Geometric object with magnitude (length) and direction.

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Forces as vectors in Newtonian mechanics

I seem to be confused about the nature of forces as vectors, in the basic Newtonian mechanics framework. I know what a vector is as a mathematical object, an element of $R^3$. I understand that if a ...
3
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3answers
99 views

What is the relative velocity of this plane relative to the helicopter? [closed]

There is a plane moving 100 m/s due east relative to the ground without vertical motion. There is a helicopter facing north moving straight up at 20 m/s. From the perspective of the helicopter, is the ...
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2answers
91 views

Scattering geometry question

While reading up on light scattering I came across this slide: My vector maths is a bit rusty and I am having trouble understanding the last term (scattering geometry). What is the significance of ...
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2answers
76 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 ...
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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 ...
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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 ...
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1answer
1k views

Electric field a distance $z$ above the center of a circular loop. The Hard way [closed]

Problem 2.5: Find the electric field a distance $z$ above the center of a circular loop of radius $r$ which carries a uniform line charge $\lambda$. This problem is in refereced here (with ...
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1answer
307 views

Why can we use just one angular velocity vector to describe the rotation of a whole non-inertial reference frame?

The other day in class the professor was explaining non-inertial reference frames. We were working out how to find the acceleration of a point as measured from the non-inertial reference frame, and ...
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1answer
58 views

Show that getting parallel transported does not change angle between them- Tensors [closed]

I must tell you that I have never seen this kind of question in Tensor Analysis. Our professor had set up this question in our exam, but I don't know whether it belongs to tensors or not. The question ...
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3answers
617 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 ...
3
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1answer
115 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 ...
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0answers
86 views

Sound - for purposes of vibration

What is the best way to distribute noise from more than one source (I'm envisioning a system with many), within a dome, with the ground as its primary target, at optimal frequencies and volumes to ...
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3answers
16k views

Uses of Vectors In Real Life

I always wonder how vectors are used in real life.Vectors and decomposition of vectors,dot and cross products are taught in the early stage in every undergraduate physics course and in every ...
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3answers
604 views

The velocity formula $\mathbf{v} = \mathbf{u} + \mathbf{a}t$ for 1D, 2D, 3D . What is the difference?

Could I use $\mathbf{v} = \mathbf{u} + \mathbf{a}t$ for calculating velocity in these 3 different dimensions? If not, what's the difference between these 3 dimensions? How would you calculate ...
2
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3answers
318 views

How to distinguish 4D and 3D vectors in handwriting?

Usually vectors are denoted with bold font in printbooks and with arrows above in handwriting. In Thorn's e al. Gravitation, 4D vectors are denoted with bold and 3D vectors with bold italic. How to ...
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3answers
220 views

Dimension of vector resulting from tensorial product

I'm quoting what I found in a book about quantum computation: Individual state spaces of $n$ particles combine quantum mechanically through the tensor product. If $X$ and $Y$ are vectors, then ...
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2answers
596 views

Nature of spacetime 4-vector and tangent space?

An entry level confusion about spacetime. I understand that a 4-vector describes a point or event in spacetime. But I've also read (Bertschinger, 1999) that re spacetime "we are discussing tangent ...
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4answers
231 views

Gradient is covariant or contravariant?

I read somewhere people write gradient in covariant form because of their proposes. I think gradient expanded in covariant basis $i$, $j$, $k$, so by invariance nature of vectors, component of ...
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1answer
60 views

Considering the theory of special relativity: Is torque still a vector?

Considering the theory of special relativity: Is torque still a vector? In classical mechanics it is easy: You have 3 axes and thus 3 planes. Every plane has its own torque so torque has 3 ...
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2answers
3k views

split gravitational force into x, y, and z componenets

I am writing a program for a computer science class in which I am doing an n-body simulation in 3-dimensional space. Currently, I have figured out the gravitational force along the hypotenuse between ...
2
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2answers
165 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 ...
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4answers
288 views

Sum of acceleration vectors

If a point mass has some accelerations $\mathbf{a_1} $ and $\mathbf{a_2} $, why is mathematically true that the "total" acceleration is $\mathbf{a}= \mathbf {a_1}+\mathbf {a_2}$?
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2answers
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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
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2answers
144 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 ...
2
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1answer
137 views

What type of mathematical structure is a physicist's definition of a vector space?

A vector space as defined by a mathematician lacks the invariant scalar product that lies at the heart of what I would define as a physicist's definition of a vector space that models the physical ...
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2answers
133 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.: ...
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2answers
256 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 ...
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2answers
274 views

Coordinate transformation from earth to solar

I am building a 3d model of the solar system and need to figure out the position of the pole stars of each planet in order to tilt the planets in the correct direction the correct amount. I've already ...
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2answers
84 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 ...
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2answers
73 views

Orthogonality in curved space/spacetime

When are two vectors orthogonal in curved spacetime? From wikipedia: "In 2-D or higher-dimensional Euclidean space, two vectors are orthogonal if and only if their dot product is zero, i.e. they ...
2
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1answer
187 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 ...
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2answers
378 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 ...
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1answer
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Which are other anomalies like Divergence of 1/r^2?

As one might have learned in the basic science (ex. Electrodynamic theory), when we apply the divergence theorem to the vector function like 1/r^2 with it pointing in the radial direction (like ...
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2answers
97 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 ...
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1answer
64 views

4-vector velocity to Newtonian?

The four-vector condition for a particle free of forces is: $\frac{du}{dτ} = 0$ and the equivalence of this to the statement of newton's first law follows from the expression for four-velocity: ...
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2answers
54 views

Why should an area vector point normal to the surface?

Why is it that the direction of an area vector should be always along the normal drawn to the surface? Can't it also be some other angles with the plane?
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1answer
452 views

What does relative to something mean?

I just started learning about vector components and relative motion. I don't understand what relative to something means. I looked online but none of the explanations are helpful. If someone could ...
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1answer
4k 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 ...
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5answers
203 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. ...
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2answers
1k views

Meaning of angular velocity in a rotating system

When you study the motion of a rigid body you have $\vec\omega$, the vector associated to angular velocity. In the case you are using Euler angles and want a quick formula for the rotational kinetic ...
2
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1answer
24k views

How Does force relate to velocity

I had originally asked this question on math overflow and it was suggested that I ask it here. So I know that a force will change the magnitude of velocity if it is at an angle other that 90 degrees. ...
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3answers
845 views

negative vectors (eg velocity)

If you said someone had a velocity of -12mph and they were traveling north? Wouldn't it mean that they were traveling 12mph south? This is a quote from here: if something [object-x] moving to the ...
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3answers
94 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 ...
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1answer
49 views

Torque on wire summarized with magnetic moment

The magnetic moment of a current-carrying wire loop $L$ is $$ \boldsymbol\mu = \frac I2\oint_L\mathbf{r} \times \mathrm{d}\mathbf{r} $$ so the torque it experiences under a uniform magnetic field ...
2
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1answer
159 views

What is the physical interpretation of the dot/inner/scalar product of two vectors?

What is the physical interpretation of the dot/inner/scalar product of two vectors? See, if we multiply two scalars like 2*3 we say two times three is six. I also do understand multiplication of ...
2
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1answer
405 views

Line of action force

The task is to reduce the two forces into a single net force and then find the equation of its line of action. I chose to find the net force and momentum with respect to the origin. The magnitude of ...
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1answer
415 views

The curl of a special cross product

When given two vectors $\mathbf{A}$ and $\mathbf{B}$, the curl of the cross product of these two is given by ...
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1answer
91 views

$\hat{\imath}$ component of force exerted on an electron by a magnetic field?

The magnetic field over a certain range is given by $\vec{B} = B_x\hat{\imath} + B_y\hat{\jmath}$, where $B_x= 4\: \mathrm{T}$ and $B_y= 2\: \mathrm{T}$. An electron moves into the field with a ...
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2answers
409 views

Sum of all forces

Let us glue up these two images, where we get closed loop thrust of water. Force $F_3$ has direction $-x$ and force $F_2$ has $x$ direction. What is the sum of all forces? Can it be more than zero? ...
2
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1answer
190 views

Vector transformation in special relativity

Please note that I am very new on this website so have some difficulties in writings as required here but trying really hard to learn quickly. La-Tex is the main problem but please understand me that ...