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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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Aspect angle of object

How can I find aspect angles with respect to ground of an object in at height $h$. Object is rigid body with pitch angle $\theta$ in body coordinate.
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How can we justify time dilation if we look through an spyglass at Einstein's light clock?

Assume that a space shuttle travels in a circular path having a radius $r_s$ at a tangential speed $v_s$ - a considerable fraction of the speed of light. There is a light clock inside the shuttle ...
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How to deal with no-slip non-holonomic constraints in Lagrangian?

I'm solving a dynamical system of a ball of mass $m$ and radius $R$ rolling on a rotating platform ("turntable") for which I found the Lagrangian to be: $$L=\frac{1}{2} m (\dot{x} - \Omega y)^2 + \...
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4answers
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Is rotation absolute? [duplicate]

I was reading an article that rotation instead of linear motion is absolute. Can anyone explain why? Shouldn't an observer (A) moving in a circle around a point in an object that rotates (with respect ...
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1answer
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Lagrangian equations of motion for ball rolling on turntable

The equations governing the motion of a ball of mass $m$, radius $R$ rolling on a table rotating at constant angular velocity $ \Omega $ which are derived using Newton's laws are: (I present these for ...
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Kinematics problem…? [on hold]

Two points A and B are moving in X-Y plane with constant velocity of $V_a=(6i-9j)$ m/s and $V_b=(i+j)$ m/s respectively. At time t=0 they are 15 m apart and both of them lie on y axis with A lying ...
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5answers
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Varying constants in special relativity [on hold]

The first thing you learn in special relativity is: All "inertial" frames of reference are equivalent. There is a frame - invariant speed limit, usually called speed of "light." So, geometry is a ...
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2answers
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Relative energy [duplicate]

Suppose a ball is travelling at 5km/h, person A is travelling at 2km/h and person B is travelling at 5km/h in the opposite direction. The ball is travelling at 3km/h relative to A and at 10km/h ...
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I am confused about which point we should take moment of inertia (moi) in diff situations

A uniform rod of mass m and length l is kept vertical with lower end clamped. It is slightly pushed to fall down under gravity. Find angular speed of rod when passing through its lowest position. I ...
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3answers
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Difference between center of mass and center of gravity

Let's consider a very tall building (g would be variable) which is rotating with the earth naturally. Now do the centrifugal force and the gravitational force act on the same spot? If not why does the ...
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1answer
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Newtonian Mechanics cannot be applied in non-inertial frame of reference then how can we apply formula for normal force in an accelerating elevator?

In my physics book there is a diagram in which a block is placed on a table. The table is exerting an upward force $ F_n $ (normal force) on the block and there is a downward force $ F_g $ (...
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Why doesn't the Earth accelerate towards us?

According to Newton's third law of motion that states that every action has an equal and opposite reaction. So, if the Earth exerts a gravitational pull on us (people) then even we should exert a ...
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How does a Foucault pendulum in an Earth-sized centrifuge precess? [closed]

Imagine replacing Earth with a centrifugal arm length Earth radius and rotating to produce acceleration g. How does a Foucault pendulum mounted on the end of the centrifuge move and why ? Ignoring ...
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0answers
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Apparent FTL speeds seen by observer

MY guestion is if I was in a ship orbiting a black hole (not very close to the event horizon) I am orbiting pretty far and I am experiencing that my time is slowing down realitive to people on earth. ...
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1answer
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Doppler effect and frame of reference

We know that in an inertial frame we can never tell if the frame is really at rest or moving with constant velocity but can’t we check if there is a change in frequency by a sound emitted by the frame ...
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Mass hanging from spring in free fall

Q: A mass $m$ hangs from a massless spring connected to the roof of a box of mass $M$. When the box is held stationary, the mass-spring system oscillates vertically with angular frequency $\omega$. If ...
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1answer
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Why a rope grabbed by a single end seems to follow the hand that grabs it?

Context I am thinking about the physics of the movement of a rope in the context of a person running and grabbing a rope in one hand (the other end is "free", there is nothing attached). When the ...
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I'm clueless, need help [closed]

Easy problem but I'm clueless about my approach
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1answer
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Why do two moving inertial frames of reference atribute the same velocity to each other?

In both relativity and Newtonian mechanics, it is a self-evident axiom according to which two inertial observers who move relative to each other measure the same velocity of, say, $v$. I want to know ...
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A Scalar Function Tranformation — Question on Notation in 't Hooft Document

I started reading a document by Gerard 't Hooft which can be found here. Right at the start I am puzzled by a simple expression. It is equation 2.2 showing how a scalar function transforms. I ...
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2answers
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Angular Momentum of a Rigid body

When defining angular momentum or rather calculating angular momentum what is the difference in the use of the terms "with respect to" , "about a point" or "in the frame of" ? Are the angular ...
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1answer
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Torques in Euler equation

The Euler equation is given by $$\mathbf I\dot{\boldsymbol \omega}+\boldsymbol\omega\times \mathbf I\boldsymbol\omega= \mathbf M.$$ Also see here. It explains that The expressions for the torque in ...
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1answer
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Lagrangian of a Heavy Symmetrical Top - Inertial or Non-inertial Frame?

I'm having some confusion with the analysis of a symmetrical top (specifically, a heavy top, but this is not very important for the question). Following Landau and Lifshitz's Mechanics, on page 110 ...
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1answer
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Translatory motion of a rod

For the translatory motion of a rod, shouldn't the torque about every point of the rod be zero? There is no rotation about any point right?
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1answer
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Simple harmonic question [closed]

consider a spring with a block of mass $m$ and spring constant $k$ that is inside a lift. the cable breaks and the lift falls freely. Show that the block now executes a simple harmonic motion of ...
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1answer
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Kinetic energy of a gyroscpoe toy

Why the energy only has rotational part $\frac{1}{2}I_1\omega_1^2+\frac{1}{2}I_2\omega_2^2+\frac{1}{2}I_3\omega_3^2$? The center of mass also moves in general.
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3answers
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Is spacetime-curvature relative?

Velocity is relative, which means kinetic energy is. Since, according to general relativity, energy bends spacetime around it, wouldn't this mean observers moving in different inertial frames measure ...
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2answers
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Why is the Moon's Centre of gravity different to its centre of mass? [duplicate]

All the places that I've seen an answer to this question simply state that it's because there is a stronger gravitational pull on the near side of the moon, facing the earth. But I'm wondering how ...
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2answers
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Which force described the “absolute” speed change of the moon in Newtonian mechanics?

In the world of "absolute" speed values in the Newtonian mechanics, the moon must move faster (i.e., must have a higher speed) if he travels with the earth (i.e., has the same velocity direction) than ...
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2answers
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Shouldn't ball has to move in the circle even after cutting the rope by which it was attached? [closed]

Since the tension force is a central acting force, the torque on an orbiting ball about that center is zero. But if the rope is cut down during motion the torque would still remain zero. This would ...
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1answer
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How to get the acceleration of a rotating mass from it's centrifugal and centripetal components

Suppose I pull out a rope and rotate a small mass as in the diagram with its speed constantly increasing Where: $Q_1$ is the path of the rotating mass $m$ $Q_0$ is the center of the rotating mass ...
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1answer
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Centrifugal force in effective potential

$$E = \frac { 1 } { 2 } m v _ { r } ^ { 2 } + \frac { L ^ { 2 } } { 2 m r ^ { 2 } } + U ( r )$$ This is the formula of total energy of an object with mass $m$ orbiting an assumed stationary body of ...
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1answer
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Deep concept of Rotation Dynamics

If angular velocity about axis of rotation passing through COM is × then why value of angular velocity remains same( i.e ×) If we assume axis of rotation anywhere which parallel to the original one?
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1answer
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How did Einstein generalise the Einstein elevator thought experiment to conclude with the equivalence principle?

Suppose a reference frame S1 is accelerated in the x direction with a constant acceleration g. A second frame S2 is at rest in a homogeneous gravitational field which imparts to all objects an ...
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1answer
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Special and general relativity

Is the light postulate in special relativity (that the speed of light is constant in all frames of reference) correct if the equivalence principle shows that light slows down in gravitational field? ...
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4answers
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Question on equivalence of acceleration and mass with respect to gravity

Layman’s question here. Let’s say I’m standing on the inside rim of a rotating space station spun at right rate to produce earth-like gravity. Does the spinning warp space time? If so, how can a small ...
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0answers
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Why do bodies fall identically in uniform acceleration and uniform gravitational field? [duplicate]

In his reformulation of Einstein’s Elevator thought experiment, James Robert Brown (1993) says that an observer in a uniformly accelerating spaceship in space (free of gravitational effects) will see ...
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2answers
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How to change a formula when changing the axis?

I have been lerning about acceleration and free fall recently, and we were told the formula for distance is $s=s_0+v_0t+\frac {1}{2}at^2$ (for movement along $x$-axis) but when we change the axis (to ...
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3answers
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Angular momentum in different points

I have a question about angular momentum: Is it possible to have a system where angular momentum is conserved relative to 1 point,but not conserved relative to another?
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4answers
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Gravity, falling bodies, and the equivalence principle

Why is that bodies in a box accelerating uniformally in space that is sufficiently removed from gravitational fields fall identically to bodies in a box located in a homogeneous gravitational field (e....
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1answer
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How did Einstein use the conclusions of special relativity to reach the equivalence principle (using the Elevator thought experiment)?

Could someone please explain how Einstein used the Elevator thought experiment and the principles of special relativity to conclude that uniform accelerates creates uniform gravitational field (...
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2answers
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Unit Vectors in physics

I'm reading the Massachusetts Institute of Technology: "Review of Vectors" , and I've found this: I can't see any relationship between the text that is highlighted in yellow and what's depicted in ...
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3answers
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Proof of center of mass formula [closed]

You know the center of mass equation: X=(x1*m1+x2*m2)/(m1+m2) Can you please demonstrate a proof of this? Maybe usimg torques?
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1answer
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Einstein's Elevator thought experiment and relativity

Einstein's elevator thought experiment contains the following premise: An observer in a box will see free bodies moving identically between when the box is uniformly accelerating in gravitational ...
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1answer
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Moment of inertia graph

To find the moment of inertia of an object, we take each individual mass element and multiply it by the square of its radius, and then find the sum of all these products. If the object is continuous,...
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3answers
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Newton's Third Law in an elevator

Some misconception I'd like cleared up. From what I understand, when an elevator accelerates downwards with you, there must be a net force acting downwards on you. Since your true weight remains the ...
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1answer
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In case of torque on sliding block on horizontal surface, why $y$ component of $\vec{r}$ is taken negative?

I've attached the picture above. In case of the torque on a sliding block on horizontal surface why r component is taken negative.
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7answers
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If gravity is a pseudoforce in general relativity, then why is a graviton necessary?

As far as I’m aware, gravity in general relativity arises from the curvature of spacetime and is equivalent to an accelerated reference frame. Objects accelerating in a gravitational field are in fact ...
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3answers
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A question on rigid body dynamics.

What is the intuition for angular momentum of a point mass relative to a inertial point? Does the definition of angular momentum of a point mass holds true in non inertial reference frame? How?
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0answers
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Is there some general theorem concerning the impossiblity of synchronizing an accelerated reference frame?

Discussions either around Born's rigid motion, or Dewan-Beran-Bell spaceships paradox, or Rindler hyperbolic motion, all seem to imply that a body which is accelerated with respect to an inertial ...