Physics 110A: Midterm Study Guide

Fall Term, 2012

These are the key concepts you should understand and on which you should be able to perform related problems on the midterm.

- Understand polar coordinate constructions and basis vectors.
- Whether linear or quadratic drag, be able to pull the terminal velocity
out of the differential equation, and be able to solve the differential
equation in one dimension (horizontal or vertical, linear or quadratic) to
get
*x*(*t*) or*y*(*t*) and match to initial conditions to replace the constants of integration. - Be familiar with the
*v*-dot =*v*d*v*/d*x*"trick" so that you can solve*v*(*x*) (or*v*(*y*)) directly rather than*v*(*t*). - Understand complex exponential notation, Euler's formula, etc.
- Be able to compute integral properties of solid bodies, such as volume, center of mass, moment of inertia, etc.
- Get yourself straight on angular motion: angular momentum, torque,
moment of inertia, and how all of these are related (e.g.,
*L*-dot = torque;*L = Iω*, etc.). - Develop a reflex for invoking conservation of energy and momentum.
- Understand path integrals and how to evaluate them given a specified path.
- Be familiar with the grad/del/nabla doohicky and its application in
constructing and evaluating conservative forces (e.g., grad-
*U*and curl-*F*). - Given total energy,
*E*and potential*U*(*x*), be able to construct a differential equation for the motion that can be solved to arrive at*x*(*t*). - Be able to evaluate the stability of a system based on the potential energy as a function of some (not necessarily Cartesian) coordinate or parameter.
- Given the differential equation for a damped oscillator, be able to
walk through its solution for the over- and under-damped cases, and match
the ultimate solution for
*x*(*t*) to initial conditions. - Understand how a periodic driving force results in long-term behavior at the drive frequency, with an amplitude that exhibits resonant qualities.