37 votes

Can imaginary (illusionary) forces cause acceleration, and what exactly are they?

The fictitious forces appear in non-inertial frames of reference. The forces can cause acceleration when viewed in such a frame. Riding in a car that swerves left, my coffee and donuts slide across ...
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  • 34.3k
10 votes
Accepted

Using time dilation to find universal frame of reference

I'm afraid your idea won't work. Time dilation is symmetrical. Suppose your frame of reference and mine are moving inertially relativity to each other. A clock in your frame will seem dilated relative ...
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  • 18.8k
7 votes

Why is proper time equated to $ds$?

Generally speaking, the line element can be written as $$ds^2=g_{\mu\nu}(x)dx^{\mu}dx^{\nu},$$ where $g_{\mu\nu}(x)$ are the metric components at the point $(x^0,x^1,x^2,x^3)$. For example, working in ...
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  • 546
4 votes

Can imaginary (illusionary) forces cause acceleration, and what exactly are they?

Fictitious forces seem to exist only from a Newtonian perspective: if we insist on thinking that the correct equation of motion is the Newton's second law: $$m\frac{\text{d}^2x^i}{\text{d}t^2} = F^i$$ ...
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  • 581
4 votes

Using time dilation to find universal frame of reference

Axis Omega asked: "can a frame of reference in which time runs the fastest (there is the least amount of dilation) be found in which to compare to the rest of the universe?" That is the ...
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  • 7,757
3 votes

Interpretation of momentum in special relativity

There are many questions here about mass in S.R. The contemporary interpretation is that there is only rest mass. Rest energy is an invariant quantity. Therefore mass, $m = E_0 / c^2$, is too. Your ...
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  • 5,460
3 votes

How does an Object at event horizon stop to the observer?

At a correct moment enough light to last for an eternity was send after the object. A one second pulse for example, and infinite brightness of course. The front part of the pulse arrives back after 10 ...
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  • 1,566
3 votes

How does an Object at event horizon stop to the observer?

Instead of dealing with light being reflected off the falling body, I'd like to give the falling body a flashlight, so we won't deal with ingoing and outgoing light rays, only outgoing. I'll give you ...
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  • 389
2 votes
Accepted

Angular momentum in non-inertial frame of reference (König's theorem)

In König's theorem, you aren't free to choose any non-inertial frame for $\vec{L}'$. $\vec{L}'$ is defined in what's called the center of mass frame: its origin is the center of mass of the system (as ...
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  • 2,256
2 votes

What is meant by 'The components of a force along a given axis'?

Say you know a force of magnitude $F_a$ acts along the direction $\hat{a}$ The force vector is thus $$\vec{F} = F_a\, \hat{a}$$ In reverse, to find out the magnitude, you can use the dot product $$ ...
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  • 33.5k
2 votes

Help finding an paper about a simulation hypothesis

I imagine your teacher was referring to this paper: ARE YOU LIVING IN A COMPUTER SIMULATION? by Nick Bostrom
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2 votes
Accepted

Angular Acceleration of Spinning Body About a Rotating Axis

Let's first start with a picture. The object (blue ball) is rotating around the AB axis with angular velocity $\vec\omega_0$. Next, the $AB$ axis is rotating around the vertical with an angular ...
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  • 6,420
2 votes

Does time really slow near the speed of light or does it only seem that way to an outside observer?

I'm curious if I came to the correct conclusion You raise a reasonable question - whether the non-intuitive predictions of special and general relativity might be simply due to a time delay in light ...
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  • 51.8k
2 votes

At what constant speed should I travel one light-second to make my time and a stationary person's time 1 second off?

It will depend what speed you are travelling at. However, dealing purely with time dilation effects from special relativity, if it takes you $\tau$ amount of time to travel a certain distance as ...
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  • 717
2 votes

When to apply $I_c \underline{\omega} = \underline{M_c}$?

The expression $ \underline{M}_c = \mathrm{I}_c \,\underline{\omega}$ is never correct. I think you forgot the time derivative of rotational velocity here. Also, the are Coriolis torques that relate ...
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  • 33.5k
1 vote

Does time really slow near the speed of light or does it only seem that way to an outside observer?

No, time really does slow down, and this is established in literally billions of experiments at colliders like the LHC. It's not some kind of optical illusion. Actually, it's probably not helpful to ...
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  • 6,128
1 vote

Problem 6.3 from David Morin (classical mechanics)

Note that the Euler-Lagrange's equations for a set of $\{q_1,\dots, q_n\}$ generalized coordinates are valid if the $n$ coordinates are independent from each other. The $x$ coordinate of your problem ...
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1 vote
Accepted

Acceleration of a projectile along an inclined plane

Question 1: Your $v_{x}$ and $v_{y}$ are not labelled correct. This does not represent the horizontal and vertical component relative to our original basis vectors. Using geometry the new basis ...
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  • 4,346
1 vote

Acceleration of a projectile along an inclined plane

The horizontal velocity is constant. Notice that in the basis you're using, neither vector is horizontal or vertical. The easiest way to see it is to restart the exercise directly in another basis, ...
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  • 2,256
1 vote

Why is proper time equated to $ds$?

This answer considers the generalization of special relativity to general relativity: The infinitesimal arclength $ds$ between 2 infinitesimally close spacetime events/points $P$ and $Q$ on a ...
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  • 170k
1 vote

Why is proper time equated to $ds$?

In general, the separation between two events contains a spatial component and a time component. If the separation is time like, the time is large and the distance is small. You can travel between the ...
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1 vote

Interpretation of momentum in special relativity

The easiest way to work such problems in relativity is to use the concept of four-vectors. There is a little bit of a learning curve, but if you are going to spend any time doing relativity the ...
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  • 65.8k
1 vote

Confusion regarding pseudo force

To (badly) quote Einstein, pseudo-forces are an ugly way to express the fact that the chosen frame isn't inertial. Say you're in a bus. As long as the bus goes in a straight line with constant ...
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  • 2,256
1 vote

Confusion regarding pseudo force

Well, they accelerate to the same rate relative to what? Let say they both have acceleration a relative to an inertial frame. So in the inertial frame there must be a (real, not pseudo) force ...
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  • 6,568
1 vote

Velocity of one particle w.r.t. another

You can convince yourself that the first method does not work in general by looking at a simple example. Take the two objects moving with constant headings in the world frame, starting from the origin....
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  • 6,568
1 vote

How we will choose reference point for more than two particle system to calculate potential energy as in the case of of equilateral triangle?

The point of the potential energy is that its difference gives you work and thus it is determined up to an additive constant. You can use any constant whatsoever, but for certain problems some choices ...
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  • 5,553
1 vote
Accepted

Physical Meaning of Pullback metric vs. Effective Spatial Metric

If the spacetime in question is static - so $\partial_t g_{\mu\nu}=0$ and $g_{0i}=0$ in the appropriate coordinates - then the issue is resolved by the fact that $h_{ij}=\gamma_{ij}$. If the spacetime ...
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  • 51.8k
1 vote
Accepted

Is a stress tensor still symmetric when the object is rotating?

I will answer your questions below. Yes. The Cauchy stress is still symmetric. The thing is that this stress measure is not energy conjugate with the strain measure that you picked. This means that ...
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  • 1,378
1 vote

Angular momentum in non-inertial frame of reference (König's theorem)

The expression you provide is the angular momentum for a system of particles (not necessarily a rigid body) segregated into two terms: (1) the angular momentum of the CM plus (2) the angular momentum ...
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  • 6,436
1 vote

Spinning top fixed point

When calculating rotation problems, with torques and suchlike, it is necessary to choose an origin for the coordinate system. This choice is ultimately arbitrary since the equation of motions are ...
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