Geometric object with magnitude (length) and direction.

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Is a vector and a unit vector dimensionless

Lets say I have a position vector $\vec r$. Is it dimensionless or does it have a dimension of length i.e $[L]$. Also does the unit vector $\hat r$ have a dimension?
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78 views

Isn't this statement regarding projectile motion wrong?

Isn't this statement regarding projectile motion wrong? If a body is thrown at an angle to the horizontal with initial velocity $u$, then displacement of body as a function of time is $\vec{s}=\...
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Confused on how to properly use right hand rule

I am having trouble using the right hand rule properly and often find myself putting my hand in awkward orientations. I know you point your hand in the direction of $r$ and then point your fingers in ...
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5k views

How do I find the tension in additional strings in this problem? [closed]

A mass of 5.00 kg hangs attached to three strings as shown in the figure (see image below). Find the tension in each string. Hint: Consider the equilibrium of the point where the strings join. So ...
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1answer
48 views

Norm of the momentum 4-vector

The norm of the momentum 4-vector is $\mathbf{P}.\mathbf{P}$ $= (\gamma mc, \gamma mv).(\gamma mc, \gamma mv) = \gamma mc^2 - \gamma mv^2$ But why is $\gamma mc^2 - \gamma mv^2 = mc^2$?
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86 views

Can we find a vector if its dot product and cross product with another vector is given?

If I have two vectors $\vec{b}$ and $\vec{v}$, and I know that $$ \vec{b} \times \vec{v} = \vec{c} $$ and $$ \vec{b}\cdot\vec{v} = \lambda $$ can I find the $\vec{v}$ vector in terms of the $\vec{c}$ ...
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122 views

Why taking components of a component of a vector is invalid?

Suppose there's a force $F$ of magnitude 10 newtons in the direction of positive y-axis acting on a particle A. I know that the particle would not experience any force in the positive x-direction ...
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192 views

Tension on a string

A string is attached at both extremities and put under tension $T_0$ at rest. We know that if we pull the string upwards from the middle, the tension will increase. But why is it that, admittedly, $$T\...
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339 views

What force $\vec{F_{1}}$ is needed to balance the beam in the diagram below? [closed]

What force $\vec{F_{1}}$ is needed to balance the beam in the diagram below? I know that $\sum \vec{F}$ must equal zero. I also know that since the unknown force is farther from the pivot, it ...
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1answer
224 views

Question about resolving forces

Say, in the example below, the weight $mg$ of the object is $800N$. To find $R$, the conventional method is to use $R\sin(28^\circ) = 800$. But why isn't it possible to use instead the component of ...
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156 views

How to derive the commutation relationship between $\hat{L}^2$ and $\hat{\textbf{p}}$ [closed]

How to prove that $$[\hat{L}^2,\hat{\textbf{p}}] = i\hbar(\hat{\textbf{p}}\times\hat{\textbf{L}} - \hat{\textbf{L}} \times \hat{\textbf{p}})$$ I tried to expand $\hat{L}^2$: $$[\hat{L}^2,\hat{\...
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450 views

Mathematically determining the direction of torque?

I need to mathematically derive the direction of torque in a 2D plane(clockwise/anticlockwise), for a physics engine. I have torque calculated, but it is always positive, so rotation always is in the ...
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2answers
256 views

Relative velocity of boat

I am trying to understand fully the following question: A boat is traveling west at 100m/s and is partially helped by a strong wind blowing at 20m/s 30 degrees north of west. What speed could the ...
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1answer
761 views

A very elementary question regarding force of friction

When I first studied friction I faced f = $\mu$ N where f is force of friction, $\mu$ is coefficient of friction for the surface considered and N is the normal force for the body on surface. Now f is ...
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362 views

Meaning of juxtaposition of vectors

I came across some notation that I can't quite understand: $$ \hat{r}\hat{r} - \textbf{1}_3$$ where $\textbf{1}_3$ is the 3$\times$3 identity matrix, $\hat{r}$ is a unit 1$\times$3 vector, and the ...
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135 views

Showing $ m\int \frac{d\textbf{v}}{dt} \dot \normalsize \textbf{v}dt = \frac{m}{2}\int \frac{d(v^2)}{dt}{}dt$

Can someone please explain how this equation is valid, using intermediate steps if available? $$ m\int \frac{d\textbf{v}}{dt} \dot \normalsize \textbf{v}dt = \frac{m}{2}\int \frac{d(v^2)}{dt}{}dt$$ ...
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Direction of Magnetic force from a current running through a coil of wire

What is the direction is the magnetic force vectors pointing from a coil of wire that has current running through it? http://www.ndt-ed.org/EducationResources/CommunityCollege/MagParticle/Graphics/...
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404 views

vector cross products

Lets say you have a free particle in a rotating frame of reference with constant angular velocity $\mathbf{\omega}$. By free, I mean there are no real forces on it. Lets call the moving system "primed"...
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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. $$v=x \hat i+y \hat j+z \hat k$$ $$v=xe_x+ye_y+ze_z$$ ...
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2answers
51 views

Can vector components be in turn decomposed? [duplicate]

I've a basic (and maybe obvious even if I don't see it) question on the decomposition of a vector in physics. An example of situation I'm confused about is the inclined plane with an object on it. ...
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192 views

Definition of Position Vectors

I have a few (possibly very stupid) questions relating to position vectors; more specifically my confusion about them. Following Halliday and Resnick's text, we define vectors by their magnitude and ...
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69 views

The Vectors in $v=f\lambda$

We are learning about waves in physics and I was just wondering what are the vectors and what are the scalars in this function:$$v=f\lambda$$ I know the velocity $v$ is a vector so that means that: ...
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3answers
105 views

Confusion in distinguishing between scalars and vectors

Torque is an example of cross product of two vectors. But in that example length of the spanner is taken as one vector. But length ,distances are all scalars. How can we take it as vector ,it has no ...
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113 views

Difference between $|d{\bf r}|$ and $d|{\bf r}|$

What is the difference between $|d{\bf r}|$ and $d|{\bf r}|$ and why are both of them not always equal to each other? My question might seem stupid to some and will probably get downvoted but I have ...
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2k views

Can we have physical quantities which have magnitude and direction but are not vectors?

I am not able to understand how to approach the question. Vectors are defined as quantities having magnitude and direction, then how is it possible? Please explain.
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227 views

Force vs. impulse: what is the math description of their interaction?

In this image there are two forces acting on the same body, and we can decribe them mathematically and geometrically using vectors and the palallelogram rule. NOw, suppose the box (stone, bullet..., $...
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1answer
859 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 boat....
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2answers
291 views

Is there a difference in handwritten nabla $\vec{\nabla}$ with an overset arrow and typeset nabla $\nabla$?

According to some physicist at KIT it is usual to write the following when using pen and paper: whereas in typeset texts you write $\nabla$. Is that true? Are there sources for this convention?
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1answer
137 views

Can a vector be defined by invariance of some algebraic operation to translations rather than rotations?

Every physics book I've come across defines a vector as an n-tuple of numbers that can be combined via an inner product that's invariant to rotations. Is it possible to instead define a vector via ...
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1answer
275 views

Flow rate is calculated only using the parallel component of the velocity vector

Flow rate is calculated using only the parallel component of the velocity vector to the area vector. Why is this? How can I mathematically prove this? Namely, how do I prove any perpendicular ...
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4answers
298 views

The work done by running in a rectangle

This may be quite off-topic but please help me. Is there any work done when I run in a rectangle? I thought that the answer should be no. But my teacher says that we should calculate each side ...
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576 views

We need to find unit vector along the reflected ray [closed]

A ray of light on a plane mirror comes along a vector $i+j-k$ The normal on incidence point is along $i+j$ we need to find unit vector along the reflected ray. I am not able to solve and draw the ...
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250 views

Animating an Acceleration Vector - Acceleration of object on a crested path in gravitational field

So I was reading in Chapter 3 of my textbook, Sears & Zemanksky's University Physics with Modern Physics by Young and Freedman, 13th Edition, and the discussion took us to a definition of the ...
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1answer
171 views

Vectors and motion in a plane [closed]

A particle travels with speed $50 m/s$ from the point $(3,-7)$ in the direction $7i-24j$ . Find its positional vector after 3 seconds. My approach: It has travelled a distance of 150m in the ...
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1answer
202 views

Vector Addition — Direction

Say we have three forces $F_1, F_2, F_3$, such that $$ F_1 + F_2 - F_3 = 0\hspace 10mm (1) $$ And let us say that $F_1$ and $F_2$ have the same direction and magnitude, and that $F_3$ has double the ...
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1answer
326 views

Component of force field tangent to a curve

I recently had to solve the following problem: A force $F=10\hat x- 8\hat y$ is applied to an object that is constrained to travel towards increasing values of x along the path defined by $y=x^2$ ...
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Vector Nature Of Angular Velocity

I am currently reading about angular position, angular velocity, and angular acceleration. I came across this paragraph that was particularly confusing, and was wondering if someone could perhaps help ...
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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 ...
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3answers
64 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 ...
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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 ...
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2answers
84 views

Am I wrong about the right hand grip rule?

The right hand grip rule (also known as right hand screw rule) tells you the direction of a magnetic field due to a current. If you point your thumb in the direction of the current, your fingers will ...
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1answer
76 views

Why does the equality $\int \mathbf{r}\times \nabla f d\nu=0$ holds? [closed]

My question comes from Problem 4. Classical laws for angular motion of Practical Quantum Mechanics. And the Prob.4 is that, To show that the classical relation between angular momentum $\mathbf{...
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4answers
117 views

When is the direction of the static friction negative?

i thought that the force of static friction exerted on an object is always going in the opposite direction of any other force exerted on the same object. however, this problem seems to disregard that ...
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1answer
71 views

Why does vector addition work in physics? [closed]

How do we know for sure that vector addition works while working in 2D?Is there a mathematical proof for this?
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72 views

Find the magnitude of the resultant force which these engines exert on the rocket?

A rocket fires two engines simultaneously. One produces a thrust of 760N directly forward while the other gives a thrust of 484N at an angle 34.0 degrees above the forward direction. What is the ...
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88 views

When writing a differential equation, when do you take $+\text{d}x$ and when do you take $-\text{d}x$?

When writing a differential equation I'm confused as to when to write $+\text{d}x$ a and when to write $-\text{d}x$ a where $x$ represents some quantity. For example, I wanted to derive the equation ...
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1answer
82 views

How should speed be expressed in Frenet-Serret frame of reference? [closed]

I'm looking for the equation of motion of the ball on a vertical plane with a cylindrical profile. I guess that means I have to use the frame of reference of Frenet-Serret here. Why is the speed of ...
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1answer
76 views

Bounced ray angle of normal direction? (SOLVED) [closed]

TL;DR whats the position of C. I'm currently programming something and for some reason I having problem figuring this one out, imagine having a ray / or ball bouncing (without mass or gravity etc) ...
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1answer
42 views

New direction vector after collision of spheres [closed]

I have a volume in 3-space in which random spheres are spawned in motion. They have the following attributes to them: position known (in three axes) a direction vector (in three axes) a scalar speed ...
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2answers
123 views

When does angular position, or angular displacement, not obey the rules of vector addition?

The only examples I've found talk about rotating an object about one axis and then about another axis. When you reverse the order, the object ends up in a different position. However, as those ...