Non-Galilean Reference Frames

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Questions and Answers

What is the primary focus when describing motion in physics, particularly when using multiple frames of reference?

  • Describing the motion using only one, universal frame of reference.
  • Calculating the average speed of the object.
  • Ignoring external factors like friction and air resistance.
  • Analyzing the motion of a mobile in different reference frames. (correct)

What parameters are essential when describing the movement of one reference frame relative to another?

  • The relative position, velocity, and acceleration between the reference frames. (correct)
  • The psychological impact on observers in each frame.
  • The color and texture of the objects in each frame.
  • The historical context in which the frames were developed.

What does the formula of Bour enable when analyzing motion from different reference points?

  • It simplifies the calculation of distances in complex systems.
  • It relates the time derivative of a vector in two different reference frames. (correct)
  • It calculates the economic impact of transportation.
  • It details the energy consumption of moving objects.

In a scenario where a reference frame R' is undergoing translational motion relative to another frame R, what characteristic remains constant?

<p>The orientation of R' with respect to R. (C)</p> Signup and view all the answers

What is the implication if the vector (R'/R) equals zero?

<p>R' is in translation relative to R. (D)</p> Signup and view all the answers

When analyzing motion involving a rotating reference frame R' relative to another frame R, what physical quantity defines the rotation?

<p>The angular velocity vector. (C)</p> Signup and view all the answers

In classical mechanics, what is a fundamental characteristic of Galilean reference frames?

<p>They are in uniform rectilinear translation relative to one another. (A)</p> Signup and view all the answers

How does the observed path of a moving object differ when viewed from different reference frames?

<p>The path can appear drastically different depending on the relative motion of the observer. (B)</p> Signup and view all the answers

What parameters must be accounted for when transitioning between different reference frames to accurately describe a mobile's velocity?

<p>The speed and direction of each reference frame. (D)</p> Signup and view all the answers

How is the 'entraînement' velocity of a reference frame R' defined relative to another reference frame R?

<p>It's the velocity of a point P solidary with R' that coincides with point M at a given instant. (A)</p> Signup and view all the answers

When considering the composition of accelerations in different reference frames, what characterizes the 'entraînement' acceleration?

<p>It is the acceleration of a coincident point solidary with R'. (D)</p> Signup and view all the answers

What distinguishes a pseudo-force from a 'true' force in the context of non-Galilean reference frames?

<p>Pseudo-forces arise due to the acceleration of the reference frame itself. (B)</p> Signup and view all the answers

What underlies the necessity of considering pseudo-forces when applying the fundamental principle of dynamics (RFD) in a non-Galilean frame?

<p>To correct for the effects of acceleration of the reference frame. (B)</p> Signup and view all the answers

According to Newton's laws, what is an isolated material point's condition in a Galilean reference frame?

<p>It either remains at rest or moves uniformly in a straight line. (D)</p> Signup and view all the answers

When is a moving reference frame considered a Galilean frame?

<p>When it maintains a rectilinear, uniform motion regarding another Galilean reference. (B)</p> Signup and view all the answers

Why is 'time dilation' important when transitioning between different reference frames that move at relativistic speeds?

<p>Because the rate at which time passes depends on an observer's relative motion. (C)</p> Signup and view all the answers

What principle remains invariant regardless of the Galilean frame used for measuring and is a cornerstone of special relativity?

<p>The speed of light. (C)</p> Signup and view all the answers

Why must pseudo-forces be accounted for when applying the fundamental principle of dynamics in a non-Galilean reference frame?

<p>To correct for the acceleration of the reference frame. (D)</p> Signup and view all the answers

How does the Coriolis force typically manifest itself?

<p>As a deflection of moving object relative to the rotating frame. (D)</p> Signup and view all the answers

When applying calculations to a moving object on Earth, in which cases can we regard Earth as a Galilean (inertial) reference frame?

<p>In most everyday scenarios, where the effects of rotation negligible. (B)</p> Signup and view all the answers

What defines the Copernican frame of reference?

<p>Sun at the center, distant stars for orientation. (C)</p> Signup and view all the answers

What can marées be viewed as in respect to quasi-galilean nature of geocentric frame?

<p>Gravitational perturbation in a nearly Galilean frame. (B)</p> Signup and view all the answers

Given the choice of the terrestial reference define which the following statements is true?

<p>The Earth is the reference and coordinate system are attached to it. (B)</p> Signup and view all the answers

What two effects define the vulgaire weight?

<p>Gravity and the rotation of earth. (A)</p> Signup and view all the answers

Why knowing the equation of Coriolis and Inertial pseudo helps in calculations?

<p>You can now know the effect in non-inertial system. (C)</p> Signup and view all the answers

According to first laws of Newton what can we say of the Galileo System (0G-airplane Airbus)?

<p>An inertial translation system . (C)</p> Signup and view all the answers

What is the effect of pseudo force rotation and rotation?

<p>Those pseudo force can determine the trajectory of one object. (B)</p> Signup and view all the answers

What are conditions or what can we do to improve the knowledge (with theoretical-math tools) about reality in Earth? (and any star of universe)

<p>Knowing how transform equations between different system references. (A)</p> Signup and view all the answers

What effect we can analyze in the model?

<p>We can relate one reference depending if galilean or no. (D)</p> Signup and view all the answers

What the pseudo forces are related?

<p>Those are result of frame where were are applying the RFD. (C)</p> Signup and view all the answers

How time and distances are translated in relativity cases versus classic cases?

<p>Distances can contract, time can dilate. (B)</p> Signup and view all the answers

I want to analyze one object, in what frame the measurement are less complex using those tools?

<p>In the frame of gal Galileo. (D)</p> Signup and view all the answers

Where the Galilean postulate holds more?

<p>Where you the measurement are not needed in a high precision. (A)</p> Signup and view all the answers

About the Marées what is more influencing, The Sun, Jupiter or the Moon?

<p>The moon is closer. (A)</p> Signup and view all the answers

Flashcards

Galilean Frame of Reference

A frame of reference that is not accelerating.

Change of Frame of Reference

Describes motion in two different frames.

Vitesse de rotation

The angular velocity of one reference frame relative to another.

Translation

The movement of a reference frame where all points maintain the same direction relative to another frame.

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Absolute Velocity

The total velocity of an object as observed from a stationary frame.

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Relative Velocity

The velocity of an object from a moving frame.

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Entrainment Velocity

The term for the influence a moving frame has on motion.

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Law of Composition of Velocities

It states how velocities relate in different frames.

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Pseudo-Forces

Force apparent in non-inertial frames due to acceleration.

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RFD in Frame

The fundamental law related to motion considering pseudo-forces.

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Centrifugal Force

Force pointing outward in a rotating frame.

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Coriolis Force

Apparent force due to Coriolis effect on a moving object.

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Copernican Frame

Frame with the Sun at its center.

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Geocentric Frame

Frame with Earth's center as its origin.

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Tidal Forces(Marées)

Attraction differences causing sea-level variation.

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Terrestrial Frame

The reference frame attached planet's surface.

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Apparent Weight(Vulgaire)

It combines gravity with frame.

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Deviation to the East

Deflection towards the east.

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Pseudo-Galilean

Adjusted frame considering the forces.

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Special Galilean transformation

Special transformations relating position.

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Time invariance

Relativistic phenomenon that affects length.

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Time dilation

An expansion of time intervals relative to some another frames.

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Postulate of Relativity

The speed of light is constant in all the frames.

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Kinetic in Non-Frames

Relates Kinetic energy on the frame.

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law of reciprocal actions

Law of action and reaction

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Study Notes

  • The study notes cover non-Galilean reference frames.
  • They discuss fundamental kinematic laws, dynamic and energetic aspects, and applications.

Change of Reference Frame: Kinematic Laws

  • It's necessary to describe a mobile's movement in two different reference frames.
  • Observers in different reference frames perceive different trajectories of the mobile.
  • Parameters are required to describe the movement of one reference frame relative to another.
  • Relations are needed to pass from one reference frame to another for velocity and acceleration.

Movement of reference frame relative to another

  • The position of the problem involves describing motion in two different reference frames.
  • Deriving a vector with respect to time results in a rotation speed vector between reference frames ($W_{R'/R}$).
  • The derivative of a vector "U" in frame R is equal to its derivative in frame R' plus $W_{R'/R} \land U$

Translation vs. Rotation

  • In translation, reference frame directions don't change.
  • In uniform rotation, $W_{R'/R} = w * k$
  • The absolute velocity is the relative velocity plus the entrainment velocity, $V_{a} = V_{r} + V_{e}$
  • Composition of accelerations involves relative, entrainment, and Coriolis accelerations.

Galilean Reference Frames

  • Galilean reference frames are those in uniform rectilinear translation relative to each other.
  • The speed of light is invariant under a change of Galilean reference frame.
  • Newtonian mechanics postulates invariance of time.
  • Special (uniaxial) Galilean transformation equations are provided.

Change of Reference Frame: Dynamics and Energetics

  • Newton's three postulates are recalled: inertia, F = ma, and action-reaction.
  • In non-Galilean frames, pseudo-forces appear, such as Coriolis and inertial forces.
  • The fundamental relation of dynamics (RFD) is modified in non-Galilean frames.
  • Expressions for kinetic moment and kinetic energy are adjusted for non-Galilean frames.

RFD (fundamental relation of dynamics)

  • The RFD is explored in the simple case of translation by a reference frame.
  • $ma = \sum F + F_{ie} + F_{ic}$ is the sum of all forces
  • In a translation R'', the forces: $md(M)/R' = Forces - md(O')R$.
  • The force "centrifuge" and the force of Coriolis are discussed.

Useful Reference Frames and Properties

  • Examines the Copernican, geocentric, and terrestrial reference frames.
  • Highlights the non-Galilean nature of the geocentric and terrestrial frames
  • The geocentric frame is quasi-Galilean because of tidal forces.
  • The weight combines gravity and "centrifugal" pseudo-force.
  • Coriolis force is considered.

Applications

  • Examples include accelerated translation and rotation.
  • It mentions a pendulum in a vehicle.
  • Airbus "0G" provides microgravity conditions.
  • A car on a roundabout experiences "centrifugal" force.

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