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Thursday, December 22, 2016

Mechanics Semester Review

Here is a list of topics for our final, the second week back from winter break:

Basics:
Vector algebra - vector addition, multiplication (dot and cross products)
Derivatives - finding them; what does it mean graphically; instantaneous values
Define v = dx/dt; a = dv/dt
Antiderivatives - finding them; what does it mean graphically
Motion graphs

Kinematics:
Constant acceleration equations, how to use them in a variety of problems
Free fall
Relative motion (e.g. boat going across a river)
Projectiles

Newton's laws:
Know them by number; conceptually what do they mean? Examples.
Finding resultant forces (vector addition)
Equilibrium, balancing forces in multiple dimensions
Applications of Fnet = ma, all types
Tension, friction, on inclines (gravity triangle), springs
Systems problems, such as multiple blocks tied together
Circular motion, how to set up mv^2/R in problems; horizontal vs vertical problems
NON-constant forces and accelerations
Air friction, f = -kv; derivation of v(t); chain rule
Gravity - Newton's law of universal gravitation; Einstein's thoughts on warped space-time
Orbital motion - orbital speed, Kepler's laws; Binary orbits

Energy:
Conservation law
Different types, conversions of energy
Work redefined as an integral; work is the amount of energy transferred between objects
Using work and conservation to solve a variety of problems, especially with speeds and non-constant forces
Potential energies (gravity, springs)
How to do gravity the right way with energy, U = -GMm/r; what does - sign mean?
Potential wells - U-x graph vs F-x graph; positive force vs negative force
Gradient, F = - dU/dx; what this means
Escape velocity; Schwarzschild radius
Power
Special relativity implications, Einstein's energy equation

Resources:
Videos on most of the topics above. For practice multiple choice, the SAT II site has notes, sample questions, and explanations on all these topics. There is a Learn AP Physics C site, with practice questions. We have our AP Exams folder (but you must be logged in only on your eths202.org account).  Note there is a multiple choice folder, with hundreds of practice questions. There are review sets in each of our unit folders. Read up on any topic and check out dozens of worked examples in Chapter 1-7, which is what we have covered so far. You have your old quizzams and solutions, homework sets, and labs.

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