Geometric object with magnitude (length) and direction.

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2answers
94 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 ...
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1answer
91 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 ...
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4answers
156 views

Find a central force given the orbit

I've been trying to solve the following problem for a long time. Let's consider a particle of mass $m$ in $\mathbb{R}^3$ with polar coordinates $(r,\theta,\phi)$. The particle moves on the orbit ...
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4answers
161 views

Dot product of vector and its derivative with respect to time? How does $L \cdot\frac{dL}{dt} = \frac{1}{2}\frac{d(L^2)}{dt}$? [closed]

How does: $$L \cdot\frac{dL}{dt} = \frac{1}{2}\frac{d(L^2)}{dt}$$ where L is a vector (I dunno how to make it bold in the equation). How do they reach to this right hand side equation? And what is ...
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5answers
827 views

If the velocity vector of a moving particle is always perpendicular to the position vector, is the path a circle? [closed]

A Newtonian physics question: If the velocity vector of a moving particle is always perpendicular to the position vector, is the only possible path a circle? What if the magnitude of the velocity ...
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1answer
145 views

Quantum states and state vectors

Does a state vector correspond to only one quantum states and the components in the state vector correspond to different states of this quantum state or is it that the components of the state vector ...
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2answers
38 views

How are the angles equal?

At the back of my mind I know they should be equal, but mathematically, how are the two $\Delta \phi$ angles equal? The only explanation present in the text is that, "both velocities are ...
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2answers
100 views

Polar coordinates explanation needed on calculation [closed]

This is the question. Here is the answer. But honestly I cant figure it out. Maybe my lecturer's handwriting is quite illegible too (just kidding). Sorry if I ask too simple question but ...
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2answers
94 views

How is it that the cross product of two vectors is always perpendicular to the given vectors? [duplicate]

Vector addition, subtraction and dot product seem logical enough, but I don't understand how two vectors acting on the same plane maybe, can give a perpendicular resultant.
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2answers
110 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 ...
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2answers
186 views

Difference between the two equations for acceleration

I came upon this while studying S.H.M. Well,is there a difference between writing $$a=\frac{dv}{dt}\;$$ and $$a=v\frac{dv}{dx}\;$$ do they differ on the basis of one being a vector and the other ...
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2answers
129 views

Stellar Power(Luminosity) Flux

So I was applying some mathematical techniques I learned to physics, and one thing that captured my interest, is the power or luminosity flux of a star. So modeling the situation, taking the scalar ...
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1answer
2k views

Find angle of force vector in equilibrium

So my question is Rope BCA passes through a pulley at point C and supports a crate at point A. Rope segment CD supports the pulley and is attached to an eye anchor embedded in a wall. Rope segment ...
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1answer
74 views

Asking the vector form of the equation about velocity

In the undergraduate text of physics, the equation for velocity and displacement at constant acceleration are given in scalar form. For example, my text reads $$v^2 = v_0^2 + 2a(x-x_0)$$ But today, ...
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2answers
132 views

Position vector, length/modulus function and differentials

If $\vec r$ and is the position vector of a point in motion and $r$ is its length/modulus/magnitude/size, then: Can it be true that: $$\|\mbox{d} \vec r\| \neq \mbox{d}r? $$ I think that this is ...
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2answers
59 views

Is it incorrect to explain the direction of a coded vector quantity?

For example, let's say that in a linear physics problem, all the data are given to a certain direction, and coded positively for direction to the right. So +5m/s would be a velocity of 5m/s to the ...
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1answer
2k views

Relative Velocity problem

I was solving many problems on relative velocity and observed that when the question asks, "what is the minimum time taken by the boat/man to cross the river.?" so the solution says that he ...
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1answer
139 views

Is it necessary to know initial y velocity to solve this projectile motion problem?

A marble is launched horizontally off a 93.0-cm high table causing the marble to land on the floor 1.85 m from the base of the table. a.) How long was the ball in the air? b.) With what ...
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1answer
135 views

Can the zeroth-component of a 4-velocity be negative?

Is it allowed to have the zeroth-component of a four-velocity be negative? I presume the answer is yes, but I just want to make sure. Many thanks. This is referring to $V^0$ for a curved space ...
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1answer
632 views

A Lawnmower Problem

For my physics class we were just given an exam that asked the following: A 12Kg lawnmower is pushed with a constant force along the 30* handle with 80N. Break the Forces into its vector ...
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2answers
743 views

Why or how is cross product used?

I do not understand how does the result of two vectors acting on a particle require me to take the cross product to find the resultant. Won't the actual force on the particle be the result of the ...
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1answer
93 views

Showing $ \textbf{F} \cdot d\textbf{s} = -dV$ is equivalent to $ F_s = -\frac{\partial V}{\partial s}$

Can someone please explain how the following $$ \textbf{F} \cdot d\textbf{s} = -dV$$ is equivalent to $$ F_s = -\frac{\partial V}{\partial s}$$ using some intermediate steps. I don't follow this ...
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3answers
777 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 ...
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2answers
3k views

Find the Unit Vector of a Three Dimensional Vector

How can I find the unit vector of a three dimensional vector? For example, I have a problem that I am working on that tells me that I have a vector $\hat{r}$ that is a unit vector, and I am told to ...
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1answer
279 views

What causes a gyroscope to eventually rotate/fall over?

Hey so I've just learned about angular velocity and momentum and how torque changes it. Looking at a wheel spinning around an axis, with one end being held up by a rope, what causes the wheel to ...
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1answer
24 views

Co-ordinate rotations

I need help transforming a magnetic field vector from one co-ordinate system to another. I have the components of the Earth's magnetic field in a co-ordinate system with z facing radially into the ...
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1answer
50 views

Explain how $\Delta v_{\perp}=v\Delta\theta$

In The Feynman lectures, under the chapter entitled Vectors, Feynman writes: My two intimately related questions are: 1) What does he mean by the magnitude of velocity? is he talking about the ...
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1answer
59 views

Why would the norm of these vectors be 1?

Let a Cartesian coordinate system $uOx$ coincides with a vertical plane so that $Ou$ is the horizontal axis and $Ox$ is the axis oriented vertically upwards (see Fig. 1). We are looking for the ...
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1answer
76 views

Vector product in a 4-dimensional Minkowski spacetime

I'm studying relativity and I lost track of interpretation along the mathematical formalism. What does vector product mean as an event? I mean, how must one interpret the result of the vector product ...
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1answer
62 views

Are perpendicular components special in vectors?

We can split a vector (velocity/displacement vector) along any two directions as long as the resultant of the oblique components of the vector is same as my original vector. Similarly if we have to ...
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2answers
66 views

Gauss' Law and area vector

Recently I've been doing some physics exercises on electric and magnetic fields and read up somewhere that the vector area of a closed surface is equal to zero. That made me wonder why, when using ...
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1answer
49 views

Why is parallel component of velocity along position vector considered rate of change of position?

If you have a position vector and a velocity vector of a particle, then the component of velocity vector along position vector is the rate of change of distance of the particle from the reference ...
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2answers
134 views

Direction of electric field lines and electrostatic force

Direction of electric field and electrostatic force should be same by the equation $$\vec{F} = \frac{k q q_0}{r^2}$$ Electric Field $$\vec{E} = \frac{k q}{r^2}$$ Let us suppose that there is a ...
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2answers
66 views

When does $\mathbf n\times(\nabla V_2-\nabla V_1)=0$ imply $V_1=V_2$

I was reading a paper on electrohydrodynamics which has the following sentence (in my own words): At the interface/boundary, the requirement of continuity of the tangential component of the ...
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1answer
135 views

Basic question about angular momentum

I've learned that the angular momentum of an object rotating about a fixed axis is $I \omega $. Also, in absence of external torques, $I_1 \omega_1 = I_2 \omega_2 $ (meaning, two different events). I ...
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1answer
46 views

vector resolutions

I am learning Mechanics - motion in a plane. Is it possible to that a given vector can be resolved in infinite ways into two non-colinear vectors in the same plane? For example, I have a vector ...
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1answer
64 views

How the torque/moment-of-force can be mathematically defined?

Given the definition of torque/moment-of-force $\mathbf F$ applied in $P$ with respect to the pole $O$ $$ \mathbf M_O=\vec{OP}\times\mathbf F $$ and given that the vectors $\vec{OP}$ and $\mathbf F$ ...
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3answers
578 views

Find the work done in moving an object along a vector r with a force F [closed]

$$r=3i+5j-2k$$ $$F=3i-3j+2k$$ What do I do. I know that work = force x distance. However, what vector operation should I do? I was wondering whether I should possible find the unit vector of r and ...
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1answer
67 views

Relative Motion of Child and Boat [closed]

A boat is traveling upstream at $11~\text{km/h}$ with respect to the water of a river. The water is flowing at $7.0~\text{km/h}$ with respect to the ground. What are the (a) magnitude (b) ...
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1answer
108 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 ...
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1answer
183 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 $\vec{b}$ ...
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1answer
33 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 ...
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1answer
40 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 ...
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2answers
868 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
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1answer
150 views

Determining the moment of force [closed]

A force $F = 3i + 2j$ passes through through a point $P$ with respect to an origin $O$. How do I determine the moment of the force at the origin.
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1answer
113 views

Torque definition and right hand rule not arbitrary

I have read the following: http://www.feynmanlectures.caltech.edu/I_20.html#Ch20-S1 The formula for $\tau_{xy}$ is derived in this chapter: http://www.feynmanlectures.caltech.edu/I_18.html#Ch18-S2. ...
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1answer
44 views

Compute the minimal distance between two points in movement

There are two points, $A$ and $B$ that move according to these laws: $$ \vec{x_a}= 20 -10 t $$ $$ \vec{x_b}= -15 +15 t $$ $A$ moves along the x axis, $B$ along the y axis. I have to compute the ...
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1answer
170 views

The formula used to calculate electrical potential energy

Sorry for the ugly picture but it makes my question more understandable. The $\Delta V$ from $A$ to $B$ is calculated by$$\int_A^B E \, \mathrm{d}r$$ where $r$ is the distance between $A$ and $B$. ...
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1answer
3k views

Relative motion and how to calculate magnitude and velocity of objects relative to different given objects [closed]

A canoe has a velocity of 0.550m/s southeast relative to the earth. The canoe is on a river that is flowing at 0.540m/s east relative to the earth. Alright so I attempted many different things an ...
0
votes
1answer
315 views

Finding an equation to solve for the velocity of a swimmer crossing a river [closed]

Where $\theta=45^\circ$, $d_1=200\:\mathrm{m}$, and $d_2=150\:\mathrm{m}$. I do not know how to combine the following equations: $$\begin{align} t&=\frac{d_1}{v_s\cos(45^\circ)}\\ ...