Questions tagged [vectors]
Geometric object with magnitude (length) and direction.
2,604
questions
1
vote
0
answers
60
views
Vector potential of Weird loop
I have to calculate the vectorpotential of a current flowing through the loop at the origin:
where the current is given by $I(t)=kt$ for some $k>0$.
Given equations
$$\mathbf{A} = \frac{\mu_0}{4\...
- 49
-1
votes
1
answer
44
views
Components of velocity in projectile motion [closed]
I came across this question in my physics textbook (Gr12) and I was hoping someone could explain the solution to me
A ball is thrown horizontally off a building at $8.2\,\text{m}/\text{s}$. At a ...
- 3
-1
votes
2
answers
67
views
Problem with resources, Walter Lewin's third lecture
I've watched Walter's third lecture in 8.01 and I have a small problem with the last part, where he says that $$\vec r_t=x_t\cdot \hat x\ +\ y_t\cdot \hat y\ +\ z_t\cdot \hat z \\ \vec v_t=\frac{d\vec ...
0
votes
1
answer
87
views
Do gamma matrices commute with 4-vectors?
One of my exercises was to prove the identity
$$\gamma^\mu\displaystyle{\not}a\gamma_\mu=-2\displaystyle{\not}a.$$
Which is trivial if $\gamma^\mu a_\nu=a_\nu \gamma^\mu$, as follows
$$\gamma^\mu\...
- 1,775
0
votes
3
answers
52
views
Resolving gravitational acceleration
I came across a problem in physics where I had to find the acceleration down an inclined plane. I started by considering $g$ as one of the components, and the one along the inclined plane as the ...
0
votes
0
answers
47
views
The length of four-force
Recently, I'm reading the FeynmanLecture II_26 https://www.feynmanlectures.caltech.edu/II_26.html
It says that the “length” of the four-vector is an invariant under what is called the “complete ...
- 1
1
vote
2
answers
67
views
Is the $y$-component of projectile motion independent of the $x$-component or not?
In projectile motion, it is said that both the $x$ and $y$ components are independent of each other but according to the equation of the trajectory,
$$y = x \tan\phi - \frac12 g x^2/(u^2\cos^2\phi)$$
$...
- 177
1
vote
0
answers
72
views
Angular velocity versor
I am going back through the definitions of good old Euclidean vectors and trajectories to see whether when i was younger i missed important concepts.
In my notes, and reference book, i found that for ...
- 1,611
0
votes
2
answers
44
views
Equations of motion for constant acceleration
I read that the equations of motion for a constant acceleration can be represented in a scalar form as well as a vector form, but what's the need to do them in vector form what extra can we do by ...
- 51
1
vote
2
answers
119
views
Calculating the net forces in multi-mass dynamic system
I am trying to figure out a generalized method for finding the net force of each mass in a multi-mass dynamic system. We have learned methods in highschool but those don't work for more complex ...
- 11
4
votes
5
answers
197
views
Where does the four-vector potential $A^\mu$ originate?
Now the default answer to this may be, "It has no origin because it's a definition", but let me just try to justify my concern here.
On page 842, equation (22.91) of "Modern ...
- 295
-1
votes
1
answer
77
views
Can distance traveled by a body be zero?
I had seen a teacher saying on YouTube that we must note that distance traveled can not be zero then I searched for the same on net and surely some sources say same e.g. the below link
https://byjus....
- 1,357
2
votes
2
answers
86
views
How to compensate tilted accelerometer?
First of all, I only have accelerometer to solve this problem.
I have tilted accelerometer mounted in a vehicle, and I like to get the output values of this accelerometer as if this accelerometer is ...
- 23
1
vote
2
answers
59
views
Euler Rotation Equations and invariance of vectors in different reference frames
Consider two frames, one which is inertial and the other one rotating w.r.t. to the inertial frame. Say there is a rigid body having angular momentum which is same/invariant in both frames. How is it ...
- 11
0
votes
2
answers
87
views
Linear velocity on a circle
Consider a ball rotating around the z-axis with constant angular velocity $\vec{\omega}$, then the linear velocity $\vec{v}$ is given by $\vec{v} = \vec{\omega} \times \vec{r}$. It is easy to ...
0
votes
1
answer
42
views
Velocity Formula in SHM
In Simple Harmonic Motion in one dimension, if we assume
$$\text{Displacement}=x=A \text{sin} (\omega t+\phi)\implies \text{velocity}=v=A \omega \text{cos} (\omega t+\phi)$$
From here by substitution ...
- 347
4
votes
1
answer
82
views
How can I formalize better this proof that angular momentum is conserved for a small impulse?
The book I am studying is discussing Lagrange stability of circular orbits, which assumes fixed angular momentum $L$, hence in an introductory paragraph explains why, when studying stability of a ...
- 130
0
votes
1
answer
46
views
A change in the unit vector over a finite time interval
how we can write the change in unit vectors over a finite time interval, the change in unit vectors in an infinitesimally small-time interval 'dt' is given by the magnitude of the really small angle ...
- 51
0
votes
2
answers
59
views
Vectors in inertial and non-inertial frames
Trying to understand how vectors change in inertial and non-inertial frames
Am I right in saying vectors are defined by their invariance under coordinate transformations? My main question is are ...
- 75
3
votes
6
answers
168
views
Why can't rotations in general be associated with vectors?
In my textbook, there's a question:
A vector has both magnitude and direction. Does it mean that anything that has magnitude and direction is necessarily a vector? The rotation of a body can be ...
- 342
2
votes
2
answers
84
views
Dot product in optics
(Before marking this question as a duplicate, please consider I've read this post but it I didn't find the answers to it quite satisfactory regarding my doubt).
I'm trying to derive the expression of ...
- 1,616
1
vote
0
answers
25
views
Question about how force is distributed based on initial hitting angle in multiple pool balls
Suppose you have a standard triangle rack of billiard balls under ideal conditions (all balls are touching and identical, no friction, and all elastic collisions, ect). Suppose force F is applied to ...
- 11
0
votes
1
answer
58
views
String pulling sides of a triangle inwards: Force acting on each side?
Referring to the image above:
The black lines are ONE continuous string whose ends are where the red thing is.
The red thing can tension the string and can measure the force used to tension the ...
- 31
0
votes
1
answer
44
views
The locus of the velocity vectors of a boat navigating in the sea under the presence of a very strong wind?
I already asked a question very similar to this one here and I think the solution would not work when the boat navigates in the sea when a very strong wind blows. That is I am trying to find the ...
- 159
0
votes
1
answer
71
views
On covariant form of Lorentz equation
The non-relativistic version of Lorentz equation has the form
$$m\frac{d\vec{v}}{dt}=q(\vec{E}+\vec{v}\times\vec{B}) $$
Where $\vec{v}, \vec{E}, \vec{B}$ refers to the velocity of charged particle, ...
- 1,752
0
votes
2
answers
54
views
Angular velocity relative to some frame
In "Introduction to Robotics" by John Craig, we have the following statement:
The vector ${}^A \Omega_B$ describes the angular velocity of $B$ with respect to $A$, and ${}^C({}^A \Omega_B)$ ...
- 202
0
votes
1
answer
35
views
Question regarding resultant of force vectors
This problem is being asked in the regards of the following question
The resultant of two forces has magnitude $20\hspace{1mm}N$. One of the forces is of magnitude $20\sqrt{3}\hspace{1mm}N$ and makes ...
- 173
11
votes
8
answers
4k
views
Why do we associate negative sign to electric charges when they are a scalar quantity?
My confusion arose when going through the additive property of charges where charges with opposite signs subtract each other. My knowledge of electrostatics is limited, but I am sure that signs are ...
- 121
1
vote
2
answers
94
views
What is the locus of the velocity vectors of a boat navigating in the sea under the presence of some force?
I am a mathematician and know nothing about physics, although I am trying to solve a problem related to physics. If someone could help or provide some suggestions, I would be grateful.
I have a speedy ...
- 159
2
votes
1
answer
65
views
Integral Quantity Interpretation
Is there any natural interpretation for the following quantity?
$$\int_{\vec{r}(t)} \nabla(\vec{v} \cdot \vec{A})dt \ .$$
Where: $$\vec{v} = \frac{d \vec{r}(t)}{dt} \ ,$$ is the velocity of the path ...
- 2,599