Geometric object with magnitude (length) and direction.

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-3
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2answers
97 views
-4
votes
3answers
29 views

Net force of the following? [on hold]

The following objects are attached to one another and have difference force directions: Where is the direction of force? And What is the net force? I'm trying to calculate it using their angles, ...
-2
votes
1answer
33 views

Norm of summation of vectors

If we have a vector $\partial_v$ and we want o find its norm, we easily say (According to the given metric) that the norm of that vector is:$ g^{vv}\partial_v\partial_v$. My question what if we have ...
2
votes
2answers
33 views

Another condition of calculating work

Let's imagine that there is a box placed at the corner of a table, and I push it so that my applied force makes an angle of 30° from the table's surface. The box would move and, due to the effect ...
0
votes
2answers
110 views

Animating an Acceleration Vector - Acceleration of object on a crested path in gravitational field

So I was reading in Chapter 3 of my textbook, Sears & Zemanksky's University Physics with Modern Physics by Young and Freedman, 13th Edition, and the discussion took us to a definition of the ...
6
votes
2answers
165 views

Infinite dimensional vector spaces vs. the dual space

I just happened across this over on Math Overflow. It references the following theorem from linear algebra: A vector space has the same dimension as its dual if and only if it is finite ...
0
votes
1answer
20 views

What is the work done said when angle between force and displacement>90 and <180?

If the angle between $Force$ and $Displacement$ is obtuse then by using the formula of $Work$ we get negative quantity so is it said then that the system is losing energy or it is merely for the case ...
-1
votes
0answers
26 views

Determine a gradient field [on hold]

Given the following field of force, $$ \vec F(\vec r) =\begin{pmatrix} 2x+2y+az \\ 2x-3ay \\ 4x+c+2z+yd \\ \end{pmatrix} $$ My exercise is to determine $a,b,c$ ...
2
votes
2answers
70 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
265 views

How can I split a resultant force into its $x$ and $y$ components?

Point charge 3.5μC is located at x = 0, y = 0.30 m, point charge -3.5μC is located at x = 0 y = -0.30 m. What are (a)the magnitude and (b)direction of the total electric force that these charges ...
0
votes
7answers
24k views

What does the magnitude of the acceleration mean?

I am a little confused as to what the magnitude of acceleration is and what it means.
0
votes
2answers
241 views

Relative motion. Setting course of closest approach

Let $r_{P/Q}$ be the position vector of $\overrightarrow P$ relative to vector $\overrightarrow Q$ and $v_{P/Q}$ the velocity vector of $\overrightarrow P$ relative to $\overrightarrow Q$. Suppose ...
1
vote
1answer
169 views

Relative wind velocity explanation - understanding Irodov problem 1.6

I am having trouble understanding the reasoning behind the solution in this Irodov General Physics problem. The problem is 1.6: 1.6. A ship moves along the equator to the east with velocity vo = ...
0
votes
0answers
20 views

Force component at inclined plane [closed]

A downward force acts upon the triangle (e.g. gravity) and a force acts upon the square that is directed horizontally to the left. The inclined plane is fixed. What force has to act to the left for ...
0
votes
2answers
97 views

confusion on vector quantities

How can we define simply that velocity is a vector quantity without mentioning that velocity has vector properties. How can we simply say it needs both magnitude and direction for its complete ...
1
vote
1answer
24 views

How can kinetic energy be conserved in an elastic collision

How can kinetic energy be conserved in an elastic collision as collision is said to occur between two bodies if they physically collide against each other or if the path of one of then is affected by ...
0
votes
0answers
28 views

How to calculate the horizon line of a satellite?

I need an equation to calculate a list of Earth-centered, Earth-fixed (ECEF) XYZ coordinates on the earth that represent the visibility limit of satellite given its ECEF XYZ coordinates. For any ...
0
votes
1answer
52 views

Is velocity always tangential to trajectory?

So I was doing an exercise and they find find the angle between the tangential of trajectory and the vertical I was stuck but then I read in a site that the velocity is ALWAYS tangential to the ...
2
votes
3answers
151 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, ...
0
votes
0answers
10 views

Overall Velocity of Body with Multiple Wheels

Let's say you have some object, a car or whatever, that has multiple wheels going in multiple directions, each of which can spin at different speeds. How would one go about getting the overall ...
0
votes
1answer
22 views

Torque on shaft

Consider a generator which supply power using a shaft to a turbine. The torque applied on shaft by generator is $T$. As the shaft has constant angular velocity the turbine should also be applying ...
1
vote
1answer
15 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 ...
5
votes
4answers
7k views

Why is current a scalar quantity?

Current has both magnitude and direction. As per the definition of vector defined in encyclopedia, current should be a vector quantity. But, we know that current is a scalar quantity. What is the ...
1
vote
3answers
31 views

Find time-parametrization given path and speed of a particle

Consider a particle in two dimensions with position vector $r(t)=<x(t),y(t)>$ and the shape of the path is described by a function $y(t)=f(x(t))$ (Thus $r(t)$ is a parametrization of $f$ with ...
1
vote
1answer
23 views

How to expand this equation considering acceleration due to gravity into 3D vector space?

How can we expand this following equation into 3D vector space? I learned this equation from this answer: Don't heavier objects actually fall faster because they exert their own gravity? The ...
1
vote
3answers
256 views

Why does the moment of force (aka. torque) depend on the perpendicular distance?

Couyld anyone explain how the lecturer concluded that $$(\underline{r_2} - \underline{r_1}) \times \underline{H} = \underline{p} \times \underline{H}$$
0
votes
2answers
133 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 ...
0
votes
1answer
54 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, ...
6
votes
4answers
3k views

Direction of angular velocity

Angular velocity is the rate of angular displacement about an axis. Its direction is determined by right hand rule. According to right hand rule, if you hold the axis with your right hand and rotate ...
2
votes
3answers
67 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 ...
1
vote
4answers
128 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 ...
3
votes
2answers
86 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
95 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
vote
0answers
25 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 ...
3
votes
1answer
136 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
2answers
58 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
136 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 ...
0
votes
3answers
679 views

Question involving Vectors and Forces

This is a question I found in Mechanics for Engineers by Beer & Johnston. A 600-lb crate is supported by the rope and pulley arrangement as shown below. Write a computer program which can be ...
11
votes
4answers
364 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 ...
1
vote
1answer
18 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
votes
0answers
22 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 ...
7
votes
3answers
711 views

Covariant and contravariant vectors

Reading Weinberg's Gravitation and Cosmology, I came across the sentence (p.115, above equation (4.11.8)) The partial derivative operator $\partial/\partial x^\mu$ is a covariant vector, or in ...
2
votes
2answers
99 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
104 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 ...
0
votes
1answer
24 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
28 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, ...
1
vote
1answer
68 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 ...
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 ...
0
votes
0answers
39 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 ...
0
votes
1answer
60 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 ...