Phys 7221 Homework #2
Gabriela Gonzlez
a
September 18, 2006
1. Derivation 1-9: Gauge transformations for electromagnetic potential
If two Lagrangians dier by a total derivative of a function of coordinates and time,
they lead to the same equation of motio
Phys 7221, Fall 2006: Midterm exam
October 20, 2006
Problem 1 (40 pts)
Consider a spherical pendulum, a mass m attached to a rod of length l, as a constrained
system with |r| = l, as shown in the gure.
a) (15 pts) What are the conserved quantities of the
Phys 7221 Hwk #9: Small Oscillations
Gabriela Gonzlez
a
December 5, 2006
Prob 6-4: Double Pendulum
We follow the conventions for angles in Figure 1.4 (notice that 1 is counterclockwise, and
2 is clockwise!). We set up a coordinate system with the origin a
Phys 7221 Homework # 8
Gabriela Gonzlez
a
November 15, 2006
Derivation 5-6: Torque free symmetric top
In a torque free, symmetric top, with Ix = Iy = I , the angular velocity vector in body
coordinates with axes along the principal axes, is given by
x = 0
Phys 7221 Hwk # 7
Gabriela Gonzlez
a
November 6, 2006
Derivation 4-4
Show that if A is a real 3x3 antisymmetric matrix, then the matrices 1 A are nonsingular, and the matrix B = (1 + A)(1 A)1 is orthogonal.
If A = A, then A has only three independent comp
Phys 7221, Fall 2006: Homework # 6
Gabriela Gonzlez
a
October 29, 2006
Problem 3-7
In the laboratory system, the scattering angle of the incident particle is , and that of the
initially stationary target particle, which recoils, is ; see Fig. 3.24, or Fig
Phys 7221, Fall 2006: Homework # 5
Gabriela Gonzlez
a
October 1, 2006
Prob 3-11: Collapse of an orbital system
Consider two particles falling into each other due to gravitational forces, starting from rest
at a distance a. The system has zero angular mome
Phys 7221, Fall 2006: Homework # 4
Gabriela Gonzlez
a
October 2, 2006
Problem 3-10: A comet striking a planet
A planet has a very eccentric orbit about the Sun, with eccentricity e = 1 with
1.
When the planet is at the greatest distance from the Sun (aph
Phys 7221 Homework #3
Gabriela Gonzlez
a
September 27, 2006
1. Derivation 2-4: Geodesics on a spherical surface
Points on a sphere of radius R are determined by two angular coordinates, an azimuthal angle and a polar angle :
r = x + y + z k = R(sin cos +
Phys 7221 Homework #1
Gabriela Gonzlez
a
1. Derivation 1-1: Kinetic energy and power
T
=
mT
=
d(mT )
dt
=
1
1 p2
pp
mv 2 =
=
2
2m
2m
1
pp
2
dp
p=Fp
dt
If mass is constant,
d(mT )
dT
=m
dt
dt
dT
dt
= Fp
= F
p
=Fv
m
Notice that F v = F (ds)/dt = d(F s)/dt =
Physics 7221 Fall 2006 : Final Exam
Gabriela Gonzlez
a
December 14, 2006
NAME: .
1
(10 pts) Question 1: A two mass system.
Consider the following arrangements of two masses, shown in the gure: (a) two masses not connected to each other; (b) two masses con