物理专业英语lecture-review.doc

Chapter 1. Vectors and Scalars Units（International , dimensions), Scalars，Vectors, Adding vectors, parallelogram of vectors, multiplying vectors, components, equilibrium重点：Addition，Subtraction and Production of Vector难点：scalar product,vector productChapter 2 Motion and MomentumI.Fundamental Laws of Motion(Newtons Law of Motion)a) Newtons first Law of Motion (the law of inertia )An object at rest will remain at rest unless acted on by an unbalanced force. An object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force. b) Newtons Second Law of MotionAcceleration is produced when a force acts on a mass. The greater the mass (of the object being accelerated) the greater the amount of force needed (to accelerate the object). orFORCE = MASS times ACCELERATIONEveryone unconsciously knows the Second Law. Everyone knows that heavier objects require more force to move the same distance as lighter objects.c) Newtons third Law of MotionFor every action there is an equal and opposite re-action. This means that for every force there is a reaction force that is equal in size, but opposite in direction. That is to say that whenever an object pushes another object it gets pushed back in the opposite direction equally hard.ii) Drawing Free-Body DiagramsFree-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation.The only rule for drawing free-body diagrams is to depict all the forces that exist for that object in the given situation. Thus, to construct free-body diagrams, it is extremely important to know the various types of forces.iii) Types of ForcesA force is a push or pull acting upon an object as a result of its interaction with another object.Contact ForcesAction-at-a-Distance ForcesFrictional ForceGravitational ForceTension ForceElectrical ForceNormal ForceMagnetic ForceAir Resistance ForceApplied ForceSpring Force II. Momentuma) Momentum can be defined as mass in motion. Momentum = mass velocity is a vector quantityAttention: Linear momentum is dependent on the frame of reference:It is important to note that the an object can have momentum for one frame of reference but the same object if kept in another reference frame can have zero momentum. b) Conservation of momentum The total momentum in a closed or isolated system remains constant. It states that the momentum of a system is constant if there are no external forces acting on the system.e.g. a collisionSuppose we have two interacting particles 1 and 2, possibly of different masses. The forces between them are equal and opposite. According to Newtons second law, force is the time rate of change of the momentum, so we conclude that the rate of change of momentum of particle 1 is equal to minus the rate of change of momentum of a particle 2,(1)Now, if the rate of change is always equal and opposite, it follows that the total change in the momentum of particle 1 is equal and opposite of the total change in the momentum of particle 2. That means that if we sum the two momenta the result is zero,(2)But the statement that the rate of change of this sum is zero is equivalent to stating that the quantity is a constant. This sum is called the total momentum of a system, and in general it is the sum of all individuals momenta of each particle in the system.Attention:1) It holds true for any component.2) An alternative of this is the law of conservation of angular momentum.3) If no external force acts on a system in a particular direction then the total momentum of the system in the direction remains unchanged.c)Impulse-momentum theorem1)The change of momentum is also termed as impulse. Impulse = Change in Momentum2) When large force acts for a very short time,a force comes in to play. This is called Impulse. It is a vector quantity denoted by . If the force does not vary with time, thenThe unit of Impulse are gcms-1 or kgms-1.3) What is the relationship between impulse and momentum? It is simple - and extremely powerful. The impulse-momentum equation says:The change in momentum of a particle during a time interval equals the impulse of the net force that acts on the particle during that interval.III. The Work-Energy Theorema) Mechanical Energy: Mechanical energy is the energy that is possessed by an object due to its motion or due to its position. Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position).E.g. A moving car possesses mechanical energy due to its motion (kinetic energy). A moving baseball possesses mechanical energy due to both its high speed (kinetic energy) and its vertical position above the ground (gravitational potential energy).When net work is done upon an object by an external force, the total mechanical energy (KE + PE) of that object is changed. Attention: It is vital to distinguish between external forces and internal forces.external forces include the applied force, normal force, tension force, friction force, and air resistance force. Because external forces are capable of changing the total mechanical energy of an object, they are sometimes referred to as nonconservative ernal forces include the gravity forces, magnetic force, electrical force, and spring force. When only forces doing work are internal forces, energy changes forms - from kinetic to potential (or vice versa); yet the total amount of mechanical is conserved. Because internal forces are capable of changing the form of energy without changing the total amount of mechanical energy, they are sometimes referred to as conservative forces.b) Deriving Kinetic EnergyKinetic energy is closely linked with the concept of work, which is the scalar product (or dot product) of force and the displacement vector over which the force is applied.An examination of how the theorem was generated gives us a greater understanding of the concepts underlying the equation. Because a complete derivation requires calculus, we shall derive the theorem in the one-dimensional case with a constant force. Proof:From Newtons Second Law of motion, we know that F = ma, and because of the definition of acceleration we can say that If we multiply both sides by the same thing, we havent changed anything, so we multiply by v: But remember that v = dx/dt: We rearrange and integrate: F dx = mv dv Fx = m(v2) = mv2 = EkBut Fx = Work; therefore Work = Ek.It is powerfully simple, and gives us a direct relation between net work and kinetic energy. Stated verbally, the equations says that net work done by forces on a particle is equal to the change in kinetic energy of the particle.IV. Conservation of EnergyEnergy can be defined as the capacity for doing work. It may exist in a variety of forms and may be transformed from one type of energy to another. However, these energy transformations are constrained by a fundamental principle, the Conservation of Energy principle. 1) One way to state this principle is Energy can neither be created nor destroyed. 2) Another approach is to say that the total energy of an isolated system remains constant. V.Gravity1. Newtons Law of GravityNewtons law of gravity defines the attractive force between all objects that possess mass. Understanding the law of gravity, one of the fundamental forces of physics, offers profound insights into the way our universe functions.- Gravitational ForcesIn the Principia, Newton defined the force of gravity in the following way (translated from the Latin):Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.Mathematically, this translates into the force equation shown to the equation , where the quantities are defined as: Fg= The force of gravity (typically in newtons) G= The gravitational constant, which adds the proper level of proportionality to the equation. The value of G is 6.67259 x 10-11 N * m2 / kg2, although the value will change if other units are being used. m1& m1 = The masses of the two particles (typically in kilograms) r= The straight-line distance between the two particles (typically in meters)2. Gravitational Fields (P34:textbook)Sir Isaac Newtons law of universal gravitation (i.e. the law of gravity) can be restated into the form of a gravitational field, which can prove to be a useful means of looking at the situation. Instead of calculating the forces between two objects every time, we instead say that an object with mass creates a gravitational field around it. The gravitational field is defined as the force of gravity at a given point divided by the mass of an object at that point, as depicted to the right.3. Gravitational Potential EnergyGravitational Potential Energy on EarthOn the Earth, since we know the quantities involved, the gravitational potential energy U can be reduced to an equation in terms of the mass m of an object, the acceleration of gravity (g = 9.8 m/s), and the distance y above the coordinate origin (generally the ground in a gravity problem). This simplified equations yields a gravitational potential energy of: U = mgyThere are some other details of applying gravity on the Earth, but this is the relevant fact with regards to gravitational potential energy.Notice that if r gets bigger (an object goes higher), the gravitational potential energy increases (or becomes less negative). If the object moves lower, it gets closer to the Earth, so the gravitational potential energy decreases (becomes more negative). At an infinite difference, the gravitational potential energy goes to zero. In general, we really only care about the difference in the potential energy when an object moves in the gravitational field, so this negative value isnt a concern.This formula is applied in energy calculations within a gravitational field. As a form of energy, gravitational potential energy is subject to the law of conservation of energy.Chapter 4 Dynamics of Rigid BodiesPart I Center of the mass i) concept of center of mass -point mass-Calculating center of mass ii) law of center of mass Ask students to derive the equation, based on the newtons second law.iii) application of center of mass A fisherman stands at the back of a perfectly symmetrical boat of length L. The boat is at rest in the middle of a perfectly still and peaceful lake, and the fisherman has a mass 1/4 that of the boat. If the fisherman walks to the front of the boat, by how much is the boat displaced?If youve ever tried to walk from one end of a small boat to the other, you may have noticed that the boat moves backward as you move forward. Thats because there are no external forces acting on the system, so the system as a whole experiences no net force. If we recall the equation , the center of mass of the system cannot move if there is no net force acting on the system. The fisherman can move, the boat can move, but the system as a whole must maintain the same center of mass. Thus, as the fisherman moves forward, the boat must move backward to compensate for his movement.Because the boat is symmetrical, we know that the center of mass of the boat is at its geometrical center, at x = L/2. Bearing this in mind, we can calculate the center of mass of the system containing the fisherman and the boat:Now lets calculate where the center of mass of the fisherman-boat system is relative to the boat after the fisherman has moved to the front. We know that the center of mass of the fisherman-boat system hasnt moved relative to the water, so its displacement with respect to the boat represents how much the boat has been displaced with respect to the water.In the figure below, the center of mass of the boat is marked by a dot, while the center of mass of the fisherman-boat system is marked by an x.At the front end of the boat, the fisherman is now at position L, so the center of mass of the fisherman-boat system relative to the boat isThe center of mass of the system is now 3 /5 from the back of the boat. But we know the center of mass hasnt moved, which means the boat has moved backward a distance of 1/5L, so that the point 3/ 5Lis now located where the point 2 /5 L was before the fisherman began to move.Part II angular momentum& TorqueReview: terms for circle parameter 1)Angular displacement: measure in radius(why?)2)Angular velocity 3)Period4) Centripetal acceleration/forcei) angular momentum (vs linear momentum)-rigid body-centripetal acceleration/forcean idealization of a solid body in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it.-angular momentum of a material objectExample: /html_books/lm/ch15/ch15.html#Section15.1The angular momentum of a moving particle isL= mvr , (explain why?)where m is its mass, v is the component of its velocity vector perpendicular to the line joining it to the axis of rotation, and r is its distance from the axis. Positive and negative signs are used to describe opposite directions of rotation.The angular momentum of a finite-sized object or a system of many objects is found by dividing it up into many small parts, applying the equation to each part, and adding to find the total amount of angular momentum.Note that r is not necessarily the radius of a circle. (As implied by the qualifiers, matter isnt the only thing that can have angular momentum. Light can also have angular momentum, and the above equation would not apply to light.)ii) Torque and Work Energy Theorem/physics/phys-200/lecture-9-momentum of inertia Note that it is dependent on the point of rotation-Torque(Derive from the previous kinetic energy)represented by the Greek letter tau, , the rate of transfer of angular momentumiii)Conservation of angular momentumConservation of angular momentum has been verified over and over again by experiment, and is now believed to be one of the three most fundamental principles of physics, along with conservation of energy and momentum.Example: skater pulls in her arms so that she can execute a spin more rapidly When a figure skater is twirling, there is very little friction between her and the ice, so she is essentially a closed system, and her angular momentum is conserved. If she pulls her arms in, she is decreasing r for all the atoms in her arms. It would violate conservation of angular momentum if she then continued rotating at the same speed, i.e., taking the same amount of time for each revolution, because her arms contributions to her angular momentum would have decreased, and no other part of her would have increased its angular momentum. This is impossible because it would violate conservation of angular momentum. If her total angular momentum is to remain constant, the decrease in r for her arms must be compensated for by an overall increase in her rate of rotation. That is, by pulling her arms in, she substantially reduces the time for each rotation.Chapter 5 Special RelativityReview: nertial frame/non-inertial frameI. Galilean transformation1. Galilean transformations, also called Newtonian transformations, set of equations in classical physics that relate the space and time coordinates of two systems moving at a constant velocity relative to each other. Adequate to describe phenomena at speeds much smaller than the speed of light, Galilean transformations formally express the ideas that space and time are absolute; that length, time, and mass are independent of the relative motion of the observer; and that the speed of light depends upon the relative motion of the observer.1) Derivation Suppose there are two reference frames (systems) designated by S (un-primed frame) and S (primed frame) such that the co-ordinate axes are parallel (as in figure 1). In S, we have the co-ordinates and in S we have the co-ordinates. S is moving with respect to S with velocity (as measured in S) in the direction. The clocks in both systems were synchronised at time and they run at the same rate. We have the intuitive relationships This set of equations is known as the Galilean Transformation. They enable us to relate a measurement in one inertial reference frame to another. For example, suppose we measure the velocity of a vehicle moving in the -direction in system S, and we want to know what would be the velocity of the vehicle in S.This is the result our intuition is familiar with. (2) ExplanationWe have stated the we would like the laws of physics to be the same in all inertial reference frames, as this is indeed our experience of nature. Physically, we should be able to perform the same experiments in different reference frames, and find always the same physical laws. Mathematically, these laws are expressed by equations. So, we should be able to transform our equations from one inertial reference frame to the other inertial reference frame, and always find the same answer.Suppose we wanted to check that Newtons Second Law is the same in two different reference frames. (We know from experiment that this is the case.) We put one observer in the un-primed frame, and