Geometric object with magnitude (length) and direction.

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2
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2answers
113 views

Is multiplication in physics purely mathematical or is there a physical explanation to it?

Here is what I mean: We always use mathematics in physics, which is pretty powerful, but I still need to ask whether multiplication in physics has a better explanation to what I already think. For ...
0
votes
2answers
105 views

Unitary operators evolving the set of Pauli matrices

Consider the Heisenberg picture of Quantum Mechanics. For a two state system we have the Pauli matrices evolving according to the relation $$\sigma_i(t)=U^+\sigma_i(0)U$$ where $U=e^{-iHt/\hbar}$ and $...
-2
votes
2answers
82 views

How can gravity have a horizontal component?

$mg$ obviously has no horizontal component, but on resolving it into components it seems to have a horizontal component $mgcos\theta sin\theta$. I know I'm doing something wrong here. How is this ...
0
votes
3answers
82 views

Dot product approaches zero as the magnitude of the vectors increase?

Is there such thing? I'm doing some computations on mathematica and I noticed the dot product between two vectors are getting smaller and smaller as I increase the magnitude of the vectors, I'm not ...
0
votes
0answers
40 views

Electron in a Magnetic Field: Force parallel to velocity?

According to the four-force given in this question, Force is parallel to velocity. But the Lorentz Force is perpendicular to velocity in a constant magnetic field. Is this a contradiction? [a ...
4
votes
2answers
89 views

What does $(\delta\vec{r}\cdot\nabla)^2$ mean in the derivation of the Lamb shift, and how do you find its expectation?

The Wikipedia page on the Lamb shift includes the following first steps: $$\Delta V = V\bigl(\vec{r}+\delta \vec{r}\bigr)-V(\vec{r})=\delta \vec{r} \cdot \nabla V (\vec{r}) + \frac{1}{2} \bigl(\delta ...
5
votes
2answers
113 views

How is the dot product a generalization of multiplication?

I've seen an interesting explanation for lots of what I previously thought were unmotivated definitions in Newtonian mechanics, namely that power is always defined as effort times flow. But when ...
0
votes
1answer
38 views

Vector interpretation of Kepler's 2nd law ( r X a = 0 )

I just read the vector interpretation of Kepler's second law and the conclusion put me in a confusion. The interpretation concludes by demonstrating that r X a = 0, where boldfaced r and a are ...
0
votes
0answers
20 views

if a force vector is acting horizontally, on a curved object, how will the object accelerate?

The force vector is acting horizontally, but the plane surface it is acting on is inclined at an angle to the horizontal. How will he plane surface accelerate?
0
votes
0answers
13 views

Velocity in harmonic motion - Why are these angles congruent?

I learned about harmonic motion and I found the derivation of the formulas: And so, the velocity in harmonic motion is the projection of the velocity in angular motion. The only thing that is not ...
1
vote
1answer
50 views

Orthogonal of tangent vector in Rindler coordinates [closed]

For 2D space time from $(t,x)$ to $(u,v)$ the transformation are $$t = u \sinh(v)$$$$x=u\cosh(v)$$ Asking to show that two families of curves $u = \textrm{constant}$ and $v = \textrm{constant}$ ...
0
votes
2answers
34 views

Difference between a magnitude and a component

Studying the basic concepts of vectors, I am very confused with the definitions of vector components and magnitudes. And why does the magnitudes always have to be positive? How about the components? ...
-1
votes
1answer
67 views

Dot product in index notation [closed]

This is a question about a small exercise I am trying to do in order to check if I am correct. Such type of quantities can appear in propagators in QFT. Since I am not an index expert I need some ...
-1
votes
2answers
29 views

Proof regarding angle between velocity vectors

Consider a casual trajectory of a point and the velocity vector at two istants $v_1$ and $v_2$. In picture (1) I considered the osculating circle with center $O$ and radius $R$. In the picture (2) I ...
0
votes
3answers
42 views

Flux - Scalar Multiplication in Integral?

No textbook and website seems to answer this so here is my question: When we have a scalar flux: I understand that you take the scalar product of the vectors. And I understand the need for using an ...
0
votes
0answers
53 views

Force conversion in a barrel cam-follower mechanism

A barrel cam-follower mechanism consists of a (cylindrical) barrel with a cam track, a cam-follower (roller) inside of the track, a fork connected to the cam-follower and a guide along which the fork ...
0
votes
2answers
66 views

How to determine the net velocity change applied by a force vector [closed]

I am a little stumped by the answer of this question. The question reads, "In three situations, a single force acts on a moving particle. Here are the velocities (at that instant) and the forces: ...
0
votes
1answer
38 views

Is it possible that the magnitude of the resultant of two equal vectors be equal to the magnitude of either vector?

Is it possible that the magnitude of the resultant of two equal vectors be equal to the magnitude of either vector? What does this question mean? Does the zero vector(null vector) satisfy the ...
1
vote
0answers
25 views

Correct resolution of vectors [closed]

There's a sum given as an example in my physics textbook which I tried to solve in a different manner but ended up with a wrong answer. Here's a picture of the sum given in my textbook along with the ...
0
votes
0answers
22 views

How is equilibrium achieved when masses are unbalanced?

Consider the see-saw scenario shown below (This image was from a Phet simulation) If you place a 5kg mass 0.25m from the pivot point, the seesaw will have net torque in an anticlockwise direction, ...
0
votes
1answer
41 views

Basic tension and equilibrium confusion

The following is what I did: $$Fsin\theta = 60 => F = 93 N$$ $$Fcos\theta = 40 => F = 52 N$$ Why do I get different results? Does this mean the object isn't in equilibrium? How can I proceed ...
1
vote
1answer
42 views

Component of Component of a vector [duplicate]

NOTE : By perpendicular component of $\vec{F}$, I mean a vector which is a component of $\vec{F}$, but perpendicular to it. In the image above, the red vectors are a possible set of rectangular ...
20
votes
9answers
2k views

How to interpret the units of the dot or cross product of two vectors?

Suppose I have two vectors $a=\left(1,2,3\right)$ and $b=\left(4,5,6\right)$, both in meters. If I take their dot product with the algebraic definition, I get this: $$a \cdot b = 1\mathrm m \cdot 4\...
1
vote
2answers
70 views

What is the power given by centripetal force?(in circular motion)

A particle of mass $m$ is moving in a circular path of constant radius such that the centripetal acceleration is varying with time as $a_c = k^2rt^2$ where $k$ is constant. The power given to the ...
2
votes
3answers
58 views

Force at axis of spinning wheel

This is a newbie question, but I don't quite understand the forces at work when an object is rotating. So I've read that i can use my right hand to determine the direction of the force at the axis ...
2
votes
1answer
147 views

The Physics Behind the American Death Triangle [closed]

I've heard a lot about the American Death Triangle and how it is awful for belaying. The Death Triangle is set up as such: you have two anchor points with a single rope or line running through both ...
3
votes
2answers
99 views

About reference frame in Newton's second law?

Classical physics models events occuring in the spacetime $\mathcal E\times \mathcal T$ where $\mathcal E$ is a dimension 3 euclidean point space and $\mathcal T$ is an interval of $(\mathbb R, <)$...
1
vote
1answer
66 views

what is the energy required to change only direction of a vector? [closed]

Does change in velocity vector change Kinetic energy of a system? Does any energy change when we change direction of a vector of a system?
1
vote
2answers
61 views

Vector addition forces with law of cosine

Given two vectors $\mathbf{F_1}, \mathbf{F_2}$ and an angle $\alpha$ between two vectors we can derive the resulting force $F_R:=\Vert \mathbf{F_R}\Vert$. $$F_R^2=\Vert\mathbf{F_2}-\mathbf{F_1}\Vert^...
1
vote
1answer
41 views

Correct way to write Pauli matrices

This is purely a question of notation for the Pauli matrices. What is the correct way to write them for use as operators? Would I just write the vector of the matrices as a vector i.e $$\vec{\sigma}\,,...
2
votes
3answers
99 views

Meaning of the Vector Wave Equation

So I thought I would try my luck here on physics stack exchange about an intuitive meaning of the Vector Wave Equation. I know there are a lot of resources out there that explain this equation, but ...
1
vote
2answers
302 views

Why does something on an inclined plane move forward at all?

We just started studying about the inclined plane and vectors in motion, but i don't understand one thing: Why on earth does the object on the inclined plane move forward (I.e in the direction where ...
0
votes
2answers
49 views

Why is 90 degrees the standard for independence in vectors? [closed]

Why do so many laws and ideas in physics act separately if they are separated by 90 degrees? Say you have a force in one direction, x. You can't add a force within 0-90 degrees without changing the ...
1
vote
1answer
59 views

Why is the spatial term for contravariant 4-gradient negative, whereas for other 4-vectors it is the covariant part that is negative spatially?

The contravariant 4-displacement is: $${x}^{\alpha} = (ct,\mathbf{r})$$ And the contravariant 4-gradient is: $${\partial}^{\alpha} = (\frac{1}{c}\frac{\partial}{\partial{t}},-\nabla)$$ From what I ...
2
votes
7answers
413 views

Why is force a vector? (The Feynman Lectures)

A vector is a quantity that transforms just the way the coordinates transform under rotation (while a scalar remains invariant under rotation). In FLP, he says suppose $F$ is a vector and probably ...
1
vote
0answers
30 views

Direction of motion 1 [closed]

A man on a bike travelling east on straight road at 8km/h sees a car driving north at 60km/h. What is the apparent speed and diretion of motion of car to the cyclist?
1
vote
2answers
97 views

Physicists definition of vectors based on transformation laws

First of all I want to make clear that although I've already asked a related question here, my point in this new question is a little different. On the former question I've considered vector fields on ...
0
votes
1answer
55 views

Using the Metric in Book Gravitation (MTW)

Here is the whole Box 2.2, at Page 55 The dot behind the second $-p^2$ seems to be a "planck mass" (sarcasm, flea egg) or just the book's style to use Dot behind the equations. So the Equation is ...
3
votes
1answer
64 views

Is time a vector in Minkowski space? [duplicate]

I am arguing about this topic with my school teacher in so long time, I want to finish this debate. My teacher's opinion is "Yes, Time is vector" because four-vector has $t$ component, and mine is "...
1
vote
1answer
52 views

Vector Navigation and equations [closed]

So I am taking a grade 12 physics online course and I am getting stuck on the Vector Navigation equations as there isn't much explanation in my course. The following text is found in my online course....
0
votes
1answer
48 views

How does angular velocity transform on the surface of a sphere?

If we consider the earth as a sphere than it will have an angular velocity of $\boldsymbol{\omega}=\omega\mathbf{e}_z=\frac{2\pi}{T}\mathbf{e}_z$ where $T\approx24h$. Now we have given a location in ...
0
votes
1answer
62 views

when does Newton's third law of motion come into effect

I'm a bit confused about when does Newton's third law come into effect and when it does not. For instance, lets say i was swinging a YoYo in a vertical circular motion, I would obviously have to ...
-3
votes
1answer
107 views

Can you answer these two difficult vector questions? [closed]

Figure 1 1) Determine the value of FB. 2) Determine the magnitude of FA + FB. (I know that the answer must be in Newtons. But other than that, I've very lost on what to do next. Please help!)
0
votes
4answers
117 views

When is the direction of the static friction negative?

i thought that the force of static friction exerted on an object is always going in the opposite direction of any other force exerted on the same object. however, this problem seems to disregard that ...
0
votes
0answers
36 views

Why are dot products scalar, intuitively? [duplicate]

Why are dot products scalar (in the general sense) if seen from an intuitive point of view ? i am not asking about a particular case like kinetic energy or work but a i want the answer for general dot ...
0
votes
0answers
32 views

What is the derivative of the length vector in the direction of the original unit vector?

What is the derivative of the length vector? I am asking this question becuase I have seen, in Prof. M. S. Sivakumar's youtube video, the result that $\dot{|r|} \hat{r} = \dot{r}$ Where, $ \mathbf{r}...
0
votes
1answer
92 views

Does the complex conjugate of a vector have the same direction as the vector?

Looking at reflected and transmitted optic waves, the $\overset{\rightharpoonup }{E}_t$ vector is always perpendicular to $\overset{\rightharpoonup }{k}_t$ (as seen in the attached image). So $\...
0
votes
2answers
51 views

Can vector components be in turn decomposed? [duplicate]

I've a basic (and maybe obvious even if I don't see it) question on the decomposition of a vector in physics. An example of situation I'm confused about is the inclined plane with an object on it. ...
0
votes
1answer
59 views

Laws and Intuition for physical problems

So I've been reading the book 'Feynman: Tips on Physics' recently and in chapter 2 (the book is available for free online) he works out the answer for this problem using his intuition rather than ...
1
vote
2answers
153 views

What is total acceleration?

I'm currently taking a Physics class and we are studying motion in a circular path. and i'm kind of fuzzy on what the total acceleration actually is. take this problem for example An automobile ...