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7 votes
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Difference between point force and force

Newtons law do not only work with point forces, It works with all forces associated with a vector field. Finding the force to a non point object requires integration. The most standard way a force is ...
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6 votes
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Meaning of "$=$" in $\vec{F}=m\vec{a}$ (for example)

I don't understand how the two could really be one and the same. E.g. we can exert forces $F$ and $-F$ on a body and it's acceleration will not change. $\vec{F}$ in the $\vec{F}=m\vec{a}$ is the net ...
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4 votes

About Contact, Normal and Friction force

We know that the basic expression for the friction is $$f_a = \mu N$$ That's the basic equation for kinetic friction where $f_{k}=\mu_kN$ and $\mu_k$ is the coefficient of kinetic friction. In the ...
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3 votes

Meaning of "$=$" in $\vec{F}=m\vec{a}$ (for example)

In physics equations (as in mathematics), symbol "=" (equals) means equality in value, not identity of concepts. So in the equation $$ \mathbf F = m\mathbf a $$ the two sides are not "...
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3 votes

Difference between point force and force

An object, or a body, consists of particles. You can think of body as a collection of particles. Each particle has its mass and its coordinates in respect to origin of chosen coordinate system. Body ...
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3 votes

Difference between point force and force

In most problems in high school we assume the body as rigid,so it doesn't make any difference if the force is point load or a distributed load. But if you see in practice the point load will cause ...
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3 votes

Why does Griffiths Example 5.5, assume the distance from wire to be $1$?

Remember that $\hat{r}$ denotes a unit vector. So $|\hat{r}| = 1$ by definition.
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  • 1,610
2 votes
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On the superposition of forces

Don't vectors of the same kind add according to the superposition principle? All forces are indeed vector quantities as is dictated by geometry (force equals to change of momentum and change of ...
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  • 5,451
2 votes
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Show that the contraction of a covector and a vector is Lorentz invariant

$s=\omega_\mu V^\mu$ is scalar. It has "no" indices; the $\mu$ that looks like an index is internal to the definition of $s$ (it is summed over), in the same way that $c=\int_0^5x\,dx$ is a ...
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2 votes

How would I normalize this ket vector?

Let \begin{equation} |\phi \rangle = |x\rangle + | y \rangle - | z \rangle \end{equation} Then the normalized state $|\Psi\rangle$ satisfies $\langle \Psi | \Psi \rangle = 1$ and is given in terms of $...
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2 votes
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Minkowski's equation of motion

I'm trying to prove $f^{\mu}U_{\mu}=0$ for four-force $f^{\mu}=c\frac{dP^{\mu}}{ds}$ and four-velocity $U_{\mu}$. I start by using the chain rule, $f^{\mu}=c\frac{dP^{\mu}}{dt}\frac{dt}{ds}=\gamma\...
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1 vote
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Contravariant Vector Component Transformation from Polar to Cartesian

It's because basis are defined with satisfying normalization condition. Basis are covariant, because they are partial derivatives(Consider them as gradient). $$\hat{r} = \frac{\partial}{\partial r} = ...
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  • 193
1 vote

How do we assume the direction of $u_{\theta}$ and $u_{r}$ in polar coordinate systems?

As a rule, $\hat{u}_X$ is always pointing in the direction along which $X$ grows. It works when $X$ is a linear parameter ($x$, $z$, $r$...) as well as when it's an angular parameter ($\theta$, $\phi$....
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  • 240
1 vote

How do we assume the direction of $u_{\theta}$ and $u_{r}$ in polar coordinate systems?

The unit radial vector is always away from the origin. The unit tangential vector is always anti-clockwise around the origin such that $\hat{r}\times\hat{\theta}$ is out of the diagram. Not knowing ...
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1 vote

Meaning of "$=$" in $\vec{F}=m\vec{a}$ (for example)

To add on top of good answers already present: I don't think it makes sense to say that a body at rest is accelerating equally in all directions In a way it does. Acceleration is a vector quantity. ...
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  • 5,451
1 vote

When defining a coordinate system, does it matter if it is right- or left-handed?

Choice of coordinate system is physically arbitrary, but may be important for reasons of convention, consistency, and transparency. The universe doesn't care how you describe it, but your readers ...
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  • 8,068
1 vote

Please explain statement in a book on Loop Quantum Gravity

Since no one is try to answer this, I try to work out it by myself using hint given by Andrew. So, suppose I have a tetrahedron whose vertices are the points A (2, -1,-3), B (4,1,3), C (3,2,-1) and D (...
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