Physics 26: 611 General Relativity
Homework
Reading Preparation
Text Reading: Giancoli, Physics  Principles with Applications, Chapter 27: Sections 6 to 11
Study Points
 Section 6: In the fourdimensional view of the universe, three space and one time dimensions are equivalent and necessary to locate an object with reference to a point.
 Section 7: Because time and distance are modified at relativistic speeds, dependent concepts such as velocity, momentum, and energy must also be modified. At relativistic speeds (v > 0.1c),
p = γ m_{0}v
where m_{0} is the rest mass of an object.
 Section 8: Note that when v = c, the relativistic mass m_{rel} = m_{0}γ becomes m_{0}/0: an undefined value. This indicates that an object with actual mass can never move at light speed.
 Section 9: Einstein showed that relativistic kinetic energy = γm_{0}c^{2}  m_{0}c^{2} = (γ 1) m_{0}c^{2}. For a particle at rest in a given reference frame, E = m_{0}c^{2}. Mass can be converted to energy and energy can be converted to mass.
 Section 10: If v is the speed of an object A with respect to an observer O, and u' is the speed of an object with respect to moving object A, the velocity observed y O is u = (v + u') / ( 1 + vu'/c^{2})
 Section 11: According to the correspondence principle, classical mechanics is a special case of general relativity, valid where the difference between general relativity predictions and its own are too small to be observed.
Key Equations
Principles 
Equation 
Variables 
Relativistic momentum 
$$p\text{}=\text{}\frac{\mathrm{mv}}{\sqrt{1\text{}\text{}\frac{{v}^{2}}{{c}^{2}}\text{}}}\text{}=\text{}\gamma \mathrm{mv}$$

p: momentum
m: rest mass
v: velocity
γ: Lorenz factor 
Rest mass vs relativistic mass 
$${m}_{\mathrm{relativistic}}\text{}=\text{}\frac{{m}_{0}}{\sqrt{1\text{}\text{}\frac{{v}^{2}}{{c}^{2}}\text{}}}$$

m: relativistic mass
m_{0}: rest mass
v: velocity 
Relativistic kinetic energy: 
$${\mathrm{KE}}_{\mathrm{relativistic}}\text{}=\text{}\frac{m{c}^{2}}{\sqrt{1\text{}\text{}\frac{{v}^{2}}{{c}^{2}}\text{}}}\text{}=\text{}(\gamma \text{}\text{}1)m{c}^{2}$$

m: rest mass 
Adding relativistic velocities: 
$$u\text{}=\text{}\frac{v\text{}+\text{}u\text{'}}{1\text{}+\text{}\mathrm{vu}\text{'}/{c}^{2}}$$

v: speed of rocket relative to stationary observer
u': speed of secondary rocket relative to moving observer
u: speed of secondary rocket relative to stationary observer 
Web Lecture
Read the following weblecture before chat: General Relativity, Space, ad Time
Study Activity
Use the Fermilab Interactive exercise for Orbits in Strongly Curved Spacetime to explore what happens when you change the mass of a black hole orbited by a small satellite. Read the introduction and descriptions, then run the simulator by varying the mass, angular momentum, and radius of the black hole.
Chat Preparation Activities
 Forum question: The Moodle forum for the session will assign a specific study question for you to prepare for chat. You need to read this question and post your answer before chat starts for this session.
 Mastery Exercise: The Moodle Mastery exercise for the chapter will contain sections related to our chat topic. Try to complete these before the chat starts, so that you can ask questions.
Chapter Quiz
 Required: Complete the Mastery exercise with a passing score of 85% or better.
 Go to the Moodle and take the quiz for this chat session to see how much you already know about astronomy!
Lab Work
If you want lab credit for this course, you must complete at least 12 labs (honors course) or 18 labs (AP students). One or more lab exercises are posted for each chapter as part of the homework assignment. We will be reviewing lab work at regular intervals, so do not get behind!
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