# Questions tagged [vectors]

Geometric object with magnitude (length) and direction.

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### Using $v_f = v_0 +at$ for objects in free fall [closed]

I have a question about the difference of using $v_f = v_0 +at$ and $s = v_0t + \frac{1}{2}at^2$ for objects in free fall. I'm trying to solve a problem where there's a ball rolling along an inclined ...
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### How to specify the orientation of an area vector?

We all know that the area of a triangle having consecutive sides as $\vec { a }$ and $\vec { b }$ is $\frac { 1 } { 2 } | \vec { a } \times \vec { b } |$, but what is the direction of that area vector?...
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### Positive work along path [closed]

Consider I have a simple formula for the work along some path (in 1 dimension): $$W~=~\int_{x_0}^{x_1}\vec{F}\cdot d\vec{x}.$$ If I now move from left to right ($x_1 > x_0$) along the axis (...
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### Expressing Fresnel Equations in terms of $\mathbf k$-vectors

Write the Fresnel Equations in terms of the k-vectors (or the propagation constants $\gamma$). Assume that the x-direction is normal to the interface, and the z-direction is parallel to the interface, ...
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### Coriolis force decomposition of angular velocity [closed]

I can’t for the life of me understand how the $\omega$ in this is decomposed to $$\vec{\omega}= \omega (-\sin(\theta),0, \cos(\theta))$$ Any help would be greatly appreciated!
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### Is this Question correct? Newtonian Motion - Relative Motion of Rain

There is a question in a textbook which states: "A cyclist is riding north at 12km/h when it starts to rain. The rain appears to be falling towards her at an angle of 10 degrees relative to the ...
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### What is the real notion/feel of a tensor quantity? [duplicate]

I have been just introduced to the term tensor while studying Rotational Dynamics, particularly about Inertia. But I just don't get a clear line separating vector from a tensor. What does someone mean ...
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### Isn't the velocity in an orbit always tangential, not radial and tangential?

In this video the person resolves the momentum vector into two components, tangential and radial. But isn't the velocity at every point on the orbit tangential?
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### How to determine the direction of instantaneous acceleration in a 2D motion? [duplicate]

How do we determine the direction of instantaneous acceleration when the body is moving in a plane (or a 3D space)? This question has been truly bothering me for nearly two weeks. I looked it up, ...
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### Can velocity in $y$-axis be equal with velocity in $x$-axis?

So if $u_y=30 m/s$ and $u_x=30 m/s$ can we say that $u_y=u_x$? my confusion is because velocity is vector they are not equal ( equal in magnitude but not dimension). But can we say that they are ...
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### What is the difference between a state vector and a basis vector in Quantum mechanics?

I searched about the difference between state vector and basis vector in Quantum mechanics but couldn't find any clear explanation. Can someone please give a simple and clear explanation of this?
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### Instantaneous velocity

So here’s a question I’ve been thinking of for a while. Suppose we say, “an object is having an instantaneous velocity along a particular direction ( say 10 m/s along the $x$-direction)” . Is it fair ...
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### Why, when calculating work done when a person climbs stairs, the distance is the height of the stairs but not the distance the person travels?

I was thinking, since Work Done = Force * Distance moved in the direction of the force , the distance moved in the direction of the force would be the distance of the slanted stairs instead of the ...
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### Basic question about a point mass and the geometry of a general trajectory

Just to ruin the punchline upfront: With this question, I'm trying to do a sanity check about the logic of insisting on a trajectory and only then thinking about forces. I took Classical Mechanics ...