Chapter 2 Kinematics
kinematics(动力学)1动力学课件
The subjects that occupied physical scientists through the end of the nineteenth century----mechanics, light, heat, sound, electricity and magnetism-------are usually referred to as classical physics.
Velocity is the rate at which the position changes. • Average Velocity The average velocity of a particle during the time interval Δt is defined as the ratio of the displacement to the time interval.
It is classical physics we must master to understand the macroscopic world we live in, and classical physics is the main subject of the first part of the course.
K Δr and Δr
K Δr ≠ Δr
#mech001
Which of the following statements is (are) true ? (a) Δr is the magnitude of the displacement .
G (b) Δr is the magnitude of the displacement.
z
P1
G v1
北京大学物理系英语教材
北京大学物理系英语教材Beijing University Physics Department English TextbookIntroduction:The Beijing University Physics Department English textbook is designed to be a comprehensive resource for students studying physics in English at Beijing University. This textbook aims to provide students with a solid foundation in the principles and concepts of physics while simultaneously improving their English language skills. The content of this textbook has been carefully selected to ensure an effective and efficient learning experience for students.Chapter 1: Introduction to PhysicsIn this chapter, students will be introduced to the fundamental concepts of physics. They will learn about the scientific method, units and measurements, and the basic principles that govern the behavior of matter and energy. Through interactive exercises and real-life examples, students will develop a strong understanding of the key principles that form the building blocks of physics.Chapter 2: MechanicsThe study of mechanics is essential in understanding the motion of objects. This chapter delves into the laws of motion, including Newton's laws, kinematics, and dynamics. Students will explore various types of motion, such as linear, circular, and rotational motion. Through practicalexamples and problem-solving exercises, students will gain a deeper understanding of how forces and motion interact.Chapter 3: ThermodynamicsThermodynamics is the study of heat and energy transfer. In this chapter, students will learn about the laws of thermodynamics and their applications. Concepts such as temperature, heat, entropy, and energy conservation will be explored in detail. Students will also be introduced to various thermodynamic processes and cycles, enabling them to analyze and solve problems related to energy transfer.Chapter 4: ElectromagnetismThis chapter focuses on the principles of electromagnetism. Students will learn about electric fields, magnetic fields, and the relationship between them. They will explore topics such as electromagnetic induction, electric circuits, and the behavior of charged particles in magnetic fields. The chapter also covers important concepts like Gauss's law, Ampere's law, and Faraday's law.Chapter 5: OpticsOptics is the branch of physics that deals with the behavior of light. In this chapter, students will study the properties of light, including reflection, refraction, and diffraction. They will explore the principles of geometric optics and learn about the formation of images by mirrors and lenses. The chapter also covers topics such as interference, polarization, and the wave nature of light.Chapter 6: Modern PhysicsThe final chapter of the textbook introduces students to the fascinating world of modern physics. They will explore topics such as quantum mechanics, the theory of relativity, and the structure of atoms. Students will gain insights into the behavior of particles at the atomic and subatomic levels, and understand the fundamental principles that govern the physical world.Conclusion:The Beijing University Physics Department English textbook provides students with a comprehensive and accessible guide to physics in English. By combining the principles of physics with English language learning, this textbook aims to enhance students' understanding of physics while improving their language skills. With its clear explanations, engaging examples, and challenging exercises, this textbook is a valuable resource for students at Beijing University and beyond.。
完整版)大学物理笔记
完整版)大学物理笔记Chapter 1: Proton Kinematics1.Reference frame: A standard object chosen to describe the n of an object.2.Coordinate system3.Particle: Under certain ns。
the n of an object can be represented by the n of any point on the object。
which can be treated as a point with mass。
This point is called a particle (ideal model).4.n vector (displacement vector): A vector pointing from the origin of the coordinate system to the n of the particle.5.Displacement: The increment of the n vector in the timeint erval Δt.6.Velocity: Speed of n.7.XXX: The average rate of change of velocity.8.XXX quantities.9.ns of n.10.Principle of n of n.n vector: r = r(t) = x(t)i + y(t)j + z(t)k Displacement: Δr = r(t+Δt) - r(t) = Δxi + Δyj + Δzk In general。
Δr ≠ ΔrVelo city: v = lim Δr/Δt = i(dx/dt) + j(dy/dt) + k(dz/dt) XXX: a = lim dv/dtCircular nj + k = xi + yj + zkXXX: ω = dθ/dtXXX: α = dω/dtXXX: a = an + atNormal n: an = v^2/R pointing towards the center of the circleXXX: at = Rα along the XXXLinear velocity: v = RωArc length: s = RθChapter 2: XXX1.XXX:XXX's First Law: An object at rest will remain at rest。
机器人学运动学分析_Kinematics
Dynamic Analysis of Mechanical Systems
Kinematics
Joints can be classified by the degrees of freedom allowed or restricted. The commonly used joints are listed in Table 1. 3.2.3 Mobility Analysis One of the basic steps in the kinematic analysis of mechanical systems is to determine the number of degrees of freedom or independent coordinates required to determine the configuration of the system. It can be shown that the number of constraints provided by a joint is equal to the number of degrees of freedom eliminated from the unconstraint system as a result of using this joint. In the planar system, the configuration of a rigid body undergoing unconstrained motion can be described by three independent coordinates due to the common constraints. Therefore, a planar system with n unconstrained movable bodies has 3 n DOF. If the system has p joints, each of which provides two constraints (note the common constraints), then the number of degrees of the system can be evaluated by the mobility (Glubler) criterion
物理公式1(英文版)
小学六年级数学教研组工作计划模板一、指导思想本学期六年级数学教研组以学校教学工作计划为指导，加强课程理论学习，进一步转变教育观念，更新教学方式，提高自身的教育科研能力，提高课堂教学效率。
探索高效课堂下的课堂常规管理模式，提高课堂教学水平，使得教研组在课题研究和教学质量等方面进一步得到稳步提高。
创设高效、民主、合力的教育氛围，全面提升各位数学教师的教学质量。
二、工作目标1、把集体备课落到实处。
做好集体备课教案的二次修改和反思。
上好每一节课。
2、进一步提升教师的自身素质和业务水平努力，提升教师素养，提高教学水平。
3、注重学生兴趣的培养，提高学生的积极性，全面提高学生的综合素质。
4、重点做好毕业生思想健康方面的工作，确保学生安全健康的发展三、主要工作1、加大口算训练力度，努力提高学生计算水平。
口算是一切计算的基础，让口算训练体现在天天练中，每节数学课都训练一定数量的口算题，并在训练过程中逐步提高要求。
2、继续学习新课程理论，加强教育教学的理论学习本学期我们全体数学教师继续以高效为主要的学习内容。
组织切实有效的学习和讨论活动，用先进的教育理论，改变传统的教学模式。
要求教师们把高效课堂的理念渗透到教学中，教学注重以培养学生的合作交流意识和实践创新能力为主，注重尊重学生的需要，培养学生的自学能力。
3、精心备好每一节课本学期我们组备课力求体现学生的主体性，在备课中充分发挥团队的作用，做到资源共享。
充分利用集体研讨的时间，讨论交流一周工作的得与失，并对下一阶段教学提出自己的看法4、认真上好每一节课本学期根据学校要求，上好示范课、教研课和汇报课，做到各种课型都能上到。
在评课时每位教师认真总结，积极写好案例。
5、做好培优补差工作，提高教学质量。
在大面积提高教学质量的同时，坚持不放弃每一个后进生，以良好的心态接纳他们，给他们以更多的关心和爱护，相信每一个学生都能学到自己适合的数学，让他们在数学学习上有所进步，以提高的数学成绩合格率。
物理英文版
Beijing University of Posts and TelecommunicationsUniversity PhysicsDepartment of Physics School of Science2006Professor XiaoguangZhangReference BooksPhysics for Scientists and Engineers with Modern Physics: D. C. Giancoli. (高等教育出版社)Sears and Zemansky’s University Physics: 西尔斯物理学，Young & Freedman, (机械工业出版社)《大学物理学》(五本)，张三慧，(清华大学出版社)《大学物理学》(三本)，吴百诗主编，(高等教育出版社) 习题指导书——《吴百诗大学物理学习题分析与解答》，李存志等，(高等教育出版社)。
Chapter 1 Introduction and VectorsImportant contentsSignificant figures （有效数字）.¾How to denote the significant figures for a number?¾Scientific notation.¾How to treat the number of significant figures when multiplying or dividing, and adding or subtracting.SI unit system （单位制）.¾Base units & derived units; 7 base units for SI unit system.¾The standards of Length, Time, and Mass.¾Unit prefixes.Dimensions and Dimensional analysis （量纲与量纲分析）.¾Check an equation by dimensional consistency.Order-of-magnitude.§1 Measurements, Estimating (Self taught)The transmission speed for optical fiber telecommunicationsAmerican standard: SONET (synchronous optical network).International standard: SDH (synchronous digital hierarchy).bit rate for OC-768 (STM-256)=39.813 Gbit/s ≈40Gbit/s, the bit period T B ≈25 ps20.0 ps/div40 Gbit/s RZ code50.0 ps/div10 Gbit/s RZ codeThe screens of an oscilloscopeAn older unit of length used for atomic scale: angstrom (A)In Bohr theory of hydrogen, the orbits of the electron around the proton are quantized: r n =n 2a 0The smallest radius a 0is called the Bohr Radius .。
运动技能学习与控制第2章运动操作的测量
第二章 运动操作的测量
图2. 3运用半径误差RE测量 操作准确性的范例。操作任 务是个体向圆形目标投掷飞 镖，投掷的目标是击中圆形 的中心(在图中用+表示)。个 体击中目标的位置用O表示。 RE就是有X轴和丫轴围成的 直角三角形的斜边(h)。
图2. 4个体每次反应与目标之间的差异用 均方根误差《RMSE)计算《经授权摘自F ranks，I .M .et al.，1982 .The generatio n of movement patterns during the acqu isition of a pursuit tracking task. Human Movement Science，1:251-271.Copyrig hts 1982 Elsevier/North-Holland，Amst erdam，The Netherlands)。
•
图2. 6角-角图显示熟练跑步者(上图)和三例肘一膝切断手术患者(下图)在跑步时膝-大腿之间的关系。 图中的缩写同侧支撑( IFS)、同侧腾空(ITO )、对侧支撑(CFS)、对侧腾空(CTO》表示跑步的四个组 成部分
六、动力学（kinetics）
• 动力学是指在运动研究中对力的探讨。 运 动学在不考虑运动产生原因的条件下对运 动的描述。 • 举例：实验室中将要进的测力板。 • 七、肌电图的测量（EMG） 记录激活开始 和结束的时间。 观察肌肉激活记录序列可 以了 解动作过程的协调性。
0101Chapter 1 Kinematics of a Particle
(1.3)
where the rectangular components see Fig. 1. l (b). Sample problem 1.1 In Fig. the crank OA of the scotch yoke is turning with a constant angular velocity ω rad/s. Derive the expressions for the displacement, velocity, and acceleration of the sliding member.
y 8mm / s 2 ay v
Substituting t=2.090s, we obtain
机械程系
3
机械基础
Vector Mechanics
Statics and Dynamics
a x 37.8mm / s 2
and
a y 8mm / s 2
Therefore the acceleration vector at y=30mm a=37.8i +8j mm/ s 2 The pictorial representation of a is
R sin2ωt 2
z=Rsin 2 ωt
where R and ω are constants. (1) By calculating the magnitude of the position vector r show that the path line on a sphere of radius R, centered at the origin of the coordinate system. (2) Determine the rectangular and the magnitudes of the velocity and acceleration vectors. Solution Part 1 The magnitude of the position vector can be calculated using r 2 x 2 y 2 z 2 . Substituting the given Expressions for the rectangular coordinates we obtain
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Quiz questions:
Two stones are release from rest at certain height one after the other
• A) Will the difference in their speed increase, decrease or stay the same
Instantaneous velocity
• Using motion diagrams and graphs
Vs lim s ds t0 t dt
Stop to think 2.2 Which velocity-versus-time goes with the position –versus-time graph
B) Will their separation distance increase, decrease or stay the same
x (t 3 3t)m 1.What is particle’s position at t = 2s?
x = -8+6 = -2 m
2. What is the velocity at t = 2s V dx (3t2 3)m / s dt
V|t=2 = -3(2)2+3=-9 m/s
Finding position from Velocity
g = 9.8m/s2 If we choose the y-axis to point vertically up
a( freefall) g
Example 2.16 A falling rock A rock is released from rest at the top of 100-m-tall building. How long does the rock take to fall to the ground, what is impact velocity?
a) What was the rocket’s acceleration during the first 16 s.
The rocket launched with Vo = 0, after 16 s
V1 0 at 16a
y1 0 1/ 2at 2 128 a
b) After motor stops, the acceleration is –g as free fall.
Motion in one dimension
• Determining the signs of position, velocity and acceleration
Motion along a straight line
1s 2s
3s
4s
Can be illustrated by
position-versus-time graph:
tf
Sf Si Vsdt
tiபைடு நூலகம்
Sf Si area under thevolocitycurveVs between tiand tf
Example 2.9
1.Where is particle’s turning point? 2.At what time does the particle reach the origin?
Instantaneous Acceleration
a lim V dV t0 t dt
tf
Vf Vi adt
ti
Homework 2.50
• A 1000Kg weather rocket is launched straight up. The rocket motor provides a constant acceleration for 16s, then the motor stops. The rocket altitude 20 s after launch is 5100m. You can ignore the air resistance
x
Continuous
(smooth) curve
Origin (x=0)
10 20
40
cm cm
cm
x
70 cm
1
2
3
4 t(s)
Position vs time graphs
Interpreting a position graph
1.What is the position at t =0min 2.What is the position at t =30min 3.What is the velocity at t = 20min 4.What is the velocity at t = 50min 5. What is the acceleration at t=20min 6. If this is V vs. t graph, and x = 0 km at t = 0min. What is the position at t = 80 min
Chapter 2: Kinematics
• 2.1 Uniform Motion • 2.2 Instantaneous Velocity • 2.3 Finding Position from Velocity • 2.4 Motion with Constant Acceleration • 2.5 Free Fall • 2.6 Motion on an Inclined Plane • 2.7* Instantaneous Acceleration
Finding velocity from position graphically
Uniform Motion
• V(avg)= comstant • The position-vs-graph
is a straight line • Vs = ∆s/ ∆t • Sf = Si + Vs ∆t
y2 y1 (v1t 1/ 2g(t2 t1)2 ) 128 a 16a 4 1/ 2 9.8 42
192a 78.4 5100 a 27m / s2
c) The rocket’s speed as it passes through a cloud 5100m above the ground
C
Relating a velocity graph to a position graph
The value of the Tvelocity at Any time equals the slope of The position graph
• Using calculus to find the velocity Ex. A particle’s position is given by the function
Two objects dropped from the same height will, if air resistance can be neglected Hit the ground at the same time and with the same speed
Free Fall
a( freefall) g, vertically downward
Stop to think 2.1 P38 Stop to think 2.2 P44 Stop to think 2.3 P48 Stop to think 2.4 P54 Stop to think 2.5 P61
Example 2.3 P 40 Example 2.4 P 41 Example 2.7 P 45 Example 2.10 P 47 Example 2.14 P 53 Example 2.16 P 56 Example 2.18 P 58
What is the maximum velocity of the rocket sled? What is the total distance traveled?
The apple and feather in this photograph are falling in a vacuum
s (Vf Vi) t (Vf Vi) (Vf Vi) Vf 2 Vi2 2as
2
2
a
See page 57
Example 2.13
A rocket sled accelerates at 50m/s2 for 5.0 s. Coasts for 3.0 s, then deploys a parachute and decelerates at 3.0m/s2 until coming to a halt.
Motion with constant acceleration
a V Vf Vi
t
t
Definition of acceleration
Vf Vi at
If set t0=0s, ∆t = t
s (Vf Vi) t (Vi at Vi) t Vit 1/ 2a(t)2
2
2
• Y0=100m Y1=0m • Vy0= 0 m/s t0 = 0 s
y1 y0 1/ 2gt 2
t 2(y0 y1) 2(100 0) 4.52s
g
g
V1y V 0y gt 9.8 4.52 44.3m / s
Motion on an inclined plane
| as | g sin