Questions tagged [reference-frames]

A reference frame is a particular coordinate system chosen to represent physical entities. The notion is most often used in special and general relativity to denote particular coordinates chosen on the spacetime manifold.

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What is the work done by friction on a body from the perspective of different observers using the formula $-μmgl$?

Consider two observers moving with respect to each other at a speed $v$ along a straight line. They observe a block of mass $m$ moving a distance $l$ on a rough surface. The change in KE of the block ...
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Konig's Theorems

In the proof of Konig's Theorems the following identity is used: $$ \underline{v_i} = \underline{v_i'} + \underline{v_c} $$ which is the law of transformation of velocity when passing from the ...
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Angular velocity along a fixed rotational axis in space

I've been having some trouble getting my head around angular velocity and it's tangential movement, From what I think I understand the angular velocity has always a direction which is perpendicular to ...
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Can a center of mass frame be non-inertial?

If I have a system with particles moving with varying accelerations such that it's center of mass is moving with accelerations (there is a non-zero net force on the system (acting on one or all of the ...
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Why do equation of motion fail to apply in non-inertial frame even after applying pseudo force?

I considered two cars of equal mass moving towards each other with speed 30m/s and 18 m/s respectively and when they are 100 meters apart they both start de accelerating at 6m/s² each. So if we ...
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What does size of an inertial frame mean?

It is the equivalence principle that provides the bridge between the ideal $SR$ model and the real world. According to it, we can find at each event a set of local inertial frames (LIFS), which may be ...
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Time differential between two signals sent at two different near-relativistic speeds

There is something I don't quite get about relativistic velocities, which I am hoping to clarify with this question. Suppose you have an emitter and receiver both located somewhere far away from one ...
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The chronology of taking approximation changes the answer?

The problem is to find the time it takes a particle dropped from a height $h_0$ above the surface of the earth to reach the surface (exactly, not approximately i.e. $g$-value is not constant, in the ...
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For someone staying on Earth, what is the minimum possible time to send a spaceship to Alpha Centauri and have it back?

Suppose we want to send a spaceship to Alpha Centauri and calculate the minimum possible time it will take for us here on Earth to have the spaceship back. We are not interested in how fast the time ...
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How can one calculate the torque around this point? [closed]

I'll link to one of my previous problems, since the setup is very much alike this one for the problem I'll be solving: What happens with the pendulum when we choose this angular velocity for a ...
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Are curvilinear coordinates inertial?

At 1:46:34 of this lecture by Frederic Schuller, Inertial coordinates are defined as ones which satisfy the following equation: I am confused by the above equation because it would imply any ...
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Why the proper time of photon is zero? [duplicate]

I'm currently taking classes on General Relativity, and whilst working on Geodesis equation: Find out that for mass particle q is equivalent to proper time but in case of photon the proper time of ...
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How could any frame of reference be inertial?

The image below shows that a bystander watching the merry-go-round is in an inertial frame of reference. However, to nitpick, wouldn't the observer still be accelerating because it's on Earth?
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Does the speed of an object underwater change when viewed above?

Let's say a submarine is coming to surface with a velocity $v$ normal to the surface of water and let's say you are the admiral of the navy viewing the submarine from the top. The submarine is exactly ...
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A question about relativity and time dilation from a lay-person

Observer A is in a spacecraft flying toward earth Observer B is standing on earth A is traveling at near light-speed and will reach the earth in 1 week. When B looks at A's clock, he sees it moving ...
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Calculation of center of mass of a bar with linear density by branches

A query. If a bar of lengt $d$ has a linear density $\rho(x)=\begin{cases} x & x\in [a,b] \\ x^2 & x\in [b,c]\\ x^3 & [c,d] \end{cases}$ then its center of mass is $\overline{x}=\frac{\...
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Null conserved angular momentum

If the angular momentum of a particle is conserved and it is also 0, then is it true that the particle moves along a line? If so, how can we derive the equation for the trajectory from both the above ...
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Angular momentum of an extended mass for fixed origin imply the same result for nonfixed origin?

Consider an extended mass (say a collection of n particles where the internal force between them is central). For any fixed origin/inertial reference frame, the angular momentum satisfies $$\begin{...
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Dependence (or lack thereof) of forces on frames of reference

Consider a block A on top of block B with a coefficient of friction of say 0.3 in between them and the path providing zero resistance (no friction), with the bottom block moving such that its ...
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Would an accelerated-time space region deflect projectiles?

Suppose a spherical region in space in which time goes faster. Would projectiles shot at it be deflected away, as light is deflected by a material with a lower refractive index? Edit: This would also ...
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Find the equation for the angle $\theta$ in which the particle leaves the semicircle. No Friction [closed]

I think I missed something in this mechanics problem. We're given a polished (no friction) and homogeneous hemicircle which has mass $M$ and a particle of mass $m$ laying on the top of it. There is ...
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How does attaching a point mass to the CM of an object affect its moment of inertia about the CM?

How does attaching a point mass to the CM of an object affect its moment of inertia about the CM? Intuitively, it seems to me that this would not affect the mass distribution about the center of mass, ...
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How do we assume the direction of $u_{\theta}$ and $u_{r}$ in polar coordinate systems?

Is there a way to correctly predict the direction of the unit radial vector and the unit transverse vector in problems like the one below or is it just better to take a guess and solve the problem ...
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Cart Pole kinetic energy

As explained in [1], the kinetic energy of a Cart Pole is: $$ \frac{1}{2} (M+m)\dot x^2 + \frac{1}{2} m L^2 \dot \theta^2 - m L cos(\theta) \dot \theta \dot x $$ Where $m$ is the mass at the tip of ...
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Observing from a reference frame moving with high speed

Suppose at a distance $x$ from earths surface,a rocket comes with $v$ velocity which is comparable with the speed of light. Suppose lifetime of the rocket is $T$. We want to know whether the rocket ...
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Why can't we use integral of $x$, $y$ and $z$ in calculating moment of inertia

I've got no problems with calculating the moment of inertia/tensor of inertia of a cube using an integral over the lamina of a cube. However, I must be missing something obvious or making some sort of ...
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How and where does air that is displaced by a constant moving vehicle flow?

How does air that is displaced by a constant moving car move? When a car is driving with constant speed, there is air displaced in front of the car. Let's say the surface of the car view flat from ...
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17 votes
5 answers
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Wouldn't the cosmic background radiation (CMB) produce drag and thus create a preferential inertial frame?

Because the CMB is everywhere and is isotropic, if an object would have a certain velocity, it could have a pressure differential produced by the CMB which would produce drag till it would stop with ...
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Is this a rigorous derivation of Coriolis effect? It seems pretty simple

Coriolis effect is usually derived in a long twice differentiated equation of motion between a lab frame and rotated frame. Afterwards you group together all the terms and you get all the fictitious ...
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Euler's Angles and Uniquely Defining the Orientation of a Rigid Body

When speaking about the orientation of a rigid body, Symon (Mechanics, 3rd ed.) writes: It turns out that no simple symmetric set of coordinates can be found to describe the orientation of a body, ...
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How is it that we are still able to talk about the speeds of other galaxies, distances and times across the universe, etc despite GR?

Science articles often say that Andromeda galaxy is approaching us with speeds such and such. Sometimes we say that the universe is expanding away faster than light. Sometimes we talk about things ...
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How do the inertia tensor varies when a rigid body rotates in space?

The inertia tensor is clearly constant the in a frame moving with the rigid body. But what is the simplest way to see why its columns can be considered rotating vectors in space with the angular ...
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5 votes
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When two systems of forces acting on a rigid body are equivalent?

My book says that "it is clear that if you replace the system of forces with a second system having the same resulting force and the same resulting moment, with the same initial conditions the ...
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If I hang from the ceiling of the elevator which is falling freely then will I experience weightlessness?

We all know that while the lift (or elevator) is accelerating downwards we feel less weight, now suppose I hang from the ceiling with the help of a stick in some cavity of the ceiling itself, then ...
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1 vote
3 answers
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(Why) Is orbital angular momentum conserved for point masses?

The introduction of the angular momentum as $\vec l = \vec r \times \vec p$ is also true for point particles. So $\vec l$ must refer to the orbital angular momentum (and not the "spin") in ...
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6 votes
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Difference between point force and force

In high school, we used to draw a free diagram, and we are asked what are the forces acting on the object. When we represent these forces, we represent them using vectors going out from a point called ...
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Is It true that If the angular momentum is zero with respect to any point then the system is at rest?

If the angular momentum is zero with respect to any point, surely the system is at rest. It is intuitive that this is the case but I would like to prove it. I guess supposing the opposite leads to ...
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2 votes
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What rotates a disk hung at center of mass when it is tilted?

when a disk is hung by a string attached to the center of mass point is tilted, what is making it fall and become horizontal again Note the white line is a light string. Here $Torque_{net} = 0$ and $...
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2 answers
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Layman question about relativistic motion

I hope I can convey my question in a reasonable way: I know that if Alice is moving towards Bob at $0.75\,c$ and Bob does the same towards Alice, then to calculate how each one of them measures their ...
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Moment of Inertia of a solid hemisphere. What am I doing wrong? [closed]

I want to calculate the MOI of a uniform solid hemisphere about Axis passing through its centre of mass (COM) and perpendicular to the circular base. Axis coinciding with any diameter at the ...
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2 votes
1 answer
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Simple Analytical mechanics problem [closed]

I am trying to solve a simple problem stated as follows: "There are two cartesian reference frames k $(o;x,y,z)$ and K $(O;X,Y,Z)$ with the first one being still (inertial) and the second one (K)...
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1 answer
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Time derivative relation between two rotating frames

I know that the time derivative of some quantity $r(t)$ in a rotating frame which rotates with angular velocity $\Omega(t)$ is related to the derivative in a fixed (i.e. inertial) frame by $$ \Big(\...
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4 votes
2 answers
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What is the angular momentum of a particle rotating around an axis in 3D?

What would be the angular momentum of the particle at position $r_i$ in the diagram above? The vector from the axis of rotation is $R_i$ and the tangential velocity is $v_i$ so the magnitude of ...
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1 vote
2 answers
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What happens with an object not originally rotating around its principal axis?

I'm wondering about this question stated in the title. Suppose we have a rigid body undergoing some sort of rotation. Let the rotational vector point in a different direction than the angular momentum ...
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Problem with Inertial reference frames Rider on a merry-go-round [closed]

MASS ON A ROTATION PROBLEM. You have a playground round-about with a rider sitting on the edge. The roundabout / rider just revolves at a constant tangential velocity of 1.5m per second. The ...
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1 vote
1 answer
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Why is the sum of torques for each particle equal to the external torque?

Let's assume we have a rigid body. The internal forces all have equal and opposite counterparts so the they will produce a net zero torque. We can therefore ignore internal forces when calculating the ...
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What happens with the pendulum when we choose this angular velocity for a rotating platform?

The problem is presented below: I've managed to find the angular frequency of the pendulum using torque, and small-angle approximation. Finally, I wanted to check my expression and see whether it's ...
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1 vote
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Why do internal torques cancel?

I don't understand why torques produced by internal forces cancel in the sum $\sum \tau$. My textbook gives the following explanation: due to N3L, if a particle exerts a force on another particle of ...
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Paradoxes of length contraction: does the radius shrink? [duplicate]

Consider this setup: The black circle is the observer, who has a $360^{\circ}$ range of observation around it. In its orbit are other circles, orbiting at relativistic speeds. They are all orbiting ...
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2 votes
2 answers
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Newton's $2^{nd}$ Law in a rotational frame

I'm having a bit of trouble following the derivation for Newtons $2^{nd}$ law in a rotating frame, mainly just finding the second derivative of position in terms of the inertial fram. I am reading ...
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