Geometric object with magnitude (length) and direction.

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2answers
75 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 ...
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2answers
6k views

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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3answers
4k 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. ...
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3answers
83 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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3answers
170 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, ...
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3answers
230 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, ...
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1answer
191 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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2answers
361 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
238 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
720 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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2answers
331 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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2answers
134 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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3answers
2k views

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? ...
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2answers
396 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 ...
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2answers
50 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
87 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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3answers
110 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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3answers
984 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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2answers
222 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, ...
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1answer
631 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 ...
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2answers
220 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
120 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
239 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
221 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
147 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 $\hat{L}^2$: ...
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3answers
372 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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votes
1answer
150 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
198 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
314 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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2answers
1k views

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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2answers
949 views

Understanding weight on an inclined plane

I'm trying to solve a problem where I have an object resting on an inclined plane, with the angle of the plan being alpha, and the weight being w. I'm having trouble figuring out how I can calculate ...
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2answers
19 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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1answer
26 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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4answers
74 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 ...
0
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1answer
62 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
69 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
32 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
78 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 ...
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2answers
67 views

Distance traveled from displacement

I am currently reading a book called Physics for Scientists and Engineers by Serway. While reading the chapter about 2-dimensional kinematics, I asked myself a ...
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3answers
724 views

resultant of 3 vectors along sides of equilateral triangle [closed]

It is a homework problem, but I really don't quite understand the question. It reads- "3 forces of magnitudes 10N, 20N, and 30N acting on a point are parallel to the sides of an equilateral triangle, ...
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2answers
94 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 ...
0
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1answer
83 views

Newton's third law of motion versus Work

Newton third law of motion says that "To every action, there is always an equal and opposite reaction". The vector study tells us that if two vectors are of same nature and equal magnitude but ...
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1answer
54 views

Can changing representation change the meaning of density operator?

I had posted a question What is the actual meaning of the density operator?. After that I understood that if I have the expression of a density operator $$\rho=\sum_{i=1}^{i=k}p_i|\psi_i\rangle ...
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2answers
510 views

How to determine velocity vector direction with respect to acceleration.

I'm currently writing a program that attempts to simulate particle movement in a gravitational field with more than one object exerting a force on it. I decided that I'd have the particle move by ...
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1answer
1k views

How can kinetic energy be conserved in an elastic collision

How can kinetic energy be conserved in an elastic collision as collision is said to occur between two bodies if they physically collide against each other or if the path of one of then is affected by ...
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1answer
65 views

Gradient of two-particle system

I'm working on problem 5.1a from Griffiths Intro to QM and given that: $$\mathbf R \equiv \frac{m_1\mathbf{r_1} + m_2 \bf r_2}{m_1+m_2}$$ and $\bf r \equiv \bf r_1 - \bf r_2$ I need to show that, ...
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3answers
337 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 ...
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1answer
99 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 ...
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2answers
160 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 ...
0
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1answer
209 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 ...