Angular Momentum III
Angular momentum and rotation
Total angular momentum
Addition of angular momentum
1
Rotation in classical physics
~
~
~
Transformation of a vector under rotation:
A ) A0 = RA
Rotation by angle about the z-axis:
0
1
cos
sin
0
~
~
c
HCI Prelim H2 Mathematics P2 Solutions
2010 HCI H2 Mathematics Preliminary Examination Paper 2 Solution
Qn
Solutions
1
Surface area of the tin and lid
= 2 x 2 2 xy 10 x = 400
y
200 x 2 5 x
x
Volume of the container
200 x 2 5 x
x2
x
200 x x 3 5 x 2
dV
Flipping Physics Lecture Notes:
AP Physics 1 Review of Waves
AP is a registered trademark of the College Board, which was not
involved in the production of, and does not endorse, this product.
A wave is the motion of a disturbance traveling through a medi
Flipping Physics Lecture Notes:
AP Physics 1 Review of Electricity
AP is a registered trademark of the College Board, which was not involved
in the production of, and does not endorse, this product.
Electric Current: The rate at which charges move.
o
Conv
Flipping Physics Lecture Notes:
AP Physics 1 Review of Rotational Kinematics
AP is a registered trademark of the College Board, which was not involved in the
production of, and does not endorse, this product.
!
rev
! rad
Angular Velocity: =
or
t s
min
o
Flipping Physics Lecture Notes:
AP Physics 1 Review of Simple Harmonic Motion
AP is a registered trademark of the College Board, which was not
involved in the production of, and does not endorse, this product.
The mass-spring system shown at
right is in s
Flipping Physics Lecture Notes:
AP Physics 1 Review of Universal Gravitation
AP is a registered trademark of the College Board, which was not
involved in the production of, and does not endorse, this product.
Newtons Universal Law of Gravitation:
r2
G = 6
Flipping Physics Lecture Notes:
AP Physics 1 Review of Electrostatics
AP is a registered trademark of the College Board, which was not involved in the production of,
and does not endorse, this product.
e = 1.6 10=19 C
=19
=19
Two examples: qelectron = e =
Flipping Physics Lecture Notes:
AP Physics 1 Review of Dynamics
AP is a registered trademark of the College Board, which was not
involved in the production of, and does not endorse, this product.
Inertial Mass vs. Gravitational Mass
o Inertial mass: the m
Flipping Physics Lecture Notes:
AP Physics 1 Review of Linear Momentum and Impulse
AP is a registered trademark of the College Board, which was not
involved in the production of, and does not endorse, this product.
!
o
!
Momentum: p = mv (remember, moment
Flipping Physics Lecture Notes:
AP Physics 1 Review of Rotational Dynamics
AP is a registered trademark of the College Board, which was not involved in the production
of, and does not endorse, this product.
Torque, the ability to cause an angular accelera
Flipping Physics Lecture Notes:
AP Physics 1 Review of Work, Energy and Power
AP is a registered trademark of the College Board, which was not involved in the
production of, and does not endorse, this product.
E = W = F!d = Fd cos : In terms of an object
TEMASEK JUNIOR COLLEGE, SINGAPORE
Preliminary Examination
Higher 2
MATHEMATICS
9740/02
Paper 2
Additional Materials:
20 September 2010
Answer paper
Graph paper
List of Formula (MF15)
3 hours
READ THESE INSTRUCTIONS FIRST
Write your Name and Civics Group o
1
Solve the inequality
x
4
,
x 2 ( x 2) 2
giving your answer in an exact form.
Hence solve
2
[3]
ex
4
x
.
x
e 2 (e 2) 2
[2]
The sequence of numbers un , where n = 0, 1, 2, 3, , is such that u0 = 2 and
(n 2)un 1
un
.
2un 1 n 1
Proof by induction that, fo
Suggested Solutions to 2010 NJC SH2 H2 Math Prelim Paper 1
1
The sum of the digits in a three-digit-number is 15. Reversing the digits in that number
decreases its value by 594. Also, the sum of the tenth digit and four times the unit digit is
five more t
Angular Momentum I
Orbital Angular Momentum L
Eigenvalues and eigenfunctions of L2 and Lz
Particle on a sphere and rigid rotator
General angular momentum : J2 and Jz
1
Orbital Angular Momentum
Angular momentum about a xed axis:
L = rp
= i! (r )
Cartes
MH 1400
ALGORITHMS &
COMPUTING I
Ivica NIKOLIC & Thomas PEYRIN
AY 2013/14 Semester 1
01.11.2013
Lecture 11: Advanced Functions
01/11/13
Lecture 11: Advanced Functions
L11-2
Midterm 2 on Lecture 13 (Nov 15)
We will have the second midterm on November
15, d
MH 1400
ALGORITHMS &
COMPUTING I
Ivica NIKOLIC & Thomas PEYRIN
AY 2013/14 Semester 1
25.10.2013
Lecture 10: MATLAB Programs, Debugging
16/10/12
Lecture 10: MATLAB Programs, Debugging
L10-2
Final Project
Your group partners are in the same Lab as you
You
MH 1401
ALGORITHMS &
COMPUTING I
Ivica NIKOLIC & Thomas PEYRIN
AY 2013/14 Semester 1
20.09.2013 Lecture 6: Loop Statements
20/9/13
L6-2
Lecture 6: Loop Statements
Erratum
a end was missing in the slides of previous lecture
(already corrected in the new v
MH 1400
ALGORITHMS &
COMPUTING I
Ivica NIKOLIC & Thomas PEYRIN
AY 2013/14 Semester 1
11.10.2013
Lecture 8: Data Structures
11/10/13
Lecture 8: Data Structures
L8-2
News
The lab session 6 (on loop statements) will be the first lab
session to be graded
We
5
Thermal Properties :
5 Thermal Properties
5.1 Thermal Excitation of Phonons
Phonons are created and destroyed by thermal excitation and make a significant contribution to the
heat capacity:
C=C phonon C electrons C magnetic
all solids
metals only
mag
SOLID STATE PHYSICS HW#6
Question 1. Kinetic energy and pressure of electron gas (Kittel 6.1-2)
(a) Consider a 3-d gas of N electrons at absolute zero. Since the model consists of free electrons,
the internal energy is equal to total kinetic energy of the
VICTORIA JUNIOR COLLEGE
2013 JC2 PRELIMINARY EXAMINATIONS
PHYSICS
Higher 2
9646/01
27 Sep 2013
Paper 1 Multiple Choice
FRIDAY
8.00-9.15 am
Additional Materials: Multiple Choice Answer Sheet
1 Hour 15 min
READ THESE INSTRUCTIONS FIRST
Write in soft pencil.