Geometric object with magnitude (length) and direction.

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45 views

Centripetal acceleration [closed]

I know if a particle is accelerating around the earth it has $$a= \omega*v$$ My question is how do I express this in terms of the unit vector. Would it go something like this. $$|a| = |\omega*v| $$ $...
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25 views

Wire with current in magnetic field $\vec{B}$has force $\vec{F_1}$. When rotated, $\vec{F_2}$. Find $B$ [closed]

I have the following question: In a wire with $10cm$ there is a current $4A$ going 'upwards' in the $z$ axis. The force over this field, under a constant magnetic field $\vec{B}$ is $F = -0.2\vec{i} +...
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71 views

Zeroth component of 4-momentum and relativistic energy-momentum relation

As I understand it one is forced to use 4-vectors since we require objects that transform as vectors under application of Lorentz transformations and 3-vectors do not (technically they do under ...
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1answer
50 views

Orthogonal of tangent vector in Rindler coordinates [closed]

For 2D space time from $(t,x)$ to $(u,v)$ the transformation are $$t = u \sinh(v)$$$$x=u\cosh(v)$$ Asking to show that two families of curves $u = \textrm{constant}$ and $v = \textrm{constant}$ ...
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25 views

Correct resolution of vectors [closed]

There's a sum given as an example in my physics textbook which I tried to solve in a different manner but ended up with a wrong answer. Here's a picture of the sum given in my textbook along with the ...
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30 views

Direction of motion 1 [closed]

A man on a bike travelling east on straight road at 8km/h sees a car driving north at 60km/h. What is the apparent speed and diretion of motion of car to the cyclist?
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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.
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47 views

Defining a room that is equally lit at every point

Imagine you were in a room designed such that no matter where in the room you stand, a sphere of volume 1 liter held at 2 meters above the ground would be exposed to the same amount of light. How ...
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24 views

How does a bikerider turn by leaning on one side? [duplicate]

I am trying to understand the following image: Could someone please help me understnding it. What I understood so far: Your angular velocity mutyplied by the impulse gives you the impulsemoment. By ...
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52 views

Calculus/Vector Calculus and so on in special relativity book recommandation

I want to learn calculus 1,2,3 vector calculus, analysis and so on in special relativity. But I never found a good and clear book/source on it. Can someone recommend an easy book or internet source on ...
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39 views

What does 'vector-like' mean?

What are properties of vector-like field/particle? What's the counterpart of it? Chiral like?
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1answer
38 views

Homework help: Finding the min speed for the normal to be zero [closed]

PROBLEM: The pipe AB of length L is moving at a constant speed $v$. Find the min speed that is needed so that point $B$'s normal force is zero $N_B = 0$ The solution starts with: $\bf{a}$$_b = \...
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43 views

Why is the angular average of the direction of the momentum squared a third instead of one?

In the article http://www.nano.northwestern.edu/intranet/pubdocs/quasiclassical.pdf (in going from eq. (6.13) to eq. (6.14)) it is stated that $$\langle\hat{p}\cdot\hat{p}\rangle_{\hat{p}}=\dfrac{1}{3}...
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318 views

Can you explain what's meant by “Effective Force” here?

A small cart is being pulled horizontally to the right with a $20$ lb force $\vec{F}$ making $45^\circ$ angle to the floor. What is the effective force moving the cart forward? Answer: since $\vec{F} ...
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1answer
36 views

A way to determine if a body accelerates or loses speed at a certain time

With given vectors for acceleration and velocity, is there a way to determine if a body accelerates or decelerates at a certain time-interval? Can this be determined, for instance, by simply observing ...
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0answers
37 views

What is a diffusionless fluid?

I'm taking a course in astrophysical fluid dynamics and have come across a problem involving "small diffusionless disturbances" of a fluid. Based on the nature of the course I expect the examiner to ...
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0answers
67 views

how to rotate scaled-vector (orientation) by scaled-vector (rotation)

Recently I seem to have gotten the physics-engine portion of my 3D simulation/game engine [apparently] working correctly. The most convenient way to store and compute position and orientation are in ...
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35 views

How do I show $e_r$ and its first- and second time derivative?

What does a charge q moving in a circular orbit with a constant velocity (a "rotating charge") and a stationary observer that measures the E field look like? And how do I show $e_r$ and its first- and ...
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1answer
278 views

Is the Mass flow rate (Mass flux) a scalar quantity?

Wikipedia states that mass flow rate is a scalar quantity, however Mass Flow Rate= Density x Cross Sectional Area x Velocity and velocity is a vector quantity, so this would imply Mass Flow Rate is ...
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35 views

Write the force as a sum [closed]

We suppose that a force $\overrightarrow{F}$ (for example, the gravity) is applied vertically downwards to an object that is placed at a plane which has an angle of $45^{\circ}$ with the horizantal ...
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1answer
748 views

Quantities that have magnitude and direction but do not obey the parallelogram law [closed]

Back in college, when I'm learning about Vectors, I remember the text book saying.. There are certain quantities that have Magnitude & Direction but doesn't follow the Parallelogram Law of ...
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1answer
499 views

Problem on relative motion involving wind speed .Finding the real velocity of wind?

Here is the question For a person running west at 7km/hr wind appears to blow from north-west .But when he walks towards west at 3km/hr the wind appears to blow from the north. What is the true ...
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49 views

How can a vector have both contra-variant and co-variant components? [duplicate]

I have read that contra-variant and co-variat vectors have different transformation properties , which distinguish them, yet at the same time I have read that a vector can have contra-variant and co-...
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134 views

Time Given Distance and Velocity Vectors [closed]

I recently came across a problem that gives velocity and two positions (which I solved for distance) in vector notations (). My question is, given the vectors for velocity and distance, how do I solve ...
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3answers
147 views

Find time-parametrization given path and speed of a particle [closed]

Consider a particle in two dimensions with position vector $r(t)=<x(t),y(t)>$ and the shape of the path is described by a function $y(t)=f(x(t))$ (Thus $r(t)$ is a parametrization of $f$ with ...
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143 views

Suspended mass in motion free-body diagram [closed]

A 20kg mass is held by two ropes which span 90 from each other. The mass is being accelerated at 1m/s^2 to the right. Draw a free body diagram for the mass and find the numerical values for each force ...
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1answer
26 views

Laboratory fixed-vector components

What are laboratory fixed-vector components? I have an effective Hamiltonian derived from a 40-something year-old Chemical Physics paper. The article mentions the term laboratory fixed-vector ...
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1answer
43 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, ...
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1answer
826 views

Kinematics simple question [closed]

Question: In order to protect himself from the rain, a person is standing holding an umbrella at right angle to the horizontal surface. The rain is falling at 10m/s when the velocity of the wind is ...
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1answer
134 views

Angular velocity vector in terms of motion of an object

May be it is small question in this forum but I'm trying to get the feel of the understanding about the angular velocity. If this question is getting rejected please kindly refer me to appropriate ...
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1answer
590 views

Where do these formulas for an object being pushed up an incline come from? [closed]

An object on an incline with an angle $\theta$ is being pushed at constant speed. Constant speed implies $a = 0$. Because $F=ma$ and the object must have mass greater than 0. If I want to find the ...
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2answers
205 views

Position with respect to time with friction

I'm interested in equations of motion when friction is present for a little graphical side project I am working on. I'm really rusty with physics, so I apologize if this is a basic question or doesn't ...
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148 views

Understanding unit vectors

Trying to understand how the unit vector ${\mathcal{\hat{r}}}$ defined as $\frac{r' - r}{|r' - r|} $ (where $r'$ is the source point) works in this problem: Work out the electric field, $E$, at point ...
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0answers
158 views

Phonon vectors and characteristic length interpretation

Basically I have a set of vectors of unit length, $\{\nu_i\}$, describing the movement of phonons (all orthogonal to each other), $\{\omega_i\}$. Lets say I only have two atoms, $m_1$ and $m_2$. In ...
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2answers
803 views

Why do we say that in Coulomb's law the force is proportional to $\frac{1}{r^{2}}$ and not $\frac{1}{r^{3}}$?

I am going over Coulomb's law and there is something that is a bit confusing for me: According to Coulomb's law, if I have a charge $q_{1}$ at a point $\vec{r_{1}}$ and a charge $q_{2}$ at a point $\...
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3answers
1k views

Basic vector addition problem [closed]

This is the entire problem: A student adds two vectors with magnitudes of 200 and 40. Taking into account significant figures, which is the only possible choice for the magnitude of the resultant? ...
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6answers
273 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 ...
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4answers
345 views

Is $\left|\frac{d\vec{r}}{dt}\right| = \frac{d|\vec{r}|}{dt}\;$?

Is magnitude of instantaneous velocity same as instantaneous speed? More specifically, is $$\left|\frac{d\vec{r}}{dt}\right| = \frac{d|\vec{r}|}{dt}\; $$ Also Is it wrong to say that $\dfrac{d|\vec{...
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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 ...
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2answers
105 views

Unitary operators evolving the set of Pauli matrices

Consider the Heisenberg picture of Quantum Mechanics. For a two state system we have the Pauli matrices evolving according to the relation $$\sigma_i(t)=U^+\sigma_i(0)U$$ where $U=e^{-iHt/\hbar}$ and $...
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3answers
326 views

A force's magnitude

In this question I asked about gravity and in the answers it came up that the magnitude is equal (of the gravity acting on the Sun and the of the gravity acting on the Earth) Does magnitude simply ...
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2answers
182 views

Splitting up a force into horizontal and vertical components?

My Bedford and Fowler textbook (4th edition) has a chapter on numerical solutions. I'm having trouble understanding how the textbook splits up the components of force in the $x$ and $y$ directions to ...
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4answers
484 views

Why can scalars have a sign?

I wondered to myself why some scalars have a sign, if they do not have a direction. After all, the plus and minus indicate the direction of the scalar on a one-dimensional axis. So, for example, why ...
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2answers
231 views

Is torque still a vector in 2 Dimensions?

In 3D, torque is defined as $\vec{r} \times \vec{F}$ which is a vector, therefore having both a direction perpendicular to the plane of $\vec{F}$ and $\vec{r}$ and a magnitude of $\text{F}\cdot\text{r}...
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3answers
295 views

How do we calculate instantaneous velocity in 2D?

Suppose a body is moving with a constant speed of $10~\mathrm{ms^{-1}}$ in negative $x$ direction in $x$-$y$ plane. Let $\vec r$ be the position vector. Then what will be the instantaneous velocity ...
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2answers
85 views

Why does $\hat n \times (\vec E_1 - \vec E_2) =0 $ imply that the tangential electric field components are equal?

On page 8: http://local.eleceng.uct.ac.za/courses/EEE3055F/lecture_notes/2011_old/eee3055f_Ch4_2up.pdfele I don't understand why $E_{t1} = E_{t2}$ is equivalent to $\hat n \times (\vec E_1 - \vec E_2)...
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2answers
2k views

What is going on in the system? How are the formulas $mg \sin(x)$ and $mg \cos(x)$ derived?

When a load is resting on an inclined plane, there is force $mg \sin(x)$ that's vertical to the inclined plane and force $mg \cos(x)$ horizontal to the plane acting on it like this: My textbook ...
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2answers
209 views

Where to take $\theta$ (theta) in a triangle?

This is an inclined surface having and unit vector A. The perpendicular and horizontal surfaces are the components of the inclined surface. We want to find out that how much flux will pass through the ...
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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 ...
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3answers
82 views

Dot product approaches zero as the magnitude of the vectors increase?

Is there such thing? I'm doing some computations on mathematica and I noticed the dot product between two vectors are getting smaller and smaller as I increase the magnitude of the vectors, I'm not ...