Geometric object with magnitude (length) and direction.

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2answers
134 views

Understanding Tensor-operations, covariance, contravariance, … in the context of Special Relativity

I'm currently learning about special relativity but I'm having a really hard time grasping the Tensor-operations. Let's take the Minkowski scalar product of 2 four-vectors: $$\pmb U . \pmb V = ...
1
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2answers
95 views

Two different formulas

My problem is simple : given a particle of mass $m$, charge $q$ and velocity $\bf{v}$. If $\bf{A}$ denotes the magnetic potential satisfying $\bf{B}= \nabla \times \bf{A}$. I want to etablish the ...
1
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0answers
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 ...
-1
votes
1answer
41 views

Unit Vector Displacement [closed]

A particle starts from the origin at $t = 0$ with a velocity of $+4.0\mathbf{j} \text{ m/s}$ and moves in the $xy$ plane with a constant acceleration of $(6.0\mathbf{i} + 4.0\mathbf{j}) \text{ ...
0
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1answer
29 views

Why direction of angular velocity is taken along the rotational axis?

I read that it is a convention. But what does that mean in physics? If it would have been a sign assigning matter, I could confess but what convention means here? When we decide the direction of ...
-2
votes
2answers
47 views

vector addition - resultant of two vectors [closed]

Suppose two ships are moving in different directions at some angle between them and we have to find the distance between them we use the formula$R^2=a^2+b^2-2ab\cos\theta$ But if we have to find the ...
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1answer
73 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) ...
-2
votes
1answer
55 views

Mnemonic for vector cross versus dot? [closed]

I'm always stuck to remember the difference between vector multiplication with dot product versus cross product? Is there any mnemonic so that I can easily remember which is which?
3
votes
1answer
105 views

What is the difference between scalar and vector mesons?

My understanding is that vectors and pseudooscalars change sign under parity operation and pseudovectors and scalars do not. However, I don't understand what the difference between a vector and ...
3
votes
2answers
77 views

Heuristic explanation of the difference between vectors and scalars in physics

I'm trying to give a student a (physically) intuitive, heuristic explanation as to why certain quantities are vectors and others are scalars. Here is what I have come up with: Scalars are quantities ...
0
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1answer
40 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 ...
1
vote
1answer
103 views

Dropping objects on a rotating disc: angular momentum?

I'm designing a very simplistic particle simulator. Particles are dropped on a spinning disc and then bounce back (although lose some momentum due to the friction of the disc). I'm working with an ...
0
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2answers
35 views

Nature of Pressure

Pressure is defined as force per unit area. Therefore, pressure = force divided by area. Since force and area are both vectors, how can we perform this division without violating the rule of vectors? ...
0
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3answers
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 $\vec{c}$ ...
0
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1answer
45 views

Why trajectories approach to origin tangent to the slower direction?

I am reading non-linear dynamics from Strogartz. Suppose, I have two solutions of a non linear system: $x(t) = x_0e^{at}$ and $y(t) = y_0e^{-t}$, where $a\in \mathbb{R}$. Now it is clear that,for ...
0
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0answers
26 views

what is significance of direction of vector product(torque & angular momentum)?how can one use them practically? [duplicate]

since i came across vector product or cross product i have one doubt that is what direction of torque shows.the direction of product is along axis of rotation(+ve or -ve).is there is any practical use ...
0
votes
1answer
79 views

Cumulative distance formula

I am working with position recordings over time. Basically, I record the position of animals in a treadmill. They can go forwards or backwards. Hence, position can increase or decrease. However, I am ...
1
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0answers
48 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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0answers
39 views

What does 'vector-like' mean?

What are properties of vector-like field/particle? What's the counterpart of it? Chiral like?
0
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0answers
75 views

Direction vector for gravity

I have co-ordinate axes on the earth's surface (and I've been told these are the axes I have to use). Ignoring z, I have x and y axes. The question asks me to calculate the acceleration due to ...
-1
votes
1answer
33 views

Velocity and acceleration (as vectors) in a straight line

A student is trying to determine the acceleration of a feather as she drops it to the ground. If the student is looking to achieve a positive velocity and positive acceleration, what is the most ...
0
votes
2answers
44 views

How can I calculate the change in velocity? [closed]

"A runner runs at 4 m/s on a circular track constantly. A and B are opposite points on the track, so A is the starting point and B is halfway around the track. Calculate his change in velocity from A ...
0
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2answers
83 views

Resolving resultant force into the components

I hate to use this medium in the wrong way, and I understand the fundamental principles to this question. However, The question goes that you must resolve the resultant force (R=500N) into its ...
0
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0answers
22 views

cross product-physical inter [duplicate]

What is the physical interpretation of dot and cross product?Geometrically axb means the area of parallelogram with two sides a&b.But what are we actually doing when we are doing axb
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1answer
248 views

Commutation of vector operators

I'm supposed to show that $\left[\mathbf A,\mathbf B\right]=0$ (for two vector operators $\mathbf A$ and $\mathbf B$) if and only if all components of $\mathbf A$ commute with all components of ...
-1
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2answers
54 views

Why not use only vectors to describe the motion of objects?

We know that kinematics terms such as distance, displacement, speed, velocity and acceleration are categorised into 2 groups, mainly scalars or vectors. Words categorised into vectors describe the ...
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votes
2answers
45 views

Magnetic field due to current, I don't get how you get the direction, can someone draw it for me? [closed]

Taken from here, 3rd problem. As you can see, no matter from which point current goes, from a to b or from b to a, in either cases, magnetic field would be down, right?
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1answer
86 views

Is there an online course in Mathematical Methods for Physics, Covering Matrices and Vector Analysis? [duplicate]

I am taking a course in Mathematical Methods for physicsPhysics (Junior Level). We are working from > Mathematical Methods for physicists, George B.Arfken . I just need online resources ...
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votes
1answer
69 views

Vectors and Scalars [closed]

How is Momentum $mv$ integrate form a Vector product to produce a Scalar [ Kinetic Energy $(1/2)mv^2$]? Is this mathematical proof of the vector to scalar change in Absolute Calculus, Number Theory, ...
0
votes
1answer
89 views

Newton Mechanics [closed]

I am confused about this question, what does it mean? A particle has a mass of $2\ \mathrm{kg}$ and a force $$F = 24t^2 i + ( 36t - 6 ) j - 12tk$$ acting on it. At the time $t = 0$ the particle is at ...
0
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0answers
34 views

Why does the angular average of the divergence result in a factor 1/3?

In going from eq.(6.13) to (6.14) in http://www.nano.northwestern.edu/intranet/pubdocs/quasiclassical.pdf it is assumed that ...
1
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1answer
75 views

Understanding elastic collisions of objects with the same velocities

I am having trouble understanding the following statement from my book: The law of cosines tells us that if the sides of a triangle obey the Pythagorean formula, they must form a right triangle. ...
0
votes
2answers
112 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 ...
2
votes
1answer
139 views

What's the difference between classical and quantum vector superposition?

$(1)$Since quantum-mechanical states between two consecutive measurements are represented as superposition of orthonormal basis vectors in a vector space, at first glance it seems like it makes sense ...
1
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1answer
28 views

Is it possible to determine when an accelerometer is in a vibrating state compared to a non-vibrating state?

I would like to know if so, how raw 3-axis accelerometer data could be analyzed and manipulated real-time to register periods of vibration. The device being used has a max sample rate of 62Hz (I ...
1
vote
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 = ...
1
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0answers
41 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 ...
2
votes
3answers
302 views

Why are triangles drawn like so when working with gravity on an inclined plane?

This is my first year as a physics student, and I've never learned about vectors past a basic level, so this is confusing me. When we have gravity on an inclined plane, we separate it into two ...
-2
votes
1answer
34 views

Using resultant vectors to calculate how long it takes to travel a distance [closed]

A box of books weighing $320 \;\mathrm{N}$ is shoved across the floor of an apartment by a force of $569 \;\mathrm{N}$ exerted downward at an angle of $36.5^\circ$ below the horizontal. The ...
4
votes
4answers
209 views

Do $\vec r$ and $d \vec r$ have the same direction?

One question is bugging me for a long time but I couldn't make out anything nor could my friends. Here it goes: We know, $\vec r$ is regarded as the position vector. So we can say, $$\vec r \cdot\vec ...
1
vote
1answer
80 views

When to use a whole vector approach vs an energy approach?

My professor has just introduced two new ways to solve projectile motions. One approach involve using trigonometry and vectors and the other involves using the idea of conservation of energy. My ...
0
votes
1answer
60 views

Why the point right below the center of a rolling ball on the ball has zero instantaneous velocity [duplicate]

Suppose there is a snooker ball rolling on a table. The velocity of the center of the ball is Rω and its direction is horizontally right. I don't understand why the point right below the center on the ...
0
votes
3answers
99 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 ...
0
votes
1answer
49 views

What is the change in velocity? [closed]

A boat moves with a velocity of 22 m/s directly west. Later, the boat is found to have a velocity of 12 m/s at 45° S of W. What is the change of velocity? I want to do this vector wise. I know that ...
0
votes
0answers
26 views

Pressure as a scalar? [duplicate]

Why do treat pressure as a scalar? We know that $P=F/A$ (Pressure = Force/Area) and force is vector quantity, so then why should pressure not be a vector?
-1
votes
1answer
58 views

Value of $g$ in projectile problems

A cannon has a muzzle speed velocity Vo of 60.0m/s, at what angle theta should it be aimed to strike a distance 320 meters away. Ignore air resistance So I get how to set this up but I am ...
1
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0answers
211 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} ...
3
votes
3answers
172 views

4-velocities in different frames

We have an observer in an inertial frame $S$ who measures a particle's 4-velocity as $U$. We then have another inertial frame $S'$ with $X'=\Lambda{X}$, where $\Lambda$ is a matrix representing a ...
0
votes
1answer
107 views

Proving the invariance of the inner product

If we define the inner product as ${\textbf{u}\cdot\textbf{v}=g_{ij}u^{i}v^{j}}$, where ${g_{ij}}$ is the metric tensor, ${S}$ and ${T}$ are transformation matrices, ${S}$-for covariant indices and ...
-1
votes
4answers
385 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 ...