Geometric object with magnitude (length) and direction.

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2answers
73 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
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2answers
72 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
67 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
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0answers
31 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 ...
0
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3answers
64 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 ...
4
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2answers
80 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 ...
3
votes
1answer
53 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 ...
5
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2answers
96 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 ...
1
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1answer
46 views

Orthogonal of tangent vector in Rindler coordinates

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
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1answer
35 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
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0answers
18 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?
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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 ...
0
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2answers
18 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? ...
3
votes
1answer
576 views

Rolling a ball into a cone; what should the forces overall be?

This is my solution to finding angular displacement/velocity/acceleration on cone so far. Consider a cone, with an apex of half-angle $\psi$ pointing down, and a height of $h$. If I roll a ball into ...
1
vote
2answers
212 views

How to find Tangential/Radial/Angular Velocity for motion in any curve?

Is the radial velocity responsible only for changing distance between objects and the component perpendicular to it only for change in direction? If so why? Please try to give a different explanation ...
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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
28 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
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3answers
27 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 ...
8
votes
7answers
807 views

Is there a physical interpretation of a tensor as a vector with additional qualities?

What is a tensor? has been asked before, with the most highly up-voted answer defining a tensor of rank $k$ as a vector of a tensor of rank $k-1$. But if a scalar is defined as a physical quantity ...
0
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0answers
20 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 ...
20
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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 ...
0
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2answers
35 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: ...
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0answers
24 views

How to find components of vector other than 90 degree between eachother [migrated]

As from the Pythagoras theorem we can find the resolved parts of a vector (with given angle and magnitude) which makes angle 90 degree with each other. How to find components of vector other than at ...
2
votes
1answer
775 views

Relative wind velocity explanation - understanding Irodov problem 1.6

I am having trouble understanding the reasoning behind the solution in this Irodov General Physics problem. The problem is 1.6: 1.6. A ship moves along the equator to the east with velocity vo = ...
0
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1answer
30 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
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0answers
16 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
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3answers
5k views

Vertical component of moving weight at a 45 degree angle

Here's an easier one. I use the leg press machine at the gym so I don't have to worrying about hurting myself while lifting heavier weight. The weight glides on a track that looks to be 45 degrees. ...
0
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0answers
16 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
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1answer
30 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 ...
0
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3answers
196 views

Confused about the direction of friction force

I'm really confused about the direction of friction force. I think about collision of two balls and think that "friction force is opposite to the relative speed of the contact point of the two ...
1
vote
1answer
35 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 ...
24
votes
6answers
63k views

What is the physical significance of dot & cross product of vectors? Why is division not defined for vectors?

I get the physical significance of vector addition & subtraction. But I don't understand what do dot & cross products mean? More specifically, why is it that dot product of vectors ...
1
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2answers
1k views

What is the physical meaning of a dot product and a cross product of vectors? [duplicate]

My teacher told me that Vectors are quantities that behave like Displacements. Seen this way, the triangle law of vector addition simply means that to reach point C from point A, going from A to B ...
1
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2answers
61 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 ...
3
votes
3answers
159 views

Geometric definition of the Lorentz inner product

In Euclidean space one can define the dot product as projecting one vector to the other and multiply the length of the projected vector with the length of the other vector. This definition doesn't ...
3
votes
2answers
95 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, ...
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1answer
56 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?
2
votes
1answer
101 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 ...
1
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2answers
48 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 $F_R:=\Vert \mathbf{F_R}\Vert$. ...
2
votes
3answers
90 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 ...
0
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1answer
43 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 ...
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 ...
0
votes
2answers
105 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
44 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
2k views

Difference between Speed and Velocity

What is the difference between Speed, Velocity and Acceleration? Could any one describe it pictorially?. I am more over confused even after investigating many times. I am unable to relate myself ...
1
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1answer
49 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 ...
0
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3answers
243 views

Animating an Acceleration Vector - Acceleration of object on a crested path in gravitational field

So I was reading in Chapter 3 of my textbook, Sears & Zemanksky's University Physics with Modern Physics by Young and Freedman, 13th Edition, and the discussion took us to a definition of the ...
2
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7answers
393 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 ...
0
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3answers
321 views

A force's magnitude

In this question I asked about gravity and in the answers it came up that the magnitude is equal (of the gravity acting on the Sun and the of the gravity acting on the Earth) Does magnitude simply ...
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0answers
29 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?