SCIE 2000: Space, Time and Motion
Homework 3 (deadline: 19/11/2012)
(by T.K. Ng)
1) Wave and Media:
a) A people sitting on a moving car with speed v threw out a stone with relative
speed u (to himself) along direction of motion of the car. What is the spe
T. K. Ng, HKUST
T.
More about Central Force and
Newtons Law
(the power of symmetry)
Keplers Law and Conic section
Actually Circular motion is just one
possible realization of motion of objects
under central force
F (r ) = f (r )r
Actually Circular motion
T. K. Ng, HKUST
T.
Symmetries of Space and Time
http:/www.youtube.com/watch?v=BX4cx-9zT1A
Symmetry in space and time not
exactly the same as above
R0
V
Symmetries of Space and Time
Geometrical Objects in Rn
- lines A line in Euclidean space Rn is a su
T. K. Ng
(HKUST)
Purpose of this course:
Using developments in human being's concepts on space, time and motion as
examples, the course intends to explain to students why abstract
scientific/mathematical concepts are essential in understanding the most
fu
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o
SCIE2000
SCIE 2000
Space, Time and Motion
by T. K. Ng, HKUST
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o
SCIE2000
GalileoversusMaxwell
1) Galileaninvariance
2) Field,waves&light
Apparentcontradiction:whatisthe
resolution?
.
o
SCIE2000
Galileaninvariance
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o
SCIE2000
WhyNewtonsLaw
Inaprevio
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SCIE2000
SCIE2000
Space, Time and Motion
by T. K. Ng, HKUST
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o
SCIE2000
RelativityEinsteinsrevolution
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SCIE2000
Einsteinsquestion
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o
SCIE2000
IsthereafundamentalreasonwhyNewtonsLawcannot
detectuniformmotions?Isitpossiblethatitisa
fundamentalprope
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o
SCIE2000
SCIE 2000
Space, Time and Motion
by T. K. Ng, HKUST
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o
SCIE2000
FromMechanicstoFieldTheory
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o
SCIE2000
Afterinventing/understandingLorentzTransformation,
thenextquestionEinsteinaskedis
IsNewtonsLaw(F=ma)stillcorrectinthenewspace
timestructu
SCIE2000
by T. K. Ng, HKUST
1
SCIE2000
How do we know the physics we learnt
are correct?
Two principles in Science
+
2
SCIE2000
A
fter learning how to measure time by a clock, Kit
decided to use his new knowledge to do some scientific
research. After reco
PHYS007
by T. K. Ng, HKUST
PHYS007
F=ma
Conservation Laws?
Thermodynamics?
=mc
2
PHYS007
PHYS007
String theory?
Hawking radiation,
string theory style
http:/www.youtube.com/watch?v=kYAdwS5MFjQ
PHYS007
How can we be sure?
Lets start from the beginning
PHYS
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SCIE2000
SCIE2000
Space, Time and Motion
by T. K. Ng, HKUST
.
o
SCIE2000
GeneralRelativity:Whyareinertialframesspecial?
.
o
SCIE2000
Intheconstructionoftheoryofspecialrelativityand
relativisticmechanics,Einsteinmadeuseofanimportant
principle,thatthela
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o
Modern
Physics
Space, time and Motion: The
Space,
Quantum World
Quantum
by T. K. Ng, HKUST
.
o
Modern
Physics
ThesuccessofNewtonianMechanics(withhistheoryof
gravity)andMaxwellstheoryofelectromagnetism
reacheditspeakattheendof19thcentury.
.
o
Modern
Ph
SCIE 2000 tutorial 1
(18/09/2012)
Content: Vector addition, subtraction, dot-product and cross product.
Example 1: Vector Addition and Subtraction.
we have two 3D vectors = (1,2,3) and = (3,0,1) in the same coordinate, calculate Vector
addition + and subt
In usual representation, an ellipse is represented by
x2 y2
+
= 1 , with b = a 1 2
a2 b2
where = eccentricity
a
In the new coordinate system where the origin is a foci, the representation is
( x'+a ) 2 y ' 2
+ 2 = 1 , since the foci is located at distance
Solutions to Homework 1
1.
Using the eight rules for integers to prove the following statements
If a+b=a then b=0, i.e. zero is unique
If a+b=0 then b=-a, i.e. negative is unique
a.(-b)=-(a.b)
Answer:
a) and b) existence of negative (-a), add (-a) on both
Assertion-reason question
Directions: Please refer to the following instructions:
A Both statements are true and the 2nd statement is a correct explanation of the 1st
statement.
B Both statements are true but the 2nd statement is NOT a correct explanation
Question Bank Topic 2
The Microscopic World
Name: _ Class: _ Class No: _
Mark: _
Date:_
Multiple choice questions
Unit 5
5.1: What is an element made of?
5.2: Symbols for elements
5.3: States of elements
5.4: How to classify elements?
(CDC guide: Elements
Answers for
21st Century Chemistry Question Bank Volume 1 (Topic 1-5) MCQs
Topic 1
Unit 1
1.3-1.4
1A
7C
2
8
C
D
3
9
C
B
4
10
C
A
5D
11 C
6
B
1.5
1D
7D
2
8
A
C
3
A
4
C
5
A
6
A
2
8
B
D
3
9
D
B
4
10
B
B
5
11
A
D
6
12
C
C
2.4
1B
2
B
3
C
4
B
5
A
6
D
2.6
1C
7A
Assertion-reason questions
Directions: Please refer to the following instructions:
A Both statements are true and the 2nd statement is a correct explanation of the 1st
statement.
B Both statements are true but the 2nd statement is NOT a correct explanatio
Assertion-reason questions
Directions: Please refer to the following instructions:
A Both statements are true and the 2nd statement is a correct explanation of the 1st
statement.
B Both statements are true but the 2nd statement is NOT a correct explanatio
Assertion-reason questions
Directions: Please refer to the following instructions:
A Both statements are true and the 2nd statement is a correct explanation of the 1st
statement.
B Both statements are true but the 2nd statement is NOT a correct explanatio
SCIE 2000: Space, Time and Motion
Homework 1 (deadline: 26/9/2012)
(by T.K. Ng)
Numbers & Vectors
1) Using the eight rules for integers to prove the following statements
a) If a+b=a then b=0, i.e. zero is unique
b) If a+b=0 then b=-a, i.e. negative is uni
SCIE 2000: Space, Time and Motion
Homework 3 (deadline: 19/11/2012)
(by T.K. Ng)
1) Wave and Media:
a) A people sitting on a moving car with speed v flows out a stone with relative
speed u (to himself) along direction of motion of the car. What is the spe
SCIE 2000: Space, Time and Motion
Homework 4 (deadline: 5/12/2012)
(by T.K. Ng)
1) Relativistic Mechanics
A particle under a constant force F at x-direction is moving with velocity v 0 at
x-direction at time t=0. What is the velocity of the particle at a
SCIE 2000: Space, Time and Motion
Homework 2 (deadline: 17/10/2012)
(by T.K. Ng)
1) Circular Motion & Keplers Law
A bicycle traveling around a circle is inclined towards the horizontal with an angle
(see figure). Show the radius of the circle the bicycle
SCIE 2000: Space, Time and Motion
Homework 4 (deadline: 5/12/2012)
(by T.K. Ng)
1) Relativistic Mechanics
i)
A particle under a constant force F at x-direction is moving with velocity v 0 at
x-direction at time t=0. What is the velocity of the particle at
SCIE 2000: Space, Time and Motion
Homework 2 (deadline: 17/10/2012)
(by T.K. Ng)
.
1) Circular Motion & Keplers Law
A bicycle traveling around a circle is inclined towards the horizontal with an angle
(see figure). Show the radius of the circle the bicyc
Assertion-reason questions
Directions: Please refer to the following instructions:
A Both statements are true and the 2nd statement is a correct explanation of the 1st
statement.
B Both statements are true but the 2nd statement is NOT a correct explanatio