# Tag Info

## Hot answers tagged vectors

### How can forces be added?

It is self-evident that successive displacements add by the tail-to-head arrow method. Velocities, being rates of change of displacement, add in the same way, as must momenta, and therefore forces, ...
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### How can forces be added?

Here is one way of looking at it that might help you. To add vector A to vector B in the diagrams you provided, take each vector and draw its horizontal and vertical component like in this image. It ...
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### How can forces be added?

The idea of vectors addition, subtraction, resolution, etc. is found everywhere in life. Using basic trigonometry, one could show that some force $F$ that makes an angle $\theta$ with the horizontal ...
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### What is $k$ in this form of the wave equation?

This is a static field, so not really a wave. This however: $$\vec{E}=E_0\vec{n}\,\cos(\omega t-\vec{k}.\vec{r})$$ is a wave. $\vec{k}$ is called the wavevector: its norm is the wave number its ...
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### How can forces be added?

Let's rearrange this last situation as you are regarding force instead of displacement. The above diagram actually more likely represent displacement. The forces seems to be on seperate points. This ...

### Does acceleration acting on velocity only change direction or magnitude both?

Well, I am not sure about your physics background so I attempt to explain the issue conceptually without the use of calculus or vectors. For starters, let us clear up what you have done in your "...

### How do you show that the temporal part of an object's 4-velocity is decreasing as that object approaches the speed of light?

In special relativity, with the most negative convention and $u^{\rho}$ the four velocity, we have: $$u^{0}=\gamma c=\frac{c}{\sqrt{1-\frac{\vec{v}^2}{c^2}}}$$ From here we see that if $\vec{v}^2$ ...
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### Why can't we take the larger angle in Cross Product?

Using the angle $2\pi - \phi$ would result in a vector pointing in the opposite direction as the standard cross product since $\sin(2\pi - \phi) = -\sin\phi.$ You could define another vector product ...
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### Is torque possible without any pivot point?

I'm assuming that the only forces actually applied to the bar are P and Q as I show in FIG 1 below. Then you are saying equivalent result force is P + Q = 15 located at point C. But you didn’t go far ...
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### Gradient of scalar field

OP's eq. (1) follows from Poincare lemma: The co-vector/1-form $$\omega~:=~\frac{ X_a\mathrm{d}x^a}{\ X^2}\tag{A}$$ is closed $$\mathrm{d}\omega~=~0,\tag{B}$$ and hence locally exact, i.e. on the form ...
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### Is torque possible without any pivot point?

The acceleration of the center of mass (CM) is determined by the net external force. The net torque is the change in the angular momentum if you use the CM as the point about which to evaluate torque ...
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### How to draw vectors?

For one thing, if $F_x$ and $F_y$ are components of $\vec F$, they are usually drawn not to extend beyond the projection of $\vec F$ in that direction. E.g. the $F_x$ arrow in Fig 1 should be much ...
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### Two forces act on a body as shown

Length of the arrows proportional to the magnitude of the force, an then draw the force parallelogram or triangle.
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### Circular motion equivalent in three dimensions

We can consider circular motion at constant angular velocity in an arbitrary number of dimensions $D$. In 2 dimensions, we have formulas like $v=\omega r$, $F=v^2/r=\omega^2 r$. We're dealing with ...
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