it?
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2answers
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What is the meaning of transverse acceleration due to work in special relativity?

If we derive the momentum in Special Relativity we get : $$ \dfrac{\mathrm{d}\boldsymbol{p}}{\mathrm{d}t} = \dfrac{\mathrm{d}m \gamma \boldsymbol{v}}{\mathrm{d}t} = m\dot{\gamma}\boldsymbol{v}+m\...
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Vertical component of friction

If we have a car of mass $m$ sliding around a banked curve of angle $\phi$ with some coefficent of friction ${\mu}$, then the normal force will be $$Ncos\phi= mg + {\mu}F_{g}\sin\phi$$ But this ...
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0answers
82 views

Angle between velocity and acceleration vector, and interpretation of pathway [on hold]

I just started studying mechanics, and I am stuck with the following question: $$\vec{r}(t)=a \sin(\alpha t^2)\hat{x}+b \cos(\alpha t^2)\hat{y}$$ I was asked to find the formula that expresses the ...
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New way to compensate for gyroscopic drift

Let us assume two points in 3D space and we only care about their orientation, no velocity, position or acceleration. Now connect those two points with a rigid body of certain length, so that the ...
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Vector quantities [closed]

Three vectors forces F1,F2 and F3 act on a particle of mass m=3.80kg. Calculate the magnitude and direction of the net acting on the particle And calculate the particle acceleration
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Vector Differentiation Identities [closed]

We conclude this section by stating some formal identities in vector differentiation, with their proofs left as exercises. Let the scalar $\:c\:$ and the vectors $\:\mathbf{A}\:$ and $\:\mathbf{B}\...
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Electric dipole torque problem

Problem 4.6 from Griffith's book: To solve it, we construct an image dipole $ \vec p_i$ with opposite polarity then find the torque $ \vec N = \vec p \times \vec E $ I'm having trouble knowing how ...
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Is four velocity always given by $U^{\mu} = d x^{\mu}/d\tau$?

I was taught that four-velocity is defined as $${\bf U} = \frac{d \bf x}{d\tau}$$ and that it has the components $$U^{\mu} = \frac{d x^{\mu}}{d\tau}$$ where $d\bf x$ is the four displacement and $\...
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1answer
67 views

Is the normalization of the wave-function preserved due to…?

Is the preservation of the inner product the same thing as the vector length of the wave-function staying constant with it's rotation through some R2 plane (ie it's evolution through time), that is ...
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58 views

I think I broke Vectors [duplicate]

I was working on the following problem, when I ran into some trouble due to some repeated division of vectors into components. I began by drawing the forces acting on the block. I pretended that ...
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Triangle law of vector addition [migrated]

I've been running my fingers through the internet and books probing why does the triangle law of vector addition works, but I've failed to find a satisfactory answer, rather, any answer at all, for ...
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3answers
105 views

Reason behind vector addition law

What is the reason behind triangle law of vector addition, in other words, how is this really justified?
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160 views

Origin of vectors with physical meaning

I was reviewing notes of physics, and i realized that something about the mathematics of vectors was wrong in my head. Suppose a vector is $\vec{A}=5\textbf{i} + 3\textbf{j}$, and other $\vec{B}=7\...
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2answers
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Identifying Vehicle Reversing

I am trying to identify if a vehicle is reversing. I have the position of the vehicle, the direction the vehicle is facing (as an angle), and the speed of the vehicle at different time points. Can ...
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2answers
93 views

Relationship between quantum projector operator and projection of vectors

In quantum mechanics, we define the projector operator $$\hat{P} = |\psi\rangle\langle\psi|$$ And we say that the action of this operator $\hat{P}$ over a ket $|\phi\rangle$ gives us the projection ...
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Why do some people write the gravitational force as proportional to $\mathbf{r}/|\mathbf{r}|^3$?

I'm reading Mathematical Aspects of Classical and Celestial Mechanics, Second Edition by Arnold, Kozlov, and Neishtadt. It occurred to me that many people like to use third power when mention the law ...
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0answers
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Suppose A and B represent two vectors (insame order), the angle between them being 60 degrees, then why is the resultant wrong? [migrated]

Let's say there are three points A,B and C: A represents the displacement between points A and B (4 cm to the east) and B represents the displacement between the points B and C (3cm to the northwest)....
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How do I know whether members are in tension or compression when using Method of Sections?

So we started doing structural analysis in my engineering class lately, and are doing trusses. However, I'm not quite sure how method of sections works conceptually. I'm getting the right numbers, but ...
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3answers
49 views

Angular momentum and angular velocity

The angular velocity $\vec{\omega}$ lies along the axis of rotation. And the angular momentum $\vec{J}$ is the cross product of $\vec{r} \times \vec{p}$. Which according to me should also lie along ...
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3answers
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Magnitude of vector quantities

The gravitational force in the vector form is defined as $$ \vec{F}=-\frac{GMm}{\boldsymbol {r^3}}\vec{r}$$ Many textbooks define its magnitude as $$F_g=-\frac{GMm}{r^2}$$ However, in the derivation ...
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1answer
241 views

Questions regarding projecting the energy-momentum tensor for perfect fluid along the four-velocity

The energy momentum tensor for a perfect fluid is defined as: $$T^{\mu \nu} = (\rho + p)U^\mu U^\nu + p \eta^{\mu \nu}$$ Where $\rho$ is the energy density, $p$ is momentum, $U$ is the four-...
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198 views

What the primed quantities really are in this context?

In this definition: The set of $N$ quantities $V_j$ is said to be the components of an $N$-dimensional vector $\mathbf{V}$ if and only if their values relative to the rotated coordinate axes are ...
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2answers
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A simple way of calculating Euler Angles from Rotation Matrix — help!

This is a follow up of this question : I have the rotation matrix $$ \left( \begin{matrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\\...
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4answers
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Is my understanding of vectors correct?

I recently learned that a vector in mathematics (an element of vector space) is not necessarily a vector in physics. In physics, we also need that the components of the vector on a coordinate ...
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Why are products of vectors just the way they are, and not the other way around? [migrated]

The scalar product and vector product of two vectors $\vec{A}$ and $\vec{B}$ are $AB\cos\theta$ and $AB\sin\theta\space\hat{\eta}$, respectively. They could have been the other way around—that is to ...
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Why does the Cross Product have to be perpendicular to the two vectors? [migrated]

I understand that the cross product of two vectors equals the area of the parallelogram. But I don't understand why multiplying the two vectors gets you a vector perpendicular to the two vectors.
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3answers
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How to prove a 4D vector is a 4-Vector?

This is a fairly open ended question. Given a set of 4 Components, that is, a 4D Vector, what is the process for determining rather or not it is a "4-Vector" as defined in special relativity? I want ...
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5answers
75 views

Intuition of 2D Velocity Vectors [duplicate]

I understand 2D vectors in terms of displacement. For example, Bob moves 3m to the east and 4m to the north, the total change in position (displacement) equals 5m to the north east. But I don't ...
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1answer
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Geometry with differential angles

In the solution to a problem, the author considers the normal force provided by an arc length of string with a differential subtended angle size, $\textrm{d}\theta$. The author reasons that this ...
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Order of positions of tensor/vector components in an inner/outer product

Show that if $T_i$ are the components of covariant vector T, then $S_{ij}=T_iT_j-T_jT_i$ are the components of a skew-symmetric covariant tensor S. The question is whenever working with equations of ...
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2answers
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Basis of 2D motion analysis

The basic argument for analysing 2D motion is that if we have a projectile we can break its 2D motion into 2 1D motions along 2 perpendicular axes. The motions along these axes and their corresponding ...
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1answer
38 views

Appropriate Vector Diagram for Force

Which of these two vector diagrams is befitting for illustrating exerted force?
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1answer
126 views

Wavelength scalar/vector ambiguity?

I have seen the de Broglie relation for wavelength written as $\lambda$ = $\frac{h}{\gamma(\vec{v})m_o\vec{v}}$ I know wave propagation in the one - dimensional case makes wavelength a scalar, as ...
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1answer
411 views

Considering the theory of special relativity: Is torque still a vector?

Considering the theory of special relativity: Is torque still a vector? In classical mechanics it is easy: You have 3 axes and thus 3 planes. Every plane has its own torque so torque has 3 ...
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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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How do you calculate the speed of air when it fills a vacuum of 1 cm³?

At different heights, atmospheric pressure is different. If a vacuum was created of say 1 cm³, how would i calculate the velocity of air filling it back in. The adjacent layer of air would obviously ...
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1answer
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Prove acceleration in orbit with newtons second law

I want to prove that the acceleration in a orbit at a given point r=(x,y) is $a=-\frac{GM}{R^3}r$ (My professor said this can be proven by newtons second law, but he never explained in detail how). I ...
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1answer
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Work-Kinetic energy theorem derivation

So I came across this derivation in the book Classical Mechanics by Herbert Goldstein. I don't follow from the second step onwards. I understand that there's a dot product, but how do you compute it? ...
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4answers
365 views

Is there a scalar acceleration?

Distance is paired with Displacement and it seems to be a bigger idea than just the magnitude of Displacement. Speed is paired with Velocity. I have always thought that there is not such pairing with ...
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1answer
3k views

Line of action force

The task is to reduce the two forces into a single net force and then find the equation of its line of action. I chose to find the net force and momentum with respect to the origin. The magnitude of ...
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1answer
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Direction of cross product of two vectors [duplicate]

Are there several ways to find the direction of a×b other than right hand thumb rule?
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Question on notation for the inner product of complex vectors [duplicate]

Regarding the wiki: https://en.wikipedia.org/wiki/Sesquilinear_form#Hermitian_form you can see that the wiki states that physics defines the inner product for complex vectors as: $$\langle \, \...
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1answer
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Where does 4N and 3N goes in this diagram?

Two forces of 3 N and 4 N are acting at a point such that the angle between them is 60 degrees. Find the resultant force. I successfully draw diagram for above sentence: But I am confused which one ...
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1answer
23 views

Why are the vectors canceled out in this scenario for angular momentum of a particle?

I have a study guide for our next test, and I'm trying to understand the professors answer but I don't understand why i^ * i^ = 0? Here is his work, Why do we know that the P Vector is on direction ...
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1answer
77 views

Why should Vector Components of a Weight be Perpendicular to each other?

So this question came to my head this morning. When analyzing such a problem, its easier to break the W component into 2 seperate components, here I've marked the components in Red & Pink arrows. ...
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4answers
52 views

What is the proof of parallelogram law of vector additon?

I have a question. How force can be defined as the magnitude of a ray? For instance, when we deal with two forces having magnitude 4 N and 5 N working 60 degree apart we solve the resultant by simple ...