Homework 1 Solutions
Phys. 105, UCSC, F2010
Due Oct. 5, Tuesday. Each problem is worth 5 points, except problems 5, 6, 7 (10 points each).
Problem 1 Assume that O1 and O2 are arbitrary orthogonal matrices of the same dimensions. For each of the followin
Homework 1
Due Friday, September 30, at the beginning of lecture
Please submit your work on clean, unfolded paper, with your work shown clearly, working from left
to right, top to bottom in a single column. Partial credit on homework solutions will be gra
Pre-exam
Phys. 105, UCSC, F2010
This pre-exam shows the type of problems that will be in the midterm. These are just
some examples, and do not cover all possible subjects.
Solutions to this pre-exam are not available. However, your group can submit, by
em
Midterm
Phys. 105, UCSC, F2010
Closed everything. No calculator. If you need other (physics or math) formula, you
may ask if it can be given. Please ask if any problem needs to be claried further.
sin(a b)
cos(a b)
sin(2a)
cos(2a)
sin
=
=
=
=
=
cos =
(1
Notes for Lecture 17
Rigid Body
17.1
Rigid body inertia tensor
The denition of the inertia tensor was given in the previous lecture, but it helps to
rewrite it in a more familiar form.
Recall that the vector si is the position vector of mass mi , si,1 . L
Notes for Lecture 16
Molecules, Many Body, Rigid Body
16.1
Normal modes of molecules
In the last lecture, we studied a classical mechanics model1 for CO2 . By choice, we
only considered one dimensional motions in which any atom moves only along the
line o
Notes for Lecture 13
Kepler problem
In the previous lecture, we set the scene for Kepler problem, by investigating the
central force problem. Let us consider the two important cases: U (r) = kr2 /2 (Hookes
law) and U (r) = k/r (Kepler problem). As we lear
Notes for Lecture 12
Central Force
Central force problems are important. All planet motion problems are of this kind.
Also, crude but useful classical mechanics models of atoms and nucleons are of this
kind. Crude, because classical mechanics fails for at
Notes for Lecture 10
Symmetry, conservations, and H
Conservation principles are very fundamental in physics. Most conservation principles
that we know arise from symmetry.
10.1
Symmetry principles
Symmetry is important. It really is. A well-known Nobel la
Notes for Lecture 9
Principle of least action
9.1
Principle of least action
Maybe a catchy name: the principle of least action (PoLA). It is also called Hamiltons principle.
In this course, this principle is completely equivalent to Newtons laws. From
a m