AA 242A Homework 1
Assigned: September 23, 2014
Due: September 30, 2014
1. Consider the vector A = Ax i + Ay j + Az k . Find the components A1, A2, A3 of the
vector A in a skewed coordinate system who
AA 242A Homework 1 Solution
September 30, 2014
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Problem 1
Consider the vector A = Ax i + Ay j + Az k . Find the components A1 , A2 ,
A3 of the vector A in a skewed coordinate system whose axes have
AA 242A Homework 4 Solution
October 25, 2014
1
1
Problem 1
There are essentially three unknowns in this problem - the x and y components of rocket velocity and the ight path angle . We need to come up
AA 242A Homework 3 Solution
October 22, 2014
1
1
Problem 1
Diagram of the mass in the tube, spinning with angular velocity . The
normal force, Fn and frictional force, Ff are shown as well.
Let us rst
Homework 9: # 8.19, 8.24, 8.25
Michael Good
Nov 2, 2004
8.19
The point of suspension of a simple pendulum of length l and mass m is constrained to move on a parabola z = ax2 in the vertical plane. Der
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 tar
Review of Matrix Algebra
AA 242A
Notation
"
$
! $
m by n rectangular matrix: a ! $
$
$
#
!
!
Transpose: a T or a
!
Inverse: a !1
!
!
Determinant: det(a) = a
a11
a12
a21
a22
#
am1
#
am2
" a1n %
'
" a2
Example: Falling Chain
AA 242A
A chain of uniform density of length b and total mass M is suspended at its ends from adjacent
points A and B. At time t = 0, the end at point B is released. Find the te
Example: Simple Pendulum
AA 242A
A simple pendulum on Earth with point mass m on a massless wire of length l is attached to a
point O and is allowed to swing in a plane. An additional force is applied
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 coordinate
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 ortho
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 clock
Homework 4: # 2.18, 2.21, 3.13, 3.14, 3.20
Michael Good
Sept 20, 2004
2.18 A point mass is constrained to move on a massless hoop of radius a xed
in a vertical plane that rotates about its vertical sy
Homework 1: # 1.21, 2.7, 2.12
Michael Good
Sept 3, 2004
1.21. Two mass points of mass m1 and m2 are connected by a string passing
through a hole in a smooth table so that m1 rests on the table surface
Homework 7: # 4.22, 5.15, 5.21, 5.23, Foucault
pendulum
Michael Good
Oct 9, 2004
4.22
A projectile is red horizontally along Earths surface. Show that to a rst
approximation the angular deviation from
Homework 5: # 3.31, 3.32, 3.7a
Michael Good
Sept 27, 2004
3.7a Show that the angle of recoil of the target particle relative to the incident
1
direction of the scattered particle is simply = 2 ( ).
An
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 coordi
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
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 a
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 th
AA 242A
TOPIC 6: Linear and Angular Momentum
Linear Momentum (p)
IF A PARTICLE IS FREE, THEN LINEAR MOMENTUM IS CONSERVED.
THIS IS A VECTOR EQUATION AND APPLIES TO EACH COMPONENT OF
LIN
AA 242A
TOPIC 7: Linear and Angular Impulse
Linear Impulse (F)
Change in linear momentum of a particle during a given time interval is equal to the total
impulse of the external forces
AA 242A
TOPIC 2: Rate of Change of Vectors
A = A
Cartesian:
r = xx + yy + zz; v = xx + yy + zz
Cylindrical:
r = rr + zz; v = rr + rr + zz
= z
r = r = z r =
AA 242A Homework 4
Assigned: October 14, 2014
Due: October 21, 2014
1. You are the launch director for a sounding rocket. On the day of the launch, you find that
there is a strong surface wind blowing
AA 242A Homework 5
Assigned: October 21, 2014
Due: October 30. 2014
1. A pendulum of mass m is attached to a cart of mass M on a spring. Take the rest length of
the spring to be zero.
a. Find EOMs by