# 6.3 Frames of reference

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## Introduction

Consider two people standing, facing each other on either side of a road. A car drives past them, heading West. For the person facing South, the car was moving toward the right. However, for the person facing North, the car was moving toward the left. This discrepancy is due to the fact that the two people used two different frames of reference from which to investigate this system. If each person were asked in what direction the car were moving, they would give a different answer. The answer would be relative to their frame of reference.

## What is a frame of reference ?

Frame of Reference

A frame of reference is the point of view from which a system is observed.

In practical terms, a frame of reference is a set of axes (specifying directions) with an origin. An observer can then measure the position and motion of all points in a system, as well as the orientation of objects in the system relative to the frame of reference.

There are two types of reference frames: inertial and non-inertial. An inertial frame of reference travels at a constant velocity, which means that Newton's first law (inertia) holds true. A non-inertial frame of reference, such as a moving car or a rotating carousel, accelerates. Therefore, Newton's first law does not hold true in a non-inertial reference frame, as objects appear to accelerate without the appropriate forces.

## Why are frames of reference important?

Frames of reference are important because (as we have seen in the introductory example) the velocity of a car can differ depending on which frame of reference is used.

## Frames of reference and special relativity

Frames of reference are especially important in special relativity, because when a frame of reference is moving at some significant fraction of the speed of light, then the flow of time in that frame does not necessarily apply in another reference frame. The speed of light is considered to be the only true constant between moving frames of reference.

The next worked example will explain this.

## Relative velocity

The velocity of an object is frame dependent. More specifically, the perceived velocity of an object depends on the velocity of the observer. For example, a person standing on shore would observe the velocity of a boat to be different than a passenger on the boat.

The speedometer of a motor boat reads 5 m $·$ s ${}^{-1}$ . The boat is moving East across a river which has a current traveling 3 m $·$ s ${}^{-1}$ North. What would the velocity of the motor boat be according to an observer on the shore?

1. $\begin{array}{ccc}\hfill R& =& \sqrt{{\left(3\right)}^{2}+{\left(5\right)}^{2}}\hfill \\ & =& \sqrt{34}\hfill \\ & =& 5,8\phantom{\rule{4pt}{0ex}}\phantom{\rule{0.166667em}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}\hfill \end{array}$
$\begin{array}{ccc}\hfill tan\theta & =& \frac{5}{3}\hfill \\ \hfill \theta & =& 59,{04}^{\circ }\hfill \end{array}$

The observer on the shore sees the boat moving with a velocity of 5,8 m $·$ s ${}^{-1}$ at 59,04 ${}^{\circ }$ east of north due to the current pushing the boat perpendicular to its velocity. This is contrary to the perspective of a passenger on the boat who perceives the velocity of the boat to be 5 m $·$ s ${}^{-1}$ due East. Both perspectives are correct as long as the frame of the observer is considered.

#### Questions & Answers

25 element of physics
an object will remain at rest or move at a constant velocity unless acted upon a net force
thank you
Thabiso
law of inertia
Joan
an object resisting the change in velocity.
Thabiso
What is a molecule
a molecule is a simplest structure unite of an elements
Else
thank you
Thabiso
Plz remind me the 1st Newton's law
Thabiso
Define the term functinal group of an organic compound
a single atom or a group of atoms which is responsible for the property and function of an organic compound
Shandre
thanks😊
Kamvelihle
What's the relationship between intensity and the current?
yu are Spi.ke spanish hola ele
Rolamf
cómo se llama el video donde disquete salgo yo
Rolamf
The intensity doesn't effect the current.
Mosa
what does the word emitted mean?
to be ejected or released
Khathutshelo
Ok thanks
Mwinga
Released
Mosa
what are the hooke laws
what's that
Mosa
what do really asked in exam
questions
Kamvelihle
lmaooo
itsssjust
Which equation do u wanna balance
Rifumo
i tried to write it but my phone just can't write it Cr2 O72-(aq) + H2S (aq) Cr3 (aq) + S(s)
Brian
show is the equation
Pride
us
Pride
hello. what is the difference between a primary, secondary and tertiary alcohol
primary the C=bonded to 1 Carbon atom.... secondary=bonded to 2 carbon atoms tertiary=bonded to 3 carbon atoms
Christina
I hope you're answered
Christina
thanks Christina
Baningi
My pleasure
Christina
Thank you Christina. This is very helpful 😀👍👍💯
Thokozani
💯💯
Thokozani
Anytime Thokozani
Christina
How to calculate pH?
Thabo
thank you guys i didn't know about the primary, secondary and tertiary alcohols
Brian
thank you Christina
Brian
Hey guys which topic does AC nd DC generator falls
Phumelele
electrodynamics
Christina
thank you
Phumelele
can somebody help me with functional isomers
function isomer has the same molecular formula but different functional group
Thokozani
what's momentum
the product of an objects mass times velocity. it is mainly prevalent in collisions.
tyrique
momentum
Sesethu
in order to produce an interference pattern, the waves used must be what?
Methane contains C and H. This compound is
ketones's functional group
Why does the carboxyl group have acidc properties?
carboxylic acids
tyrique