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大学物理： 力学, 热学
Classical Mechanics
Thermodynamics
任课教师：贺言
办公室：物理学院，306
Email: [email protected]
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教材：大学物理学
作者：卢德馨，出版社：高等教育出版社
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平时作业：10%
期中考试：30%
期末考试：60%
Introduction to physics and
mathematical background
物理绪论，数学背景
What is physics
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Physics studies the fundamental laws which govern the
motion and interaction of matters.
physics is based on experimental observations and
quantitative measurements.
Modern physics contains 3 major branches
1. high energy (elementary particle) physics
基本粒子物理
2. Condensed matter physics
凝聚态物理
3. Cosmology and astrophysics
宇宙学和天体物理
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According to different research methods, we have
1. experimental physics 实验物理
2. theoretical physics 理论物理
3. computational physics 计算物理
Physics studies most fundamental laws of nature.
Methods and results of physics have been applied to
other natural sciences such as chemistry, biology,
geology, even economy.
Physics intersect with other natural sciences, such as
biophysics, quantum chemistry
Physics is most quantitative science. Physics is written in
the language of mathematics.
History of physics
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Classical physics（经典物理）
1. Newtonian mechanics (17-19 century) 牛顿力学
2. classical electrodynamics (19 century) 经典电动力学
3. thermodynamics and statistics physics (19 century)
热力学和统计物理
Modern physics （现代物理）(20 century)
1 Special relativity and General relativity
狭义相对论和广义相对论
2 Quantum mechanics and Quantum field theory
量子力学，量子场论
3 Supersymmetry, supergravity and string theory
超对称， 超引力， 弦论
Difference between classical and modern
physics
Structure of matter
Four fundamental interaction
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Gravity 引力
Newton’s theory, Einstein’s relativity
Electromagnetism 电磁力
Maxwell’s theory, QED
Strong interaction 强相互作用
Quantum Chromodynamics
Weak interaction 弱相互作用
Electroweak theory
Standard model 标准模型
Physical quantities 物理量
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Fundamental quantities and derived quantities
3 fundamental quantities in mechanics
Length, Time, Mass
Derived quantities such as
velocity, force, acceleration, density etc.
Dimension analysis 量纲分析
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The dimension of a physical quantity can be expressed
as a product of the basic physical dimensions
Dimension is different from units.
Dimension analysis can be used to check the
correctness of equations.
One can also deduce the relation between physical
quantities by dimension analysis.
Dimensionless quantities are very important.
Dimension analysis
For circular motion with uniform speed, we know its accelaration
depends on the speed and the radius of the circle
Let
The dimension of this equation is
m2
n  1
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Planck Length: Construct a length scale with gravity
constant, Planck constant and speed of light
l  G abcc
m1m2
F G 2 ,
r
F  ma
[]  [ E ]T  [ F ]LT  ML2 / T

L2
L3
[G ]  [a] 
M
MT 2
[c ]  L / T
[l ]  [G]a []b [c]c  M  a b L3a  2bcT 2a bc  L
a  b  1 / 2,
c  3 / 2
1/ 2
 G 
l  3 
c 
 1.6 10 35 m
Math background: Calculus (微积分)
Differentiation, derivative
Definite integral
The Fundamental Theorem of Calculus
Here F is a function whose derivative is f
The same order of magnitude
Taylor expansion
Higher order infinitesimal
Properties of Vectors （矢量）
Finite rotations are not commute, they actually form
a non-Abelian group: SO(3)
Infinitesimal rotation do commute.
Decompose vector into components
Dot product （点积）
The dot product of two Euclidean vectors A and B is defined by
where θ is the angle between A and B.
In particular, if A and B are orthogonal, then the angle between
them is 90, so in that case
The dot product propert
Commutative:
Distributive over vector addition:
In components
Norm of a vector
| a | a  a
If the modular of a vector is 1, this vector is unit vector.
Cross product （叉积）
The cross product is defined by the formula
where θ is the measure of the smaller angle between a and b, ‖a‖
and ‖b‖ are the norm of vectors a and b, and n is a unit vector
perpendicular to the plane containing a and b in the direction given by
the right-hand rule as illustrated.
Cartesian coordinate system （直角坐标系）
Base vectors
Vectors can be expanded as
A  A1i  A2 j  A3k
B  B1i  B2 j  B3k
Verify
( A  B) 3  A1 B2  A2 B1
( A  B) 2  A3 B1  A1 B3
( A  B)1  A2 B3  A3 B2
A  ( B  C )  B( A  C )  C ( A  B)
A  A1i  A2 j  A3k
A  ( B  C )  A  ( B2C1k )   B2C1 ( A1 j  A2i )
B  B1i  B2 j
B( A  C )  ( B1i  B2 j ) A1C1
C  C1i
C ( A  B)  ( A1 B1  A2 B2 )C1i
Polar vector and axial vector
Scalar triple product（混合积）
Geometrically, the scalar triple product is the (signed) volume of
the parallelepiped defined by the three vectors
Det means determinant
Other Orthogonal coordinate system
Polar coordinate system （极坐标系）
Convert to Cartesian coordinate
Taking time derivative
Application：
Velocity and acceleration in polar coordinate
For circular motion, we have
Cylindrical coordinates and spherical coordinates