Geometric object with magnitude (length) and direction.

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1answer
87 views

Newton Mechanics [closed]

I am confused about this question, what does it mean? A particle has a mass of $2\ \mathrm{kg}$ and a force $$F = 24t^2 i + ( 36t - 6 ) j - 12tk$$ acting on it. At the time $t = 0$ the particle is at ...
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0answers
30 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 ...
1
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1answer
58 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. ...
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2answers
77 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
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1answer
86 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
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1answer
24 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
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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 = ...
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1answer
46 views

Deriving Konopinski's Operational Definitions of Scalar and Vector Potential

In "What the electromagnetic vector potential describes", E. J. Konopinski asserts: Operational definitions of Φ, A should now be expected to stem from the equation of motion (2) when it is ...
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0answers
41 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 ...
2
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3answers
286 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 ...
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1answer
29 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 ...
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4answers
183 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
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1answer
66 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
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1answer
49 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
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3answers
85 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
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1answer
42 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 ...
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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?
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1answer
54 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 ...
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0answers
68 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
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3answers
149 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
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1answer
63 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 ...
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4answers
227 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
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0answers
33 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 ...
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0answers
133 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
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1answer
48 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 ...
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2answers
112 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
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1answer
174 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?
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2answers
122 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 ...
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1answer
66 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 ...
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0answers
78 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 ...
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2answers
112 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 & ...
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1answer
65 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 ...
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1answer
145 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
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1answer
16 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 ...
2
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2answers
97 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
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2answers
96 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 ...
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2answers
67 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
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5answers
832 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
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2answers
137 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
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3answers
110 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 ...
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2answers
149 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 ...
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2answers
141 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 ...
1
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3answers
790 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
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1answer
65 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
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1answer
80 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
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1answer
32 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
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2answers
337 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 ...
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1answer
33 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
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1answer
63 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 ...
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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 ...