Geometric object with magnitude (length) and direction.

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7
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2answers
272 views

Can we show that time is orthogonal to space?

It's easy to show that the time we measure is "in a different direction" from the space directions we measure. However, it's not immediately obvious to me that these directions are orthogonal. How do ...
0
votes
1answer
210 views

Vector Maths to Simulate Car Physics [closed]

I'm working on a 3D program that involves controlling a Cube on-screen (which represents a car). I use C++, OpenGL and GLM (for vector and matrices etc, if you're familiar with programming; Once the ...
1
vote
2answers
245 views

Angular position vector?

I'm a mathematician, so I like my angular velocities to be vectors. It makes my angular momenta and torques vectors as well, and so they have nice operations I can do on them. Because of that, I pick ...
0
votes
0answers
55 views

How to interpret the factor $\frac{(\vec v\cdot \hat n)}{|\vec v| 4\pi r}$?

There is a small area element of size $da$ and normal vector $\hat n$. I understand that the particles with speed $|\vec v|$ that hit this area element in the time interval $(t,t+\delta t)$ lie in a ...
1
vote
3answers
6k views

Vertical and horizontal components of forces and vectors

I'm getting a bit confused when finding components of vectors and forces. In problems for vectors, I've always known that if you want to get the components of a vector, you would use the following: ...
1
vote
2answers
649 views

I don't understand the idea of perpendicular vectors being independent of each other?

So problem 71-75 is about vectors. The problem says: A river has a current flowing with a velocity of 2.0 meters per second due east. A boat is 75 meters from the north riverbank. It travels at ...
-3
votes
1answer
107 views

Vector analysis query [closed]

I cannot understand how and why those two expressions are coming (the ones I have highlighted). Please explain.
0
votes
3answers
683 views

Basic vector addition problem [closed]

This is the entire problem: A student adds two vectors with magnitudes of 200 and 40. Taking into account significant figures, which is the only possible choice for the magnitude of the resultant? ...
1
vote
3answers
9k views

Why work is a scalar and not a vector?

Work (in physics) is a scalar but why? and why not a vector?
1
vote
2answers
1k views

How to find the resultant of two forces? [closed]

I got this question in a assignment and haven't been able to figure out how to get to the correct result. A force of 6 newtons and a force of 10 newtons can be combine to form a resultant of ...
3
votes
2answers
3k views

Resultant of two forces acting in the same line

I'm quoting the definition of Resultant of two forces acting in the same line from the book "A FIRST COURSE IN PHYSICS" one of whose authors is Robert Andrews Millikan: The resultant of two forces ...
0
votes
1answer
86 views

Vector Summation [closed]

When two vectors are sketched from a single point, the angle between them is θ. Show that the size of their vector summation is given in the expression: $ \sqrt{A^2 + B^2 +2ABcosθ} $. Any ...
-1
votes
2answers
130 views

Vectors question? [closed]

I am stuck on this vectors question I have for home work. Does anything think they can help point me in the right direction on how to solve this? An explorer is caught in a whiteout (in which the ...
1
vote
2answers
274 views

Angle needed for object A to intercept with object B

Object B is 15 degrees East of North at a distance of 20km/h. Object B is moving at an average speed of 30km/h in the direction 40 degrees East of North. If object A is capable of moving at 100km/h, ...
2
votes
2answers
4k views

Derive vector gradient in spherical coordinates from first principles

Trying to understand where the $\frac{1}{r sin(\theta)}$ and $1/r$ bits come in the definition of gradient. I've derived the spherical unit vectors but now I don't understand how to transform ...
2
votes
2answers
126 views

How to determine which one would not be the resultant?

i had a physics exam yesterday, which was all in all pretty good except for this one question which i just don't get.: ...
1
vote
0answers
92 views

Understanding unit vectors

Trying to understand how the unit vector ${\mathcal{\hat{r}}}$ defined as $\frac{r' - r}{|r' - r|} $ (where $r'$ is the source point) works in this problem: Work out the electric field, $E$, at point ...
1
vote
1answer
90 views

Commutation of abstract $O(3)$ generators and vectors

I've been given the following problem, and I'm quite lost with it. Let $L_1$, $L_2$, and $L_3$ denote the abstract o(3) algebras. You are given that $\vec{A} = (A_1, A_2, A_3)$ and $\vec{B} = (B_1, ...
0
votes
1answer
70 views

Vector Isolation/ Rotation

I have a series of vectors (current speeds) based on an ENU (East North Up) system. I would like to estimate the current speed of the water headed in a specific direction. In this example I am ...
2
votes
1answer
178 views

Equivalent definitions of vectors

Equivalent definitions of vectors. In maths a vector is an object that obeys some axioms of a vector space. But in physics a vector can be thought as an object which is invariant under rotations of ...
2
votes
2answers
233 views

About vector form of friction

I read a text on mechanics and in the chapter on friction, there written that the kinetic friction is in the form $$f_k = \mu_k F_N$$ where $f_k$ is the kinetic friction, $\mu_k$ is the kinetic ...
2
votes
1answer
3k views

How do I split a vector into components parallel and perpendicular to a known line?

Given $\mathbf{F}=\langle 7.20,−12.0,28.2\rangle\text{ Newtons}$, find the component of $\mathbf{F}$ that acts perpendicular to member DA such that the vector addition of the perpendicular and ...
2
votes
2answers
336 views

Why do smaller objects become harder to break?

When grabbing a typical tree branch of at least two feet, it's so easy to snap with a less than one inch circumference that even a toddler can do it. However, after breaking it, the smaller halves ...
0
votes
1answer
273 views

Rotating point in 3D space by Unknown rotation vector [closed]

I have a random point defined by: int x = rand.nextInt(9)-4;//-4 to +4 int y = rand.nextInt(4)+2;//+2 to +5 int z = rand.nextInt(9)-4;//-4 to +4 Y happens to be ...
0
votes
3answers
793 views

How to determine direction of forces in a static problem?

I am consistently getting this wrong. To me, in the picture below, it would make sense that the structure would be pulling downward, and the cable BD would be pulling upward - thus the system is in ...
1
vote
1answer
203 views

Spinor formalism in QFT

We can describe fields by two formalisms: vector and spinor. This is the result of possibility of representation of the Lorentz's group irreducible rep as straight cross product of two $SU(2)$ or two ...
0
votes
1answer
2k views

Find angle of force vector in equilibrium

So my question is Rope BCA passes through a pulley at point C and supports a crate at point A. Rope segment CD supports the pulley and is attached to an eye anchor embedded in a wall. Rope segment ...
3
votes
2answers
1k views

Finding force vectors

A tugboat tows a ship at a constant velocity. The tow harness consists of a single tow cable attached to the tugboat at point $A$ that splits at point $B$ and attaches to the ship at points $C$ and ...
0
votes
1answer
193 views

Why Counterclockwise starts from East?

In vector lessons, we have counterclockwise angle of rotation of the vector starts from East. "The direction of a vector is often expressed as a counterclockwise angle of rotation of the vector about ...
0
votes
1answer
68 views

Asking the vector form of the equation about velocity

In the undergraduate text of physics, the equation for velocity and displacement at constant acceleration are given in scalar form. For example, my text reads $$v^2 = v_0^2 + 2a(x-x_0)$$ But today, ...
3
votes
3answers
591 views

How do I meaningfully divide by a vector?

How long does it take a baseball with velocity $(30, 20, 25) m/s$ to travel from location $r_1 = (3, 7,−9) m$ to location $r_2 = (18, 17, 3.5)m$? I am thinking that it should be the ...
0
votes
1answer
78 views

Combine forces (gravity)

I have a point at which there are (at least) two different forces (gravity to be precise) working. How do I combine those so that the force acting on the point are as realistic as possible? To put ...
2
votes
5answers
200 views

How does this shell hit the aircraft?

A fighter aircraft is flying horizontally at an altitude of 1500m with speed of 200m/s. The aircraft passes directly overhead an anti-aircraft gun. The muzzle speed of the gun is 600m/s. ...
0
votes
2answers
394 views

Why do we say that in Coulomb's law the force is proportional to $\frac{1}{r^{2}}$ and not $\frac{1}{r^{3}}$?

I am going over Coulomb's law and there is something that is a bit confusing for me: According to Coulomb's law, if I have a charge $q_{1}$ at a point $\vec{r_{1}}$ and a charge $q_{2}$ at a point ...
0
votes
1answer
163 views

Equations of circular motion

I have studied that a finite angular displacement $\triangle \theta$ is a scalar. But, $\delta \vec \theta$ is a vector. Now, when it is a uniformly accelerated motion we are dealing with, we use ...
1
vote
1answer
121 views

Interchaning a position between two reference frames?

$\vec{r}_a$ is a positional vector from reference frame $a$. What is the position of same point from reference frame $b$ ? If required, assume position of origin of frame $a$ is $\vec{m}$ and ...
1
vote
4answers
496 views

Vectors with more than 3 components

I have some confusion over Vectors, Its components and dimensions. Does the number of vector components mean that a vector is in that many dimensions? For e.g. $A$ vector with 4 components has 4 ...
0
votes
2answers
106 views

Position vector, length/modulus function and differentials

If $\vec r$ and is the position vector of a point in motion and $r$ is its length/modulus/magnitude/size, then: Can it be true that: $$\|\mbox{d} \vec r\| \neq \mbox{d}r? $$ I think that this is ...
-3
votes
2answers
177 views

Vector Components and Resultant [closed]

My sister got this homework that she don't understand, me neither. Can anyone help out? Here's the problem: Give the x-component and y component of the following vectors: a. A = 7.0 cm, E b. B = ...
1
vote
2answers
983 views

Electromagnetic wave propagation through two lossless dielectrics

In Elements of Electromagnetics (Sadiku, 3rd edition, Section 10.8), the author says to consider two lossless dielectric materials joined at an interface $z=0$. Here two lossless dielectric materials ...
0
votes
2answers
112 views

Applying the right-hand rule for magnetic forces

I am confused about the right-hand rule for the Lorentz force. I am using same method as Brightstorm.com is: http://www.youtube.com/watch?v=LK7hv4LX3ys But for some reason it does not match op with ...
-4
votes
2answers
336 views

Force and Vector question [closed]

A force of 6 Newton and another 8 newton can be applied together to produce the effect of a single force of a) 1 N b) 11 N c) 15 N d) 20 N. More generally, if I know the magnitude of one force, ...
0
votes
1answer
447 views

Calculate vector forces on object being affected by wind

I am wondering how you calculate the vector forces of the wind on an object? The information I have is the bearing direction of the wind and the speed of the wind. So how do I calculate the x and y ...
0
votes
2answers
56 views

Is it incorrect to explain the direction of a coded vector quantity?

For example, let's say that in a linear physics problem, all the data are given to a certain direction, and coded positively for direction to the right. So +5m/s would be a velocity of 5m/s to the ...
-2
votes
2answers
263 views

Vector plus vector equals scalar ? (Nabla operator)

A quick question that is currently bothering me. I have the following equation: $\mathbf{E}+\frac{\partial \mathbf{A}}{\partial t} = -\nabla V$ My question is, how can the right side, being a ...
1
vote
1answer
244 views

Navier-Stokes equations: conservation of momentum

The first Navier-Stokes equation (conservation of mass) says: $\vec \nabla \cdot \vec v=0$ For a stationary flow, the l.h.s of the second equation is (conservation of momentum): $\rho \frac{D\vec ...
5
votes
2answers
379 views

Is length/distance a vector?

I have heard that area is a vector quantity in 3 dimensions, e.g. this Phys.SE post, what about the length/distance? Since area is the product of two lengths, does this mean that length is also a ...
1
vote
5answers
877 views

What is the direction of a point vector. A vector with magnitude 0? [closed]

A simple question : Can a point on a piece of paper represent a vector ? Can i say that a point "B" ( magnitude =0, because it's a point) , is having direction towards +x axis ? Thanks
1
vote
1answer
391 views

Induced voltage of a conductor in a magnetic field

A book which I referenced for Electrical Machinery states that the voltage induced in a conductor inside a magnetic field is given by $$ \mathcal{E}=(\mathbf{v} \times \mathbf{B})\cdot \mathbf{l}$$ ...
0
votes
1answer
259 views

Vectors on Different Coordinate Systems? [closed]

Consider the product of vectors coordinated relative to a given coordinate frame, defined by $$\vec{a}\square\vec{b}=((a_{1},b_{1})\square(a_{2},b_{2})):=(a_{1}b_{1},a_{2}b_{2})$$ Explain why ...