Geometric object with magnitude (length) and direction.

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1answer
56 views

Gradient of two-particle system

I'm working on problem 5.1a from Griffiths Intro to QM and given that: $$\mathbf R \equiv \frac{m_1\mathbf{r_1} + m_2 \bf r_2}{m_1+m_2}$$ and $\bf r \equiv \bf r_1 - \bf r_2$ I need to show that, ...
1
vote
1answer
26 views

Computing the Initial Velocity of an orbiting body

I'm working on a simulation program that replicates the movement of planets around a large celestial body (the sun). This is a three dimensional simulation that uses vectors. At present, I'm ...
2
votes
3answers
72 views

What is “a vector of $SO(n)$”?

I'm watching (or trying to watch) this lecture from NPTEL on classical field theory. I've understood everything in the series up till this point, including the first half of the lecture on elementary ...
3
votes
2answers
90 views

Why scalar function of vector can only depend on norm of vector?

In Field Quantization by Greiner and Reinhardt as well as The Qunatum Theory of Fields by Weinberg, concerning the spectral function, the authors say a scalar function of the four-vector $p^\mu$ can ...
3
votes
2answers
140 views

Importance of Kronecker product in quantum computation

To get product state of two states $|\phi \rangle$ and $|\psi \rangle$, we use Kronecker product $|\phi \rangle \otimes |\psi \rangle$. Instead of Kronecker product $\otimes$, can we use Cartesian ...
1
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0answers
40 views

Suspended mass in motion free-body diagram [closed]

A 20kg mass is held by two ropes which span 90 from each other. The mass is being accelerated at 1m/s^2 to the right. Draw a free body diagram for the mass and find the numerical values for each ...
0
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2answers
65 views

Why does $\hat n \times (\vec E_1 - \vec E_2) =0 $ imply that the tangential electric field components are equal?

On page 8: http://local.eleceng.uct.ac.za/courses/EEE3055F/lecture_notes/2011_old/eee3055f_Ch4_2up.pdfele I don't understand why $E_{t1} = E_{t2}$ is equivalent to $\hat n \times (\vec E_1 - \vec ...
3
votes
2answers
145 views

The force of gravity is $F_g=+mg$ or $F_g=-mg$?

I have noticed that in my classical mechanics course and in the textbook I read for it, seem to ignore the gravitational force's position. For example, if we were dealing with a system with a ball of ...
1
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1answer
19 views

Laboratory fixed-vector components

What are laboratory fixed-vector components? I have an effective Hamiltonian derived from a 40-something year-old Chemical Physics paper. The article mentions the term laboratory fixed-vector ...
0
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0answers
52 views

Question on using Transport Theorem to Determine Angular Acceleration of a Rotating Frame

My question is regarding using the "Transport Theorem" on the angular-velocity vector of a rotating frame itself. Suppose: Frame-F has basis vectors I, J, K. Frame B is rotating with respect to F ...
0
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3answers
181 views

Force vs. impulse: what is the math description of their interaction?

In this image there are two forces acting on the same body, and we can decribe them mathematically and geometrically using vectors and the palallelogram rule. NOw, suppose the box (stone, ...
11
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4answers
420 views

Is partial derivative a vector or dual vector?

The textbook(Introduction to the Classical Theory of Particles and Fields, by Boris Kosyakov) defines a hypersurface by $$F(x)~=~c,$$ where $F\in C^\infty[\mathbb M_4,\mathbb R]$. Differentiating ...
2
votes
2answers
107 views

How do you pronounce $\vec{A} \cdot \vec{B}$ and $\vec{A} \times \vec{B}$? [closed]

I'm French. I would like to know: How do you pronounce $\vec{A} \cdot \vec{B}$ : "A scalar B" or "A dot B" ? How do you pronounce $\vec{A} \times \vec{B}$ : "A vectorial B", "A vector B", "A cross ...
2
votes
3answers
140 views

Calculating vector to aim for moving asteroid (3D asteroid game)

Considering we're in a 3D system of coordinates: our ship is at point A, motionless our ship can shoot bullets, the speed of which is known the asteroid is at point B the asteroid is moving on known ...
1
vote
5answers
641 views

How to find total force on an object?

If there are a multitude of forces acting on an object in different directions, how do we find the TOTAL force? I know we add up the $ x $- and $ y $-components of the forces individually, but how do ...
0
votes
1answer
27 views

Finding voltage between two points in space

If electric field vector is defines as : $\vec{E} = \frac{V_0x^2}{a^3} \vec{i_x} + \frac{V_0y}{a^2} \vec{i_y} $ where $V_0 $ and $a$ are known constants, $\vec{i_x}$ and $\vec{i_y}$ unit vectors of ...
1
vote
1answer
50 views

What does it mean by $t=-1$?

if the position vector of a particle is $\hat{r}=\left(4+3t\right)\hat{\imath}+\left(t^3\right)\hat{\jmath}+\left(-5t\right)\hat{k}$, i want to find at what time this particle passes through the point ...
1
vote
1answer
106 views

How to show that the force and velocity are perpendicular and that both have constant magnitude? [closed]

The force acting on a moving charged particle in a magnetic field $\hat{B}$ is $\hat{F}=q\left(\hat{v}\times \hat{B}\right)$ where $q$ is the electric charge of the particle, and $\hat{v}$ is its ...
0
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0answers
52 views

Interpretation of angular momentum in semi-classical vector model

My Professor said that when we calculate the total angular momentum of multiparticles, in this case i.e. 2 particles, we can add total angular momentum by thinking this way, if both spins allign they ...
3
votes
1answer
178 views

Rolling a ball into a cone; what should the forces overall be?

This is my solution to finding angular displacement/velocity/acceleration on cone so far. Consider a cone, with an apex of half-angle $\psi$ pointing down, and a height of $h$. If I roll a ball into ...
0
votes
3answers
128 views

Finding the Direction when resolving a Vector

When you are finding the resultant of a vector I understand that to find the magnitude you use Pythagorean Theorem and I understand that to find the direction you are going to use $\tan^{-1}$ (or ...
0
votes
1answer
102 views

What does “projection of a vector” really mean?

Let $\vec{a}$ & $\vec{b}$ be two non-collinear, non-zero co-initial vectors having angle $\theta$ between them. The projection of $\vec{b}$ on $\vec{a}$ is given by the dot product of $\vec{b}$ ...
1
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2answers
115 views

Why is force a localized vector and not a free vector?

A vector which is drawn parallel to a given vector through a specified point unlike free vector in space is called a localised vector. The effect of a force acting on a body depends not only on the ...
0
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2answers
74 views

Orientation of a rocket going in a circle?

This problem is from my physics homework: A rocket is moving at constant speed in a perfect circle in deep space, far away from any planets or stars. The diagram below shows the circle the ship ...
6
votes
4answers
438 views

In which direction does a wall exert the reaction force if it is hit diagonally?

I am confused about action-reaction forces and inertia of moving objects. As an example, take a cricket ball a bowler throws to the pitch: Suppose the ball is about to drop in the pitch with ...
0
votes
0answers
46 views

Velocity in relativity

We just started learning about 4-vectors in my physics class, and I'm a little confused about the relationship between the 4-velocity $U=\gamma(c,\vec{v}),$ and the velocity transformations given by ...
0
votes
1answer
52 views

Finding the divergence of this force [closed]

I've got to find the divergence of this force, $$ \mathbf F=\left(x^2+y^2+z^2\right)^n\left(x\hat e_x+y\hat e_y+z\hat e_z\right) $$ I would know how to do it if the $n$ superscript wasn't there. Any ...
0
votes
1answer
26 views

Various springs acting on a point mass

The force exerted on one spring is $\vec{F}=-k\vec{r}$. Now suppose we have N slinkys with stiffness $k_1,k_2,k_3,...,k_N$ where they have one end tied to fixed points in space with coordinates ...
0
votes
1answer
30 views

Projectile velocity and component $x$ and $y$ velocities

So the equations for the X and Y velocity given $\theta$ and $V_0$ are $V_x = V_0\cos\theta$, and $V_y = V_0\sin\theta$. When I test this with something like 1 m/s and and angle of $45^{\circ}$, I ...
1
vote
0answers
90 views

At time $t=0$, what are the magnitude and direction of the perpendicular component of dp/dt? [closed]

In the dark in outer space, you observe a glowing ball of known mass 4.6 kg moving in the xy plane at constant speed in a circle of radius 7 m, with the center of the circle at the origin (< 0, 0, ...
-2
votes
2answers
387 views

Is momentum of a moving body a vector or a scalar quantity?

Is momentum of a moving body a vector or a scalar?
-2
votes
4answers
184 views

What is the direction of dot product and cross product of vector A and B? [closed]

What is the direction of the dot product and the cross product of vectors A and B?
3
votes
3answers
108 views

Is it possible to have a non conservative vector field, such that the closed loop integral is $0$ for only some specific path(s)?

I was wondering whether there exists some non conservative field in which the closed loop integral over some specific path(s) is $0$, even if it's not $0$ for all the closed loop integrals. Or to put ...
1
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0answers
66 views

Four-momentum, four-velocity, energy

If given the four-momentum of any particle monitored by an observer as: p = $p^\hat{α}e_\hat{α}$ using unit vectors in observer’s reference frame and u = $e_\hat{0}$ then I get I'm just ...
-1
votes
2answers
62 views

Does Centripetal Force Change Direction?

I have been struggling with this question that I have, "Does centripetal force change direction?" From every point, it points to the center. But if we draw its vector, we draw the tails from ...
0
votes
2answers
92 views

Projections in Polar coordinate system

I really understand what projections in Cartesian coordinate system, I can imagine this, but I absolutely do not understand projection in polar system. For example, I have a speed, $U$, and I must ...
1
vote
1answer
165 views

How can I calculate the speed of an object knowing its horizontal and vertical velocity components?

Let's say a ball is thrown and it experiences typical projectile motion (moves in a parabolic arc etc.) and the only information we know are the equations for the horizontal and vertical components of ...
1
vote
1answer
32 views

Speed with wind resistance

This is probably a basic question, but it has been a while since I did anything like this. If a boat is sailing forward at speed $x$ and the direction of the wind, with magnitude $y$, is either equal, ...
2
votes
2answers
121 views

How to define pseudovector mathematically?

The textbook describes pseudovector like this: Let $a,b$ be vectors and $c=a\times b$, $P$ be the parity operator. Then $P(a)=-a,P(b)=-b$ by definition. But $P(c)=c$ since both $a$ and $b$ reverse ...
1
vote
2answers
170 views

If an asteroid were threatening the Earth, could I deviate it just by jumping on it?

An impact by a 10 kilometres asteroid on the Earth has historically caused an extinction-level event due to catastrophic damage to the biosphere. There is also the threat from comets coming ...
0
votes
1answer
75 views

Reflection - reaction force direction

Let's say object hits a wall. When the object is reflected does the direction of the reaction force caused on the wall looks like the red arrow ? Does that direction depends on how "strong" object is ...
4
votes
4answers
940 views

Can we add any two vectors?

Can we add any two vectors? If not, why is that so? I think this is not true, but I am not sure. My book says it is true, but I guess it is a misprint. For example, adding acceleration to velocity.
0
votes
1answer
132 views

Finding resultant and direction of resultant

In this question- A motorboat is racing towards north at 25km/h and the water current in that region is 10km/hr in the direction of 60 degree east of south. Find the resultant velocity of the ...
-1
votes
1answer
98 views

A particle has $\overrightarrow{r}(0)=4m(\hspace{2pt}\hat{j}\hspace{2pt})$ and $\overrightarrow{v}(0)=(2m/s^2)\hat{i}$ [closed]

I am having trouble with these problems, and I want to gain a understanding of how to solve these. I'll put what I have tried at the end, even though I don't think it'll be of help. A particle has ...
1
vote
1answer
90 views

Vectors in non-orthogonal systems

In a non-orthogonal coordinate system, what is the physically significant difference between the components of a vector on the skew axes and its projection onto each axis? Why would one want to find ...
0
votes
1answer
36 views

The vector r points from $P'(x',y',z')$ to $P(x,y,z)$ [closed]

For some reason this question is giving me a hard time :( The vector $r$ points from $P'(x',y',z')$ to $P(x,y,z)$. (a) Show that if $P$ is fixed and $P'$ is allowed to move, then ...
2
votes
2answers
88 views

Vector decomposition validity

Is force or field decomposition into component vectors always valid? Lets say a constant electric field $\vec{F}$ is acting in space such that it makes an angle $\phi$ with respect to the horizontal ...
0
votes
2answers
74 views

Find net force on a mass centered between four other masses

I'm not going to post the full question, I just want a general idea of how I should go about solving this type of problem. There is a square with 4 charged masses on each of the corners, in the ...
3
votes
1answer
273 views

How is weight distributed when legs are astride?

Is there a simple and quick formula to find the weight (the force acting) on each leg, especially when legs are astride and they are not equally stretched? (or, better) not equally distant from the ...
2
votes
2answers
189 views

A whole lot of doubts on Lorentz representation

Can someone tell me in layman's language how the $(1/2,1/2)$ represents a vector field and $(0,1/2)$ or $(1/2,0)$ represents spinors and $(0,0)$ represents scalar field. Please don't be pedantic on ...