Geometric object with magnitude (length) and direction.

learn more… | top users | synonyms

0
votes
0answers
35 views

Why does the angular average of the divergence result in a factor 1/3?

In going from eq.(6.13) to (6.14) in http://www.nano.northwestern.edu/intranet/pubdocs/quasiclassical.pdf it is assumed that $$\displaystyle\int\dfrac{d\Omega_{\vec{p}}}{4\pi}\,(\hat{p}\cdot\hat{p})\...
1
vote
1answer
76 views

Understanding elastic collisions of objects with the same velocities

I am having trouble understanding the following statement from my book: The law of cosines tells us that if the sides of a triangle obey the Pythagorean formula, they must form a right triangle. ...
0
votes
2answers
119 views

When does angular position, or angular displacement, not obey the rules of vector addition?

The only examples I've found talk about rotating an object about one axis and then about another axis. When you reverse the order, the object ends up in a different position. However, as those ...
2
votes
1answer
154 views

What's the difference between classical and quantum vector superposition?

$(1)$Since quantum-mechanical states between two consecutive measurements are represented as superposition of orthonormal basis vectors in a vector space, at first glance it seems like it makes sense ...
1
vote
1answer
28 views

Is it possible to determine when an accelerometer is in a vibrating state compared to a non-vibrating state?

I would like to know if so, how raw 3-axis accelerometer data could be analyzed and manipulated real-time to register periods of vibration. The device being used has a max sample rate of 62Hz (I ...
1
vote
1answer
38 views

Homework help: Finding the min speed for the normal to be zero [closed]

PROBLEM: The pipe AB of length L is moving at a constant speed $v$. Find the min speed that is needed so that point $B$'s normal force is zero $N_B = 0$ The solution starts with: $\bf{a}$$_b = \...
1
vote
0answers
42 views

Why is the angular average of the direction of the momentum squared a third instead of one?

In the article http://www.nano.northwestern.edu/intranet/pubdocs/quasiclassical.pdf (in going from eq. (6.13) to eq. (6.14)) it is stated that $$\langle\hat{p}\cdot\hat{p}\rangle_{\hat{p}}=\dfrac{1}{3}...
2
votes
3answers
303 views

Why are triangles drawn like so when working with gravity on an inclined plane?

This is my first year as a physics student, and I've never learned about vectors past a basic level, so this is confusing me. When we have gravity on an inclined plane, we separate it into two ...
-2
votes
1answer
36 views

Using resultant vectors to calculate how long it takes to travel a distance [closed]

A box of books weighing $320 \;\mathrm{N}$ is shoved across the floor of an apartment by a force of $569 \;\mathrm{N}$ exerted downward at an angle of $36.5^\circ$ below the horizontal. The ...
4
votes
4answers
210 views

Do $\vec r$ and $d \vec r$ have the same direction?

One question is bugging me for a long time but I couldn't make out anything nor could my friends. Here it goes: We know, $\vec r$ is regarded as the position vector. So we can say, $$\vec r \cdot\vec ...
1
vote
1answer
84 views

When to use a whole vector approach vs an energy approach?

My professor has just introduced two new ways to solve projectile motions. One approach involve using trigonometry and vectors and the other involves using the idea of conservation of energy. My ...
0
votes
1answer
60 views

Why the point right below the center of a rolling ball on the ball has zero instantaneous velocity [duplicate]

Suppose there is a snooker ball rolling on a table. The velocity of the center of the ball is Rω and its direction is horizontally right. I don't understand why the point right below the center on the ...
0
votes
3answers
103 views

Confusion in distinguishing between scalars and vectors

Torque is an example of cross product of two vectors. But in that example length of the spanner is taken as one vector. But length ,distances are all scalars. How can we take it as vector ,it has no ...
0
votes
1answer
53 views

What is the change in velocity? [closed]

A boat moves with a velocity of 22 m/s directly west. Later, the boat is found to have a velocity of 12 m/s at 45° S of W. What is the change of velocity? I want to do this vector wise. I know that ...
0
votes
0answers
26 views

Pressure as a scalar? [duplicate]

Why do treat pressure as a scalar? We know that $P=F/A$ (Pressure = Force/Area) and force is vector quantity, so then why should pressure not be a vector?
-1
votes
1answer
59 views

Value of $g$ in projectile problems

A cannon has a muzzle speed velocity Vo of 60.0m/s, at what angle theta should it be aimed to strike a distance 320 meters away. Ignore air resistance So I get how to set this up but I am confused ...
1
vote
0answers
290 views

Can you explain what's meant by “Effective Force” here?

A small cart is being pulled horizontally to the right with a $20$ lb force $\vec{F}$ making $45^\circ$ angle to the floor. What is the effective force moving the cart forward? Answer: since $\vec{F} ...
3
votes
3answers
176 views

4-velocities in different frames

We have an observer in an inertial frame $S$ who measures a particle's 4-velocity as $U$. We then have another inertial frame $S'$ with $X'=\Lambda{X}$, where $\Lambda$ is a matrix representing a ...
0
votes
1answer
121 views

Proving the invariance of the inner product

If we define the inner product as ${\textbf{u}\cdot\textbf{v}=g_{ij}u^{i}v^{j}}$, where ${g_{ij}}$ is the metric tensor, ${S}$ and ${T}$ are transformation matrices, ${S}$-for covariant indices and ${...
0
votes
4answers
442 views

Why can scalars have a sign?

I wondered to myself why some scalars have a sign, if they do not have a direction. After all, the plus and minus indicate the direction of the scalar on a one-dimensional axis. So, for example, why ...
2
votes
0answers
35 views

Difference between vacuum and pseudovacuum vector?

What exactly is the difference between the vacuum and pseudovacuum vector? In my case the ground state of a system is the vacuum vector and by letting operators act on that vacuum vector magnons are ...
0
votes
0answers
281 views

Accelerometer Pitch and Roll Calculation

I am developing an application for a device that needs to know its tilt/orientation, specifically, pitch and roll. Roll is positive if the right side of the device is elevated, and pitch is positive ...
0
votes
1answer
57 views

Gradient of dot product [closed]

I am asked to show using indicial notation that $\mathbf{u}\cdot\nabla \mathbf{u}=\nabla\left(\dfrac{\mathbf{u}\cdot\mathbf{u}}{2}\right)-\mathbf{u}\times\nabla\times\mathbf{u}$. I recognize that this ...
0
votes
2answers
175 views

Splitting up a force into horizontal and vertical components?

My Bedford and Fowler textbook (4th edition) has a chapter on numerical solutions. I'm having trouble understanding how the textbook splits up the components of force in the $x$ and $y$ directions to ...
2
votes
1answer
205 views

Differentiation of a vector with respect to a vector

Does differentiation of a vector with respect to a vector make any sense? Even if it makes sense, how does it make any physical meaning? I mean what is the physical interpretation?
-1
votes
2answers
161 views

Very basic question about vector

The vectors $a = (2,-1,-2)$ and $b = (0,-3,4)$ are given. Determine $a$:s parallel and normal vector to $b$. Obviously the parallel vector should be the dot product $a \cdot b$ times the unit vector $...
0
votes
1answer
74 views

Basic Notation Help Needed : Classical Mechanics, Unit Vectors

Can someone help me with some basic notation? Here's a situation where I'm surely missing some trivial piece of the puzzle: Example 1: given $W = \frac{1}{2}cpAv^2$ (air resistance), adding a unit ...
0
votes
0answers
104 views

Using the dipole moment to calculate the electric potential

I have the following defintion of dipole moment given: $$ \vec{p} := \int\vec{r}'\rho(\vec{r}')dV $$ Where $\rho$ is a charge density function and $\vec{r}'$ traces out the body of charge. I am ...
1
vote
2answers
123 views

Transformation of four-velocity in special relativity

I am revising special relativity introducing more matrix form in the equation. Currently I am reading book in which transformation matrix is defined as $${\Lambda= \begin{bmatrix} \gamma & -v\...
0
votes
1answer
75 views

When will the velocity of a particle be perpendicular to it's initial velocity?

I am learning kinematics with vector analysis. I was given the position equation:$\mathbf{r} = 10t\hat{\mathtt{i}} + (20t-5t^2)\hat{\mathtt{j}}$. It asks me the time when the velocity of the particle ...
0
votes
1answer
309 views

Derivation of vector cross product [duplicate]

Everyone of us know about the vector cross product. But I wonder, how the formula of $AB\sin\theta$ has been derived? Can anyone help?
0
votes
1answer
17 views

Clarification needed:Projection Or Whole Length to be considered during integration

Sometimes in magnetism,electrostatics,friction problems when a force is acting over a curved we usually take the net projection of the curved path as the distance(to avoid integration).But it certain ...
3
votes
3answers
172 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 ...
0
votes
2answers
151 views

What should the brake force in this problem be? [closed]

Alright so I think I know how to do this but I require help in calculating what acceleration would be in terms of some sort of friction coefficient. So model a particle going down a hill. The slope ...
0
votes
2answers
73 views

Distance traveled from displacement

I am currently reading a book called Physics for Scientists and Engineers by Serway. While reading the chapter about 2-dimensional kinematics, I asked myself a ...
13
votes
5answers
950 views

What does it mean for a physical quantity if its mixed second partial derivatives are not equal?

This goes for every problem (either in electromagnetism or fluid dynamics) that has to do with vector fields. Say we have a fluid flowing in a closed circular pipe (or an electromagnetic field, the ...
2
votes
2answers
208 views

What coordinate systems allows the magnitude of the basis vectors to change with position?

I'm familiar with coordinate systems where the direction of the basis vectors changes with position, but I haven't come across any where the relative magnitude of the basis vectors themselves are ...
0
votes
3answers
113 views

Difference between $|d{\bf r}|$ and $d|{\bf r}|$

What is the difference between $|d{\bf r}|$ and $d|{\bf r}|$ and why are both of them not always equal to each other? My question might seem stupid to some and will probably get downvoted but I have ...
0
votes
2answers
223 views

Is torque still a vector in 2 Dimensions?

In 3D, torque is defined as $\vec{r} \times \vec{F}$ which is a vector, therefore having both a direction perpendicular to the plane of $\vec{F}$ and $\vec{r}$ and a magnitude of $\text{F}\cdot\text{r}...
1
vote
2answers
245 views

Is the displacement vector tangent to the circular path?

My book says that when a mass travels in a curved path, like a circle for example, the instantaneous velocity and displacement vectors are both tangent to the path. I agree that velocity vector is....
4
votes
3answers
4k views

Is there a general rule for determining the direction of tension force?

Tension, for me, is a tricky thing. After finishing a related chapter of my book and watching a video, I still can't get a hang of it. Here is a situation: My knowledge is that tension, just like ...
0
votes
1answer
99 views

How do I get the angle for the $x$ and $y$ component of the electric field for four equidistant particles?

Four particles form a square of edge length $a= 5.00\ cm$ and have charges $q_1= +10\ nC$, $q_2=-20\ nC$, $q_3=20\ nC$, and $q_4=-10\ nC$. In unit vector notation, what is the net electric field the ...
2
votes
1answer
115 views

Coulomb's law with an $r^3$, not $r^2$, in the denominator [duplicate]

I am reading an older physics book that my professor gave me. It is going over Coulomb's law and Gauss' theorem. However, the book gives both equations with an $r^3$, not $r^2$, in the denominator. ...
0
votes
1answer
39 views

Co-ordinate rotations

I need help transforming a magnetic field vector from one co-ordinate system to another. I have the components of the Earth's magnetic field in a co-ordinate system with z facing radially into the ...
5
votes
2answers
343 views

How does one write Newtons 2nd Law using the language of forms?

Newton's second law says that $F=ma$. Supposing that the force is conservative and can thus be expressed in terms of a potential $V$ we have that $F=-dV$. We have that $V$, being a function, can ...
1
vote
1answer
35 views

A way to determine if a body accelerates or loses speed at a certain time

With given vectors for acceleration and velocity, is there a way to determine if a body accelerates or decelerates at a certain time-interval? Can this be determined, for instance, by simply observing ...
0
votes
1answer
70 views

Explain how $\Delta v_{\perp}=v\Delta\theta$

In The Feynman lectures, under the chapter entitled Vectors, Feynman writes: My two intimately related questions are: 1) What does he mean by the magnitude of velocity? is he talking about the ...
0
votes
0answers
28 views

Does dimensionality determine the net effects of randomly oriented forces on an object?

My question relates to the orthogonality of random vectors in high dimensional space, and the relationship of random vectors as a function of dimensionality. My question can be formulated as a ...
0
votes
1answer
67 views

Why would the norm of these vectors be 1?

Let a Cartesian coordinate system $uOx$ coincides with a vertical plane so that $Ou$ is the horizontal axis and $Ox$ is the axis oriented vertically upwards (see Fig. 1). We are looking for the smooth ...
1
vote
1answer
140 views

Vector product in a 4-dimensional Minkowski spacetime

I'm studying relativity and I lost track of interpretation along the mathematical formalism. What does vector product mean as an event? I mean, how must one interpret the result of the vector product ...