Tagged Questions

Geometric object with magnitude (length) and direction.

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1
vote
0answers
27 views

Which notation for the unit vectors is the most common: $\vec{u}$ or $\vec{e}$? [on hold]

I have seen both $\vec{u}$ and $\vec{e}$ used to denote the unit vectors. In Cartesian coordinates: ($\vec{u_x}$ , $\vec{u_y}$ , $\vec{u_z}$) and ($\vec{e_x}$ , $\vec{e_y}$ , $\vec{e_z}$) In ...
3
votes
1answer
50 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
73 views

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

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 ...
0
votes
0answers
23 views

Help with 4-velocity [on hold]

The 4-velocity $\overline{U}=(U^0,U^1,U^2,U^3)$ corresponds to the 3-velocity, $\underline{v}$, in the sense that $\overline{U}=\gamma(v)(1,\underline{v})$. Express (a) $U^0$ in terms of ...
2
votes
3answers
65 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
4answers
33 views

How to find total force on an object?

If there are are a multitude of forces on an object, acting on it in different directions, how do you find the TOTAL force? I know you add up the x components and the y components individually, but ...
-3
votes
0answers
28 views

Forces in parallel and perpendicular components [on hold]

Why is this slope 3/4 (written in green) is upside down in a force (written in blue).
-1
votes
0answers
33 views

Finding momentum using vector operations? [closed]

So I was given the following problem: and our professor said we could set it up as follows to solve for the final momentum to get the final velocity: using sine, so I did that and got the ...
0
votes
1answer
19 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 ...
0
votes
0answers
19 views

Projectile Aiming [closed]

I'm having a but of trouble with a game I'm programming. What I have is an enemy who periodically shoots a laser at the player if they're close enough. I've been trying to come up with a way to make ...
1
vote
1answer
49 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
44 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
votes
0answers
27 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 ...
2
votes
1answer
96 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
70 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
64 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
vote
2answers
57 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
votes
2answers
38 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
252 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
35 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
46 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
18 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
20 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
41 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, ...
-3
votes
1answer
52 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
121 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
57 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
vote
0answers
43 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
45 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
57 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
43 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
27 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
72 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 ...
2
votes
2answers
135 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
49 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
844 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
76 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
52 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
58 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
32 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
1answer
44 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
42 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 ...
4
votes
1answer
173 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
162 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 ...
2
votes
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: ...
0
votes
1answer
43 views

Average acceleration when more than two different velocities occur [closed]

Suppose a car travels at 5m/s north for 5 seconds, it then turn east and travel at 7m/s for 10 seconds, finally it turns north east and travel at 10 m/s for 20 seconds. What is the average ...
0
votes
2answers
197 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
1answer
44 views

Would equations for a spinning top be an (x,y,z) vector [duplicate]

I am following the equations on this page, and for torque it is $mgr\sin\theta$, but I am curious about $r$. I am working on a game and I want to correctly model the top, and am curious if $r$ should ...
2
votes
2answers
52 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?
1
vote
2answers
148 views

Inner products with orthonormal bases

Probably a stupid question here - I think it's a case of me not having sufficient mathematical background to follow this through. In Leonard Susskind's Theoretical Minimum book, he represents the ...