Physics 4001 - Classical Mechanics
Discussion Week 9
A spacecraft is being designed to dispose of nuclear waste either by carrying it out of the
solar system or crashing into the Sun. Assuming no planetary ybys are permitted and
the motion is conned to th
Physics 4001 - Classical Mechanics
Discussion Week 10
11/05/2013
A solid, uniform cube with side b is sitting on top of a xed half cylinder with radius R
such that the planes of four sides of the cube are parallel to the axis of the cylinder. Take
the con
1
Week 13 Discussion
Because the Earth is not perfectly spherical, the Sun and Moon exert torques
that lead to a precession of the Earths rotational axis. In this problem, we
will calculate the period of this precession, treating the Earth as an oblate
sp
Physics 4001 Exam 3 November 21 2011
Equation Sheet
Trigonometry:
Law of sines:
a
sin
=
b
sin
=
c
sin
Law of cosines: c2 = a2 + b2 2ab cos
Vectors:
A + B = (Ax + Bx , Ay + By , Az + Bz )
A B = Ax Bx + Ay By + Az Bz = AB cos
A B = (Ay Bz Az By , Az Bx
Physics 4001 Exam 2 October 26 2012
Equation Sheet
Vectors:
A + B = (Ax + Bx , Ay + By , Az + Bz )
A B = Ax Bx + Ay By + Az Bz = AB cos
A B = (Ay Bz Az By , Az Bx Ax Bz , Ax By Ay Bx )
|A B | = AB sin
Complex numbers:
c = a + ib, c = a ib
a = r cos , b
Classical Mechanics
Discussion #8
10/25/11
An elliptical (roughly spherical) galaxy has visible stars in dense center bulge out to roughly 2 kpc
and a collection of stars further out that rotate around the center.
1) Find the relationship between the spee
1
Week 8 - A Toy Hurricane
Tropical storms can be devastating to coastal economies, oil platforms, and honeymooners. Lets see if we can gure out what makes them tick.
Recall that Newtons 2nd Law transforms to a non-inertial frame as:
FR,e = F mA0 2m vR m
Physics 4001 - Classical Mechanics
Discussion Week 6
10/08/2013
In the metro area, the Minnesota Twins were broadcast on the AM station 1500 (fc = 1500 kHz). This
frequency refers to the carrier wave of the signal; there is also the amplitude modulation o
Physics 4001 - Classical Mechanics
Discussion Week 5
10/02/2012
The speed at the surface of a river is roughly proportional to the square of the rivers
depth at that point. A long, straight section of a river has a depth proportional to
h2 x2
0
1/4
,
wher
I.
WEEK 4 DISCUSSION PROBLEM
A simple pendulum of mass m and length l is attached to a spring of spring constant
k . The spring is attached to a wall a distance L l away. (In other words, the spring
stretches primarily due to the horizontal motion of the
Physics 4001 - Classical Mechanics
Discussion Week 3
09/17/2013
Two particles (one heavy and one light, with reduced mass ) interact with each other
under the inuence of two forces.
One is attractive and is given by the potential, V1 (r) = V0
r
a1
,
while
I.
WEEK 2 DISCUSSION PROBLEM
For this problem, the following vector identities will be useful:
1. a b = |a|b| cos ,
2. a (b c) = (a b) c.
In any Kepler problem (e.g. planetary motion), there are two conserved vectors: the angular momentum, L, and the
Lapl
Physics 4001 Exam 1 September 28 2012
Equation Sheet
Vectors:
A + B = (Ax + Bx , Ay + By , Az + Bz )
A B = Ax Bx + Ay By + Az Bz = AB cos
A B = (Ay Bz Az By , Az Bx Ax Bz , Ax By Ay Bx )
|A B | = AB sin
Complex numbers:
c = a + ib, c = a ib
a = r cos ,
Physics 4001 Exam 1 September 27 2012
Equation Sheet
Vectors:
A + B = (Ax + Bx , Ay + By , Az + Bz )
A B = Ax Bx + Ay By + Az Bz = AB cos
A B = (Ay Bz Az By , Az Bx Ax Bz , Ax By Ay Bx )
|A B | = AB sin
Complex numbers:
c = a + ib, c = a ib
a = r cos ,
1
Week 11 Discussion Problem
A thin disk of gas rotates in space with uniform angular velocity d about
its symmetry axis. The radius of the disk is Rd , and the total mass is Md .
Given that the gas only interacts gravitationally,
(a) Find the density as
Physics 4001 - Classical Mechanics
Discussion Week 15
12/10/2013
A bead of mass, m, is constrained to move on a circular wire (hoop) rotating with constant
angular velocity, , about its vertical axis. This problem is amenable to investigation using
Hamilt