Geometric object with magnitude (length) and direction.

learn more… | top users | synonyms

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 ...
1
vote
2answers
65 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 ...
2
votes
3answers
45 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
111 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
97 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
58 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
57 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 $F_R:=\Vert \mathbf{F_R}\Vert$. ...
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 ...
2
votes
3answers
94 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
189 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
45 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
52 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
401 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
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?
1
vote
2answers
94 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
53 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
60 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
47 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 ...
0
votes
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 ...
0
votes
1answer
60 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
73 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
107 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
34 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
31 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, $ ...
0
votes
1answer
85 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
49 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
55 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 ...
0
votes
2answers
99 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 ...
0
votes
2answers
48 views

How do you tell whether a force acting on an inclined plane is going up or down in its perpendicular component to the plane?

I'm practicing mechanics, and I had to resolve the following forces perpendicularly to the inclined plane in order to work out the reaction force (plus the weight of the ball) But I cannot tell ...
0
votes
1answer
66 views

Why does vector addition work in physics? [closed]

How do we know for sure that vector addition works while working in 2D?Is there a mathematical proof for this?
0
votes
3answers
79 views

$F\cos\theta$ is not proportional to $d\cos\theta$?

If Iā€™m working in two dimensions and I wanted to calculate the net electrostatic force on charge C, where charges A and B are stationary, of the same charge, and placed on the y-axis equidistant ...
-1
votes
1answer
53 views

Find the indicated quantities from the given data [closed]

This is a vector application. A rope is hung at both ends from a horizontal beam, and a weight m is suspended from it as shown in the figure. The left part of the rope exerts a force G at P, while ...
0
votes
2answers
100 views

Definition of Position Vectors

I have a few (possibly very stupid) questions relating to position vectors; more specifically my confusion about them. Following Halliday and Resnick's text, we define vectors by their magnitude and ...
0
votes
0answers
40 views

vector addition and subtraction

. Vector A has a magnitude of 20 m and makes an angle of 30āˆ˜ above the positive x axis. Vector B has a magnitude of 12 m and is oriented 60āˆ˜ to the left of the y axis.? Part 1: Find the magnitude ...
0
votes
2answers
68 views

The Vectors in $v=f\lambda$

We are learning about waves in physics and I was just wondering what are the vectors and what are the scalars in this function:$$v=f\lambda$$ I know the velocity $v$ is a vector so that means that: ...
1
vote
2answers
27 views

Why use vectors to describe velocity/force/etc instead of treating magnitude and direction as separate values?

I'm only 4 weeks into my first college-level physics course, so this is a very elementary question. Also, in asking this question, I'm just playing devil's advocate in order to better understand the ...
0
votes
1answer
54 views

Find the magnitude of the resultant force which these engines exert on the rocket?

A rocket fires two engines simultaneously. One produces a thrust of 760N directly forward while the other gives a thrust of 484N at an angle 34.0 degrees above the forward direction. What is the ...
-1
votes
1answer
52 views

Vectors finding direction include the difference between “north of east” and “east of north”

In what direction is your friend from the starting point after skiing 3 km east and then 1.5 km north? so far I know that angle= tan-1(opp/adj)=(1.5/3.0) angle= ...
10
votes
4answers
321 views

Basis independence in Quantum Mechanics

The idea that the state of a system does not depend on the basis that we choose to represent it in, has always puzzled me. Physically I can imagine that the basis ought to just yield an equivalent ...
0
votes
1answer
63 views

Path of a swinging object on a rope [closed]

With my lanyard in hand (weighted by my keys), a gentle swinging motion will put the keys in pendulum motion, swinging back and forth. Pendulum motion is relatively easy to model since it is ...
2
votes
2answers
114 views

Can an angle be defined as a vector?

In Classical Mechanics angular velocity, angular acceleration, torque and angular momentum can be defined as vectors with clear advantages such as the possibility to use vector product to simplify ...
-1
votes
1answer
63 views

Finding angle between two displacements [closed]

Consider two displacements, one of magnitude 6 m and another of magnitude 8 m. What angle between the directions of this two displacements give a resultant displacement of magnitude (a) 14 m, (b) 2 m, ...
0
votes
4answers
86 views

When writing a differential equation, when do you take $+\text{d}x$ and when do you take $-\text{d}x$?

When writing a differential equation I'm confused as to when to write $+\text{d}x$ a and when to write $-\text{d}x$ a where $x$ represents some quantity. For example, I wanted to derive the equation ...
0
votes
0answers
57 views

What is the meaning of “closure is lost” for a set of kets (or any members of a vector space)?

This is the closure relation in Quantum Mechanics: $$\sum_i |i\rangle \langle i| = 1 $$ which I understand as "the sum of the projections onto the basis vectors leaves the projected vector ...
0
votes
2answers
48 views

How to find tangential and normal unit vector to a trajectory from the equation? [duplicate]

Considering a 2D motion in a plane and the equation of the trajectory of a point $y=f(x)$, I don't understand how exactly $\frac{\mathrm{d}y}{\mathrm{d}x}$ can be used. In particular if I'm looking ...
0
votes
0answers
14 views

Relations between unit vectors in polar and curvilinear coordinates

I'm a bit confused about the relations between unit vectors in curvilinear and polar coordinates in a plane. Let $u_{R}$ be the radial unit vector in polar coordinates and $u_{N}$ the normal unit ...
-4
votes
1answer
38 views

what is the work done if force F= 3xyi-y^2 moves a particle in the xy plane from (0,0) to(1,2) along the parabola y=2x^2? [closed]

I know that work W=F.dl. But how can i apply this in above question? HOW CAN I FIND dl from the above question?
-2
votes
1answer
81 views

Dot product and divergence [closed]

Divergence is represented by dot product. How is the divergence related to dot product? And curl is represented by cross product. How is the curl related to cross product?
1
vote
2answers
58 views

Time dependent ODE involving cross product

Let $\vec{A}$ be any time dependent vector quantity, and $\vec{\alpha}$ any constant vector. I was told that a solution to the differential equation $$ \dot{\vec{A}} = \vec{\alpha}\times\vec{A} $$ is ...
1
vote
3answers
103 views

How to apply a force vector to a position vector?

A particle is present in the two dimensional space. It's position is given by the vector: $$x = \begin{pmatrix} |x| \cos(\theta) \\ |x| \sin(\theta) \end{pmatrix}$$ It experiences a force of: $$ F = ...