Geometric object with magnitude (length) and direction.

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2
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5answers
2k 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 ...
-2
votes
0answers
32 views

Flat Disk Rotating Torque [on hold]

I have been trying to work out something. If you had a top like in the following description, how would you calculate the vector torque of the disk? And would it be just due to gravity? If so is the $\...
0
votes
3answers
110 views

Why centripetal force does not increase the value of tangential velocity?

I found in a text book that the value does not change because the centripetal force is perpendicular to the tangential velocity. But I am confused, because a vector can have a component, which is ...
0
votes
1answer
104 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
862 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 = ...
1
vote
2answers
66 views

Time dependent ODE involving cross product

Let $\vec{A}$ be any time dependent vector quantity, and $\vec{\alpha}$ any constant vector. I was told that a solution to the differential equation $$ \dot{\vec{A}} = \vec{\alpha}\times\vec{A} $$ is ...
0
votes
2answers
81 views

Proving that force satisfies the laws of vector addition [duplicate]

A vector quantity has both magnitude and direction. So, for any physical quantity to be a vector, it should have a direction and a magnitude. Though this is a necessary condition for any quantity to ...
2
votes
4answers
188 views

Rotation of a vector

Is a vector necessarily changed when it is rotated through an angle? I think a vector always gets changed because its projection will change, and also its inclination with axes will always change. ...
-1
votes
1answer
48 views

Is it possible to introduce 4-velocity very early on?

I was wondering if it would be possible to teach new physics students about 4-velocity straight away at the beginning of their studies. Keeping the regular notion of the three dimensional velocity $\...
-3
votes
1answer
33 views

Calculating horizontal and vertical components of force [closed]

4a) Calculate the horizontal component A and the vertical component B of: i) a 6.0N force at 40 degrees to the vertical I'm not sure about this but would this be the way to calculate it? $$6\sin(...
0
votes
3answers
246 views

In what direction does the friction force point? [closed]

I'm really confused about the direction of friction force. I think about collision of two balls and think that "friction force is opposite to the relative speed of the contact point of the two ...
2
votes
2answers
75 views

Circular Motion. Intuition on vectors as a physics interpretation [closed]

I am a maths undergraduate. I decided to start studying some basic physics trying to be rigorous with the math and uderstand the interpretations of some of the mathematical constructs and see how ...
0
votes
1answer
71 views

Four Vectors in SR and QFT

I'm covering both special relativity and quantum field theory in the summer. I'm currently using Spacetime Physics by Taylor and Wheeler to cover SR. Since I'm covering SR on the side with QFT, I'm ...
1
vote
4answers
42 views

Particle Equilibrium and the Interpretation of Accelerations

I have a simple question regarding the interpretation of acceleration and force in the context of a particle in equilibrium. Given that the necessary and sufficient definition for particle equilibrium ...
4
votes
3answers
386 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 ...
0
votes
3answers
63 views

Why is speed defined as coordinate derivative over proper time rather than observer's time in STR?

In special theory of relativity, why is 4-velocity defined as: $$ u^\mu = \frac{dx^\mu}{d\tau} $$ and not as $$ u^\mu = \frac{dx^\mu}{dt} $$ where ${\tau}$ is proper-time and t is time in some ...
2
votes
1answer
70 views

Why does the divergence of the Poynting vector have energy flux density?

The poynting vector is defined as $\vec{S}=\mu_{0}^{-1}\vec{E}\times \vec{B}$ Taking the divergence of the poynting vector, one arrives at $\vec{\nabla} \cdot \vec{S}=-\frac{\partial u}{\...
-1
votes
1answer
42 views

How would you go about solving this graphical mass problem? [closed]

I've tried finding the x and y components of the vectors created by each mass to find the resulting vector's magnitude. However, my answer of 0.354 N keeps getting marked wrong. Any ideas on how to ...
2
votes
1answer
44 views

Cable wakeboard raley

Illustration of the problem: http://www.youtube.com/watch?v=OWRixptJaRo The non physics solution: http://www.youtube.com/watch?v=FRwHcJjfCR4 My first approach to learn this was to follow youtube ...
3
votes
1answer
630 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 ...
2
votes
2answers
270 views

How to find Tangential/Radial/Angular Velocity for motion in any curve?

Is the radial velocity responsible only for changing distance between objects and the component perpendicular to it only for change in direction? If so why? Please try to give a different explanation ...
0
votes
1answer
74 views

Unit Vector vs. Basis Vector

When reading about vectors I sometimes have seen unit vectors multiplied by the components and other times I've seen basis vectors used instead. $$v=x \hat i+y \hat j+z \hat k$$ $$v=xe_x+ye_y+ze_z$$ ...
1
vote
1answer
25 views

How can I calculate the torque on a body resulting from a spinning propeller?

If a quadcopter has all of its propellers spinning on the same direction, the body of the quad will obviously start spinning in the another direction. I know how to calculate the torque acting on a ...
0
votes
1answer
98 views

Expressing virtual force in terms of muscle contraction force

Two bodies connected with a hinge joint with axis in J. They also connected with a muscle at points M and M`. I’m trying to express virtual force Fv in terms of muscle force Fm acting at the point M ...
0
votes
2answers
50 views

Simple change in velocity question

The hand of a clock is 1cm long. find the change in velocity of the hand in 15 seconds. The question is pretty simple, $v=2\pi R/T$ and then using the vector addition one can easily get answer which ...
2
votes
4answers
132 views

How to apply a force vector to a position vector?

A particle is present in the two dimensional space. It's position is given by the vector: $$x = \begin{pmatrix} |x| \cos(\theta) \\ |x| \sin(\theta) \end{pmatrix}$$ It experiences a force of: $$ F = \...
0
votes
6answers
271 views

If gravity is additive, then how does it cancel itself out?

I understand that gravity, as far as we know, is always attractive. Also, it has additive qualities - i.e. the size and strength of the field are proportional to the quantities of mass. This seems to ...
0
votes
2answers
52 views

What is the difference between real value and abs value? [closed]

I am confused here, though I have been reading about it for years. What is the difference between a real value and an absolute value? For example, when do we take the absolute value of pressure or the ...
1
vote
3answers
254 views

Spacelike to timelike four vectors

First at all, let me just say that I'm not a Physicist, I study mathematics. So, I have this question. If you have a spacelike four vector, is there any transformation that could change it to be a ...
0
votes
3answers
995 views

Understanding weight on an inclined plane

I'm trying to solve a problem where I have an object resting on an inclined plane, with the angle of the plan being alpha, and the weight being w. I'm having trouble figuring out how I can calculate ...
5
votes
2answers
197 views

Why do we use orthogonal axes?

I have been asked several times that “why do we use orthogonal axes in coordinate systems?” and I was always replying that “because of simplicity”. But, today morning, someone asked me that question ...
0
votes
3answers
86 views

What is the Direction of area vector?

In case of closed surfaces the area vector is directed outwards the surface. But what is the direction of the area vector in case of an open surface e.g. A thin lamina type of surface. Does it depend ...
0
votes
1answer
114 views

Elemetary Rotations -imagining differential rotations - intitutive proof of such rotations being vectors

I was reading and extract from "Fundamentals Laws of Mechanics", 1980, by I.E Irodov, § 1.2. 'Kinematics of a Solid' and came across this insane text where the author asks me to imagine a 'solid ...
-1
votes
1answer
74 views

Does a resultant magnitude always have to be positive?

If components vectors can be positive OR negative, why must resultant vectors always be positive?
-1
votes
1answer
49 views

Why is the absolute value of the side in this problem taken to find theta?

To find the resultant magnitude and its direction (theta) in this problem, one must perform the following procedure: However, my point of confusion is why they took the absolute value of Rx at the ...
1
vote
1answer
44 views

Notations used to express direction [closed]

We express direction relative to a reference point and call a certain direction positive and it's direct opposite direction negative, by convention. But, what notation should we use to express a ...
1
vote
1answer
47 views

Is the net force conventionally shown in a free body diagram?

Is it standard convention to display the net force vector on a free body diagram? Internet searches seem to give mixed results.
2
votes
3answers
113 views

what does magnetic field vector mean?

I am trying to understand what a magnetic field vector tells us about the magnetic field. I understood that a vector is just a representation of a point and how much it is moved in x,y and z direction ...
-1
votes
2answers
50 views

Problem with derivation of potential enery of two body in Gravitational energy

Maybe what I'm going to ask sounds stupid but it means a lot to me that's why I'm asking. I've problem with just a single step in derivation. Let's start. I'm keeping in mind the direction of each ...
1
vote
2answers
57 views

Finding if two objects collide

The question that I'm trying to understand is this: This is the part of the solution I don't understand: From my knowledge, if $v_p-v_q$ is due south, this means $r_p-r_q$ is also due south, ...
0
votes
1answer
32 views

What would be the resultant of two vectors at 180°?

If two vectors are at 180° to each other, would the resultant be 0 (as per the head-to-tail method), or the difference of the magnitudes of the two vectors? If the former is true, then why isn't it ...
0
votes
1answer
33 views

Could we find the overall force and direction of something with a diagram only? (i.e. no calculation)

My friend, who is a geologist, and I were just debating some dynamics stuff. To make this easier, lets come up with an analogy......lets say there's a boat and it's being pulled by two smaller boats ...
1
vote
2answers
302 views

Why does something on an inclined plane move forward at all?

We just started studying about the inclined plane and vectors in motion, but i don't understand one thing: Why on earth does the object on the inclined plane move forward (I.e in the direction where ...
3
votes
3answers
371 views

Why the $r$ is cubed in the vector notation for of Newton's Law of Universal Gravitation? [duplicate]

I'm learning about astrodynamics on my own and I was wondering why the $r$ is cubed in the vector notation for of Newton's Law of Universal Gravitation: $$\vec{F}_g=\frac{Gm_1m_2}{|\vec{r}|^3}\vec{r}$...
3
votes
3answers
1k views

Negative vectors (e.g. velocity)

If you said someone had a velocity of $-12\,{\rm mph}$ and they were traveling north? Wouldn't it mean that they were traveling $12\,{\rm mph}$ south? This is a quote from here: if something [...
2
votes
3answers
58 views

Force at axis of spinning wheel

This is a newbie question, but I don't quite understand the forces at work when an object is rotating. So I've read that i can use my right hand to determine the direction of the force at the axis ...
1
vote
1answer
62 views

What is the difference between a tensor, vector, and a matrix? [duplicate]

I'm currently going through notes on a physics course and I'm having trouble understanding the difference between a tensor, a vector, and a matrix. I know that a vector is a kind of tensor and that a ...
3
votes
1answer
8k 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 ...
1
vote
1answer
39 views

Calculating relative velocity in three dimensional space

Given two points $\mathcal{A}$ and $\mathcal{B}$ in $\mathbb{R^3}$ whose position and velocity vectors are, respectively: $$\mathbf{r_A}=\begin{pmatrix}r_{A_{x}}\\r_{A_{y}}\\r_{A_{z}}\end{pmatrix}$$ $$...
0
votes
1answer
31 views

Why do we represent the axis of rotation using vectorial notation [closed]

When a body (in pure rotation) rotates along an axis passing through it, why do we represent the axis of rotation in vectorial notation? Wouldn't it be sensible enough to represent the angular ...