Home | Sign Up | Log In | RSSSaturday, 2018-05-26, 1:44 AM

eduCampUs

Site menu
Section categories
Education [150]
Videos [1]
Music [0]
Chat Box
500
Tags
learn c language learn c language branching and loop learn c language functions learn c language Pointer Basics how web page works Oracle Solaris 10 Oracle Solaris 10 How Web Pages Work Images How Web Pages Work Adding images&gr How Web Pages Work Introduction to How to Install WAMP How to Host Your Own Website for Fr How to Install the Apache Web Serve Atomic Structure The text provides 000 tons of conversations Introduction to How Radio Works Rad often over millions of miles citizens band radio Introduction to How the Radio Spect Can information travel faster than How F-15s Work by Tom Harris Browse How F/A-18s Work by Robert Valdes B How F/A-18s Work by Robert Valdes B Flying Video Game: In the Cockpit I How F/A-22 Raptors Work by Gary Wol 10 Unidentified Sounds That Scienti 10 Things You Didn't Know About Ein Is glass really a liquid? by Laurie How Radio Works by Marshall Brain B How Radio Works by Marshall Brain B 10 Most Terrifying Vehicle Manufact How a Top Fuel Dragster Works by Ch but can Siri meet our nee How Siri Works by Bernadette Johnso How the Tesla Turbine Works by Will Lecture 1: Inflationary Cosmology: Lecture 2: Inflationary Cosmology: Lecture 4: The Kinematics of the Ho Lecture 5: Cosmological Redshift an Lecture 6: The Dynamics of Homogene Lecture 7: The Dynamics of Homogene Lecture 8: The Dynamics of Homogene Lecture 9: The Dynamics of Homogene Lecture 10: Introduction to Non-Euc IBPS Clerical Cadre Exam Pattern De Institute of Banking Personnel Sele Educational Qualifications: A Degre INTERVIEW Candidates who have been official trailer for Mission Imposs How Relativity Connects Electric an in 1738 Kinetic Theory of Gases: A Brief Re Frames of Reference and Newton’s La attempts to measure the UVa Physics 12/1/07 “Moving Clocks Run Slow” pl More Relativity: The Train and the 12/1/07 The Formula If I walk from Adding Velocities: A Walk on the Tr 3/1/2008 The Story So Far: A Brief Mass and Energy Michael Fowler Energy and Momentum in Lorentz Tran How Relativity Connects Electric an Analyzing Waves on a String Michael by f even earlier than the bra Fermat's Principle of Least Time 9/ Hamilton's Principle and Noether's meaning they have Mechanical Similarity and the Viria Hamilton's Equations 9/10/15 A Dyna A New Way to Write the Action Integ Maupertuis came up with a kind of p Maupertuis' Principle: Minimum Acti Canonical Transformations Point Tra Introduction to Liouville's Theorem Adiabatic Invariants and Action-Ang Hyperbolas Michael Fowler Prelimina Mathematics for Orbits: Ellipses Keplerian Orbits Michael Fowler Pre Newton's equations for particle mot Dynamics of Motion in a Central Pot A Vectorial Approach: Hamilton's Eq Elastic Scattering Michael Fowler B Driven Oscillator Michael Fowler (c Dynamics of a One-Dimensional Cryst I usefor the spring constant (is a a mass on a spring Motion in a Rapidly Oscillating Fie Anharmonic Oscillators Michael Fowl in which the distance betw Motion of a Rigid Body: the Inertia Moments of Inertia: Examples Michae Euler's Angles Michael Fowler Intro or more precisely one our analysis of rotational motion h Euler's Equations Michael Fowler In Motion in a Non-inertial Frame of R Ball Rolling on Tilted Turntable Mi live cricket score roll the ball ba
Statistics

Total online: 1
Guests: 1
Users: 0
Home » 2015 » August » 20 » Frames of Reference and Newton’s Laws Michael Fowler University of Virginia 3/14/08
7:41 PM
Frames of Reference and Newton’s Laws Michael Fowler University of Virginia 3/14/08

Frames of Reference and Newton’s Laws

Michael Fowler  University of Virginia  3/14/08

The cornerstone of the theory of special relativity is the Principle of Relativity:

The Laws of Physics are the same in all inertial frames of reference.

We shall see that many surprising consequences follow from this innocuous looking statement.

Let us first, however, briefly review Newton’s mechanics in terms of frames of reference.

A “frame of reference” is just a set of coordinates:  something you use to measure the things that matter in Newtonian problems, that is to say, positions and velocities, so we also need a clock.

A point in space is specified by its three coordinates (xyz) and an “event” like, say, a little explosion, by a place and time: (xyzt).

An inertial frame is defined as one in which Newton’s law of inertia holds—that is, any body which isn’t being acted on by an outside force stays at rest if it is initially at rest, or continues to move at a constant velocity if that’s what it was doing to begin with.  An example of a non-inertial frame is a rotating frame, such as a carousel.

The “laws of physics” we shall consider first are those of Newtonian mechanics, as expressed by Newton’s Laws of Motion, with gravitational forces and also contact forces from objects pushing against each other.  For example, knowing the universal gravitational constant from experiment (and the masses involved), it is possible from Newton’s Second Law,

force = mass × acceleration,

to predict future planetary motions with great accuracy.

Suppose we know from experiment that these laws of mechanics are true in one frame of reference.  How do they look in another frame, moving with respect to the first frame?  To find out, we have to figure out how to get from position, velocity and acceleration in one frame to the corresponding quantities in the second frame.

Obviously, the two frames must have a constant relative velocity, otherwise the law of inertia won’t hold in both of them.  Let’s choose the coordinates so that this velocity is along the x-axis of both of them.

Notice we also throw in a clock with each frame.

Suppose S′  is proceeding relative to S at speed along the x-axis.  For convenience, let us label the moment when O′ passes O as the zero point of timekeeping.

Now what are the coordinates of the event (xyzt) in S′?  It’s easy to see t′ = t—we synchronized the clocks when O′ passed O.  Also, evidently, y′ = y and z′ = z, from the figure.  We can also see that x′ +vt.  Thus (x, y, z, t) in Scorresponds to (x′, y′, z′, t′ ) in S′, where

That’s how positions transform; these are known as the Galilean transformations.

What about velocities ?  The velocity in S′ in the x′ direction

This is obvious anyway:  it’s just the addition of velocities formula

How does acceleration transform?

since v is constant.

That is to say,

the acceleration is the same in both frames.  This again is obvious—the acceleration is the rate of change of velocity, and the velocities of the same particle measured in the two frames differ by a constant factor-the relative velocity of the two frames.

If we now look at the motion under gravitational forces, for example,

we get the same law on going to another inertial frame because every term in the above equation stays the same.

Note that  is the rate of change of momentum—this is the same in both frames.  So, in a collision, say, if total momentum is conserved in one frame (the sum of individual rates of change of momentum is zero) the same is true in allinertial frames.

Category: Education | Views: 191 | Added by: farrel | Tags: Frames of Reference and Newton’s La | Rating: 0.0/0
Total comments: 0
Name *:
Email *:
Code *:
Log In
Search
Entries archive

Copyright eduCampus.tk © 2018
Powered by uCoz