Introduction to SAT II Physics - FreeExamPapers

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Einstein’s first postulate tells us that neither the passenger on the train nor the person on the platform is wrong. It’s just as correct to say that the train is still and the Earth is moving as it is to say that the Earth is still and the train is moving. Any inertial reference frame is as good as any other. Second Postulate The speed of light in a vacuum is a constant— m/s—in every reference frame, regardless of the motion of the observer or the source of the light. This postulate goes against everything we’ve learned about vector addition. According to the principles of vector addition, if I am in a car moving at 20 m/s and collide with a wall, the wall will be moving at 20 m/s relative to me. If I am in a car moving at 20 m/s and collide with a car coming at me at 30 m/s, the other car will be moving at 50 m/s relative to me. By contrast, the second postulate says that, if I’m standing still, I will measure light to be moving at m/s, or c, relative to me, and if I’m moving toward the source of light at one half of the speed of light, I will still observe the light to be moving at c relative to me. By following out the consequences of this postulate—a postulate supported by the Michelson-Morley experiment—we can derive all the peculiar results of special relativity. Time Dilation One of the most famous consequences of relativity is time dilation: time slows down at high speeds. However, it’s important to understand exactly what this means. One of the consequences of the first postulate of special relativity is that there is no such thing as absolute speed: a person on a train is just as correct in saying that the platform is moving backward as a person on the platform is in saying that the train is moving forward. Further, both the person on the train and the person on the platform are in inertial reference frames, meaning that all the laws of physics are totally normal. Two people on a moving train can play table tennis without having to account for the motion of the train. The point of time dilation is that, if you are moving relative to me in a very highspeed train at one-half the speed of light, it will appear to me that time is moving slower on board the train. On board the train, you will feel like time is moving at its normal speed. Further, because you will observe me moving at one-half the speed of light relative to you, you will think time is going more slowly for me. 320
What does this all mean? Time is relative. There is no absolute clock to say whether I am right or you are right. All the observations I make in my reference frame will be totally consistent, and so will yours. We can express time dilation mathematically. If I were carrying a stopwatch and measured a time interval, , you would get a different measure, t, for the amount of time I had the stopwatch running. The relation between these measures is: So suppose I am moving at one-half the speed of light relative to you. If I measure 10 seconds on my stopwatch, you will measure the same time interval to be: This equation has noticeable effects only at near light speeds. The difference between t and is only a factor of . This factor—which comes up so frequently in special relativity that it has been given its own symbol, —is very close to 1 unless v is a significant fraction of c. You don’t observe things on a train moving at a slower rate, since even on the fastest trains in the world, time slows down by only about 0.00005%. Time Dilation and Simultaneity Normally, we would think that if two events occur at the same time, they occur at the same time for all observers, regardless of where they are. However, because time can speed up or slow down depending on your reference frame, two events that may appear simultaneous to one observer may not appear simultaneous to another. In other words, special relativity challenges the idea of absolute simultaneity of events. EXAMPLE A spaceship of alien sports enthusiasts passes by the Earth at a speed of 0.8c, watching the final minute of a basketball game as they zoom by. Though the clock on Earth measures a minute left of play, how long do the aliens think the game lasts? Because the Earth is moving at such a high speed relative to the alien spaceship, time appears to move slower on Earth from the aliens’ vantage point. To be precise, a minute of Earth time seems to last: 321
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SATII PHYSICS (FROM SPARKNOTES.COM)
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The Good • Because SAT II Subject
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Which SAT II Subject Tests to Take
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After grumbling, however, you still
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Waves 15-19% 11-15 Waves 10% 7-8 Op
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negative, so E, and not A, is the c
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including them anyway because it’
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Two positively charged particles, o
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will a visual representation reliev
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Physics Hint 6: Be Flexible Knowing
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There are a number of ways to label
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Adding Parallel Vectors If the vect
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The result of multiplying A by c is
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neither parallel nor perpendicular.
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Suppose the hands on a clock are ve
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Vector Addition Practice Questions
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2. A The vector 2A has a magnitude
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path, Alan has traveled a much grea
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school student called Andrea. Andre
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centimeters to the left of its star
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We can learn two things about the a
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Acceleration vs. Time Graphs After
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The variable represents the object
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Note that there are certain conveni
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1. . An athlete runs four laps of a
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10. . A woman runs 40 m to the nort
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We know the total distance the spri
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Principles of Natural Philosophy. I
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The component form of Newton’s Se
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e in the direction. And since the s
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which reflects its resistance to be
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In the diagram above, the weight an
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A student pushes a box that weighs
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1. . Each of the figures below show
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7. . In the figure above, a person
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Since the block is motionless, the
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When we are told that a person push
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EXAMPLE A water balloon of mass m i
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The graph above plots the force exe
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Though energy is always measured in
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there is a negative amount of work
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smallest. The answer to question 3
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Mechanical Energy Average Power Ins
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to a height of 8 m over a time of 4
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8. C When the book reaches the pers
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determining what those right number
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the ground. The system is initially
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calculators, you almost certainly w
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and minimize M.” With such a ques
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2. WHAT IS THE ACCELERATION OF THE
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Adding these two equations together
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force of friction: . Using Newton
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m, placed on a frictionless surface
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Frequency is given in units of cycl
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of the spring due to the gravitatio
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The oscillation of a pendulum is mu
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Velocity Calculating the velocity o
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Practice Questions 1. . Two masses,
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7. . An object of mass 3 kg is atta
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Since the system is in equilibrium,
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velocity, v. Linear momentum is den
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Conservation of Momentum If we comb
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As we might expect, the final veloc
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A pool player hits the eight ball,
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two-dimensional collision is effect
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For a System of Two Particles For a
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At the front end of the boat, the f
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4. . A scattering experiment is don
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1. B The athlete imparts a certain
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7. E Momentum is conserved in this
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The diver’s translational motion
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30 π/6 45 π/4 60 π/3 90 π/2 180
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elative position to one another. As
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acceleration given its angular velo
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To find the direction of a rigid bo
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A student exerts a force of 50 N on
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The torque that produces the angula
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The masses in the figure above are
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an object sliding down a frictionle
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Velocity Average Angular Accelerati
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3. . What is the direction of the a
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1. D An object that experiences 120
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At the top of the incline, the disk
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from a Latin word meaning “center
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Newton’s Law of Universal Gravita
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when you are beneath the surface of
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EXAMPLE A satellite of mass is laun
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Kepler’s Laws After poring over t
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Practice Questions Questions 1-3 re
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8. . A satellite orbits the Earth a
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Circumference and radius are relate
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learn how heat is transferred from
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heat, like rubber, have a high spec
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Just as specific heat tells us how
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Conduction is the transfer of heat
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Effectively, this equation tells us
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the way that it does. The Laws of T
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There are a number of equivalent fo
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If we know our formulas, this probl
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5. . An ideal gas is enclosed in a
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Asphalt, like most materials, has a
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The things we call atoms today are
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If they come up on SAT II Physics,
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will move in the opposite direction
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Work The work done to move a charge
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Much like gravitational potential e
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3. . A particle of charge +2q exert
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7. . A particle of charge +q is a d
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The vector sum of the three vectors
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Voltage The batteries we use in fla
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This equation tells us that we can
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If the two variables you know are a
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However, each resistor causes a vol
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So = 4 . WHAT IS THE CURRENT RUNNIN
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Consider again the circuit whose to
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This circuit consists of resistors
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The junction rule deals with “jun
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across the loop. We can express the
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capacitance is halved. The proporti
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The Greek letter is called the diel
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4. . Two resistors, and , are ident
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10. . A dielectric is inserted into
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The equivalent capacitance of two c
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The Earth itself acts like a huge b
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Because the velocity vector and the
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A particle with a positive charge o
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The constant is called the permeabi
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1. . The pointer on a compass is th
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7. . A positively charged particle
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1. B To solve this problem, it is h
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If the particle is to move at a con
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flowing in the counterclockwise dir
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Next, let’s calculate the flux th
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Remember that field lines come out
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pinpointing what you need to study
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If you got a question wrong because
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