Geometric object with magnitude (length) and direction.
8
votes
5answers
874 views
How is it that angular velocities are vectors, while rotations aren't?
Does anyone have an intuitive explanation of why this is the case?
1
vote
2answers
79 views
Points in Spacetime
Assume there are two points in spacetime $a=(t,x,y,z)$ and $a'=(t',x',y',z')$. Let's say that the first one is in the origin of spacetime i.e. $a=(0,0,0,0)$. The point $a'$ has two possibilities
...
0
votes
1answer
35 views
Calculating vector components from other vectors
I'm busy studying for my Physics exam this evening and I've come across a vector problem that I cant quite solve. Any help would be appreciated!
We are given the following vectors:
...
0
votes
1answer
40 views
Relative Velocity problem
I was solving many problems on relative velocity and observed that when the question asks,
"what is the minimum time taken by the boat/man to cross the river.?"
so the solution says that he ...
6
votes
5answers
189 views
In coordinate-free relativity, how do we define a vector?
Relativity can be developed without coordinates: Laurent 1994 (SR), Winitzski 2007 (GR).
I would normally define a vector by its transformation properties: it's something whose components change ...
4
votes
2answers
78 views
Why distinguish between row and column vectors?
Mathematically, a vector is an element of a vector space. Sometimes, it's just an n-tuple $(a,b,c)$. In physics, one often demands that the tuple has certain transformation properties to be called a ...
1
vote
1answer
107 views
Utilizing maximum acceleration $a$ for displacement $d$ with initial velocity $v_0$ and final velocity $v_1$
Problem
My goal is to move an object from point a to b (displacement $d$) as fast as possible utilizing the maximum available acceleration $a_{max}$, taking into account the initial velocity $v_0$ ...
0
votes
0answers
28 views
Assume the following vectors [closed]
Assume the following vectors:
$a = \frac{1}{\sqrt{2}} [0,1,1]$ and
$b = [1,2,3]$.
(a) Calculate the scalar product c = a c b
(b) Calculate the value of vector d where d = b - ca
(c) What is the ...
4
votes
2answers
111 views
Vector potential
I have difficulty understanding the following vector calculus example. Text can be found here. It is the 5th Q&A -- starting with equation (31.1035).It concerns finding the vector potential of a ...
-1
votes
1answer
54 views
man walking in rain:relative velocity
A man walking in rain at a speed of 3kmph find rain to be falling vertically. When he increases his speed to 6 kmph, he finds rain meeting him at an angle of 45 deg to the vertical. What is the speed ...
2
votes
2answers
303 views
2D - Kinematics - Linkage System using Vector Algebra
I have this question that I dont know how to solve correctly :
My question is, how do I find $V_B$ ? I will find the angular velocities myself, but I want to know the method to get $V_B$ ?
I know ...
0
votes
2answers
52 views
Where to take $\theta$ (theta) in a triangle?
This is an inclined surface having and unit vector A. The perpendicular and horizontal surfaces are the components of the inclined surface. We want to find out that how much flux will pass through ...
1
vote
1answer
27 views
Asking about centrepetal acceleration
please look at the fig first
1) How can you claim that the triangle ABC is same as the triangle PQR?
2) How can you claim that the angle between V1 and V2 is same as the angle between AC and AB?
...
5
votes
1answer
106 views
Vector and Spinor Representation in Ramond-Neveu-Schwarz Superstring Theory
I am learning Ramnond-Neveu-Schwarz Superstring theory (RNS theory). I often find the following notation, especially in the closed string spectrum etc.:
$$\mathbf{8}_s,\mathbf{8}_v $$
And it is ...
1
vote
2answers
66 views
Resolution of vectors
What is the fundamental basis of resolution of vector. Suppose we have a vector $\vec{mg}$, now we resolve it into two components, horizontal and vertical. My question is what is the basis for telling ...
1
vote
1answer
73 views
Hydrostatic pressure at lateral directions
I just read that, with respect to a stationary tiny cube, suspended in a fluid, that has a negligible weight and dimensions:
Pressure is the same in every direction in a fluid at a given depth, ...
4
votes
3answers
235 views
Meaning of the direction of the cross product
I was doing calculations with torque and then I came across something very confusing:
I understand that the magnitude of the torque is given by product of the displacement(from the center of ...
3
votes
2answers
67 views
Sign of acceleration
I'm developing an application using accelerometer sensor. I'm not good at physics so forgive me if the question is trivial. If I have 3 values of acceleration: $x$, $y$, $z$, I find acceleration ...
-1
votes
1answer
1k views
how to calculate the angle in the x-y, y-z, x-z plane given only 3D vector direction and magnitude? [closed]
Please help me solve this. I have been thinking of all sorts of ways to solve this but can't figure out how :(. Ok here's the problem:
I am given a three dimensional velocity vector (i know the ...
-1
votes
1answer
103 views
Vector Addition — Direction
Say we have three forces $F_1, F_2, F_3$, such that
$$
F_1 + F_2 - F_3 = 0\hspace 10mm (1)
$$
And let us say that $F_1$ and $F_2$ have the same direction and magnitude, and that $F_3$ has double the ...
5
votes
6answers
2k views
How is gradient the maximum rate of change of a function?
Recently I read a book which described about gradient. It says
$${\rm d}T~=~ \nabla T \cdot {\rm d}{\bf r},$$
and suddenly they concluded that $\nabla T$ is the maximum rate of change of $f(T)$ ...
1
vote
1answer
29 views
How to add magnitude data in an ENU coordiante system
I have water velocity data taken in an ENU (East, North, UP) or XYZ coordinate system. The data is contained in 3 columns like this:
...
0
votes
1answer
117 views
A very elementary question regarding force of friction
When I first studied friction I faced f = $\mu$ N where f is force of friction, $\mu$ is coefficient of friction for the surface considered and N is the normal force for the body on surface. Now f is ...
0
votes
0answers
45 views
Vector identities equivalence under different coordinates
I've learned to represent curl, rot and Laplacian in the general form using scaling factors, Levi Civita symbol and delta.
I was asked to prove some general identities in vector calculus.
I was ...
10
votes
3answers
325 views
Representing forces as one-forms
First of all, sorry if any of those things are silly or nonsense, I'm just trying to understand better how the concepts of forms, exterior derivative and so on can be used in physics.
This question ...
1
vote
1answer
68 views
rotation matrix - why am I thinking this wrong?
The rotation given in Question 1 part ii) doesn't match with this wikipedia link http://en.wikipedia.org/wiki/Rotation_matrix.
$$ \begin{array}{lcl}
x' &=& x \cos\theta - y \sin\theta \\
y' ...
0
votes
1answer
88 views
Component of force field tangent to a curve
I recently had to solve the following problem:
A force $F=10\hat x- 8\hat y$ is applied to an object that is constrained to travel towards increasing values of x along the path defined by $y=x^2$ ...
1
vote
0answers
75 views
Plane vector problem [closed]
Problem statement
A jet is flying at 600 mi/h in a direction of 450 North of West. 2.5
minutes later it is flying at 450 mi/h in a direction of 300 North of
East.
a) Sketch a vector ...
0
votes
1answer
60 views
Is it necessary to know initial y velocity to solve this projectile motion problem?
A marble is launched horizontally off a 93.0-cm high table causing the marble to land on the floor 1.85 m from the base of the table.
a.) How long was the ball in the air?
b.) With what ...
0
votes
1answer
143 views
Resultant vector problem
$\newcommand{\v}[1]{\vec #1}\newcommand{\i}{\hat i}\newcommand{\j}{\hat j}$
Problem statement (1,2)
A shopper at the supermarket follows the path indicated by vectors $\v A, \v B, \v C, \v D$ in ...
1
vote
2answers
101 views
Rotating a reference system on a vector
Assume you have a vector $\vec{x}=(\sin(\vartheta)\cos(\varphi),\sin(\vartheta)\sin(\varphi),\cos(\vartheta))$ given in spherical coordinates in a reference System "R". I want to rotate the reference ...
0
votes
1answer
77 views
Can the zeroth-component of a 4-velocity be negative?
Is it allowed to have the zeroth-component of a four-velocity be negative? I presume the answer is yes, but I just want to make sure. Many thanks.
This is referring to $V^0$ for a curved space ...
7
votes
6answers
9k 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
votes
2answers
170 views
Simple Vector Problem [closed]
I'm a bit stuck on a homework question that I've been assigned. The question is as follows:
You are paddling a canoe at a speed of 4 km/h directly across a river that flows at 3 km/h. (a) What is ...
0
votes
2answers
63 views
Meaning of juxtaposition of vectors
I came across some notation that I can't quite understand:
$$ \hat{r}\hat{r} - \textbf{1}_3$$
where $\textbf{1}_3$ is the 3$\times$3 identity matrix, $\hat{r}$ is a unit 1$\times$3 vector, and the ...
1
vote
1answer
113 views
Determine the flow and amplitude equation for thermal energy (with Del operator)
It is a question vector calculus and Maxwell's laws. I put it this way. Let's say, we are working in a $3$-Dimensional space ( e.g $x\cdot y\cdot z = 4\cdot3\cdot2$, a certain room/class of that size ...
2
votes
3answers
21k views
Linear acceleration vs angular acceleration equation
I'm learning about angular velocity, momentum, etc. and how all the equations are parallel to linear equations such as velocity or momentum. However, I'm having trouble comparing angular acceleration ...
1
vote
1answer
61 views
How to express answers where inequalities are involved?
Part of the floor of a workshop is inclined at 10 degrees to the horizontal. This is to allow the safe storage of steel cylinders. A cylinder of mass 7000 kg is stored as shown in the diagram (c the ...
0
votes
2answers
771 views
Confused on how to properly use right hand rule
I am having trouble using the right hand rule properly and often find myself putting my hand in awkward orientations. I know you point your hand in the direction of $r$ and then point your fingers in ...
1
vote
3answers
96 views
Mechanics Problem
I'm trying to follow Feynman's lecture. Unfortunately I'm a bit stuck on a small piece, so if you could show me what I'm doing wrong then I'd greatly appreciate your help. I want to exactly know how ...
2
votes
1answer
132 views
Vector transformation in special relativity
Please note that I am very new on this website so have some difficulties in writings as required here but trying really hard to learn quickly. La-Tex is the main problem but please understand me that ...
-1
votes
1answer
77 views
Determine when a light is going into the object [closed]
Please look at this image: (http://mypages.iit.edu/~smart/acadyear/refract.gif)
How can I determine when light is going into the object?
Actually, if there is, what is the simplest way to ...
0
votes
0answers
65 views
Laue diffraction/equations: Path difference, why a minus sign and not a plus?
The Laue diffraction (that reduces to the Bragg refraction in the end) has for the path difference of the incoming and outgoing beam
$$\Delta s = \vec R \cdot ( \vec k_0/k_0 - \vec k^\prime/k^\prime ...
0
votes
2answers
260 views
Vector Nature Of Angular Velocity
I am currently reading about angular position, angular velocity, and angular acceleration. I came across this paragraph that was particularly confusing, and was wondering if someone could perhaps help ...
0
votes
1answer
184 views
Solving inclined plane using diff. frame
I was trying to solve frictionless inclined plane problem using a diff. frame as shown in the figure, and can't figure out that acceleration along the plane = g.sin(Θ), but I think it should be = ...
0
votes
1answer
212 views
A Lawnmower Problem
For my physics class we were just given an exam that asked the following:
A 12Kg lawnmower is pushed with a constant force along the 30* handle with 80N.
Break the Forces into its vector ...
2
votes
3answers
134 views
What is the general approach to calculating time of impact in 3D?
Given two objects a and b moving at fixed velocities, how would you determine (a) whether they will collide at all, and if so, (b) time of impact?
(Let us assume these are spherical bodies each with ...
0
votes
1answer
77 views
Finding The Obtuse Angle [closed]
I am working on a simple force problem involving inclines. I found a reference of $48^\circ$, in the third quadrant; now, to find the obtuse angle, do I subtract that value from $270^\circ$, or do I ...
-1
votes
1answer
178 views
How to properly find equilibrium vectors when 3 or 4 vectors are present? [closed]
I'm having trouble regarding how to find the equilibrium of vectors. We were given tables with given information and had to fill them in; I'm fairly sure my initial attempts were incorrect.
first ...
1
vote
2answers
154 views
Conservation of Linear Momentum with respect to a given direction
Is linear momentum conserved in any direction? More specifically, if you project all momentum vectors in a system onto another vector, will momentum be conserved?
I know that momentum is conserved ...
