Geometric object with magnitude (length) and direction.

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4answers
76 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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1answer
75 views

What are some good resources for learning how to apply vectors in physics?

Although I don't have any problems with vectors when using them in Mathematics but I am having a hard time using them in physics. It is really frustrating me. Can you please recommend me some good ...
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2answers
64 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.
1
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1answer
64 views

Curl of a vector field with two different systems of coordinates

Let $$\mathbf{H} = H_x \mathbf{u}_x + H_y \mathbf{u}_y + H_z \mathbf{u}_z$$ be a vector field whose components are defined with respect to the unit vectors $\mathbf{u}_x$, $\mathbf{u}_y$ and ...
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1answer
46 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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1answer
96 views

Intuitive meaning of Dot Product [duplicate]

I know intuitively that the Cross Product of two vectors $\vec{A}$ and $\vec{B}$ represents another vector $\vec{A \times B}$ perpendicular to it. In study of physics we come across this situation a ...
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5answers
2k views

Can we divide two vectors?

Can we divide two vector quantities? For eg., Pressure( a scalar) equals force (a vector) divided by area (a vector).
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1answer
91 views

Contradiction of a scalar product

Can anyone resolve this contradiction: ...
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2answers
77 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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1answer
34 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 ...
2
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1answer
92 views

Understanding vectors in an example

I just read an example of vectors in my book which is confusing me. Three particles A,B and C are at the vertices of an equilateral trinagle ABC. Each of the particle moves with constant speed v. ...
3
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2answers
245 views

Why the generators of boosts transform like a vector under rotation?

$$\left[J_i,J_j \right]=i\epsilon_{ijk}J_k$$ $$\left[J_i,M_j \right]=i\epsilon_{ijk}M_k$$ $$\left[M_i,M_j \right]=-i\epsilon_{ijk}J_k$$ where $J_i$ is the generator of rotation of Lorentz group, $M_i$ ...
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1answer
34 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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2answers
59 views

2D vector components

Can any equation with a vector e.g. velocity be used with just the horizontal or just the vertical components, I am thinking of equations like Newton's laws, conservation of linear momentum etc. So ...
1
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1answer
82 views

Plane Polar coordinates for simple pendulum in moving lift(elevator) [closed]

Can any one help me with the following. A simple pendulum is suspended from the ceiling of a lift. It is moving upward with acceleration $a$. The string of the effective length of the pendulum makes ...
0
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1answer
90 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 $\hat{L}^2$: ...
2
votes
4answers
130 views

Sum of acceleration vectors

If a point mass has some accelerations $\mathbf{a_1} $ and $\mathbf{a_2} $, why is mathematically true that the "total" acceleration is $\mathbf{a}= \mathbf {a_1}+\mathbf {a_2}$?
2
votes
1answer
116 views

What is the physical interpretation of the dot/inner/scalar product of two vectors?

What is the physical interpretation of the dot/inner/scalar product of two vectors? See, if we multiply two scalars like 2*3 we say two times three is six. I also do understand multiplication of ...
16
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8answers
964 views

Is it foolish to distinguish between covariant and contravariant vectors?

A vector space is a set whose elements satisfy certain axioms. Now there are physical entities that satisfy these properties, which may not be arrows. A co-ordinate transformation is linear map from a ...
3
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2answers
86 views

Scattering geometry question

While reading up on light scattering I came across this slide: My vector maths is a bit rusty and I am having trouble understanding the last term (scattering geometry). What is the significance of ...
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3answers
160 views

More about the Right Hand Rule?

We started learning about electromagnetism in physics class, and the Right Hand Rule comes in handy as seems easy to use, but I'm curious as to how it actually works. I guess it's more of a math ...
1
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1answer
170 views

Finding angular momentum about the center of mass?

If we have a couple of particles of an equal, unknown mass: $$r_{+} = (c + e^{-Bt} \cos({\theta}))\textbf{x} + (d + e^{-Bt} \sin({\theta}))\textbf{y}$$ $$r_{-} = (c - e^{-Bt} ...
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1answer
87 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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5answers
73 views

Why is the independence of orthogonal vector-quantities always implicit in books/lectures?

The "theorem" that I can "just" separately deal with orthogonal quantities (like horizontal and vertical force or velocity, etc), I never found explicitly mentioned, but just implicitly in the ...
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3answers
112 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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1answer
137 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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1answer
285 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 ...
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1answer
98 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)}\\ ...
2
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1answer
272 views

Laws of addition of Vectors

How Triangle Law and Parallelogram law of addition of Vectors are different?Ain't they. Please don't tell me the things written in book......give me the appropriate reason.And how do i distinguish ...
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0answers
22 views

What are direction ratios? [duplicate]

What are direction ratios and how are they useful in studying vectors? How are these different from direction cosines?
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2answers
103 views

Differentiating a vector product

$$m_i\mathbf{r}_i\times\frac{\mathrm{d}^2\mathbf{r}_i}{\mathrm{d}t^2} = \frac{\mathrm{d}}{\mathrm{d}t}\biggl(m_i\mathbf{r}_i\times\frac{\mathrm{d}\mathbf{r}_i}{\mathrm{d}t}\biggr)$$ I do not ...
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1answer
161 views

Why consider only direction cosines?

Why are these called direction angles? Why do we consider only direction cosines and not direction sines or tans. What is its actual significance? And How to use them? Why are they called ...
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2answers
85 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 ...
3
votes
1answer
57 views

On a horizontal plane, why does $F_N=W$?

I keep seeing this definition everywhere, but I don't understand. The forces of the weight and the normal force are going in opposite directions, so shouldn't $F_N=-W$?
2
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1answer
242 views

Line of action force

The task is to reduce the two forces into a single net force and then find the equation of its line of action. I chose to find the net force and momentum with respect to the origin. The magnitude of ...
2
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4answers
4k views

What does the magnitude of the acceleration mean?

I am a little confused as to what the magnitude of acceleration is and what it means.
2
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3answers
558 views

The velocity formula $\mathbf{v} = \mathbf{u} + \mathbf{a}t$ for 1D, 2D, 3D . What is the difference?

Could I use $\mathbf{v} = \mathbf{u} + \mathbf{a}t$ for calculating velocity in these 3 different dimensions? If not, what's the difference between these 3 dimensions? How would you calculate ...
0
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1answer
68 views

Why does precession only occur at high angular speeds?

I'm trying to understand precession for a gyroscope or top. I do understand why precession occurs using the vectors for the weight force and torque and angular momentum. But what I don't understand ...
0
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1answer
60 views

Some subtleties in direction of drag force

Consider a body released from a height $h$ and assume a drag force is linearly proportional to the velocity. Then by Newton's Second Law, $$m\mathbf{\dot{v}} = \mathbf{F_g} + \mathbf{F_{drag}} = ...
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0answers
66 views

Vector Derivative Transport Theorem Application

I have a position vector in frame A, the derivative of which I want to take relative to an observer in frame B. I apply the Vector Derivative Transport Theorem. The obtained velocity vector is left in ...
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2answers
147 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
60 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 ...
3
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0answers
77 views

Sound - for purposes of vibration

What is the best way to distribute noise from more than one source (I'm envisioning a system with many), within a dome, with the ground as its primary target, at optimal frequencies and volumes to ...
0
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2answers
74 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 ...
2
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1answer
289 views

The curl of a special cross product

When given two vectors $\mathbf{A}$ and $\mathbf{B}$, the curl of the cross product of these two is given by ...
1
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2answers
159 views

Need clearing up on vector decomposition in motion physics

I've been pursuing physics on my own, and I need something cleared up. Say I have two arbitrary objects, I have their velocities, I know when the collide, I have their normal vectors, etc. I know ...
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0answers
49 views

Vector Equilibrium

I'm trying to understand more about this 'vector equilibrium' apparently coined by R.Buckminster Fuller. In this site (http://cosmometry.net/), it claims: "The Vector Equilibrium, as its name ...
4
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2answers
404 views

Understanding the difference between co- and contra-variant vectors

I am looking at the 4-vector treatment of special relativity, but I have had no formal training in Tensor algebra and thus am having difficulty understanding some of the concepts which appear. One ...
4
votes
4answers
4k views

Why is current a scalar quantity?

Current has both magnitude and direction. As per the definition of vector defined in encyclopedia, current should be a vector quantity. But, we know that current is a scalar quantity. What is the ...
0
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1answer
119 views

What is this vector problem asking to find, the magnitude of the force F or the component of it that goes along the ramp?

A shopper pushes a 7.5-kg shopping cart up a 13 (degree)incline. Find the magnitude of the horizontal force, F, needed to give the cart an acceleration of 1.41 m/s$^2$. I ask this because the ...