Quiz 5 Solution
L. Feng
November 23, 2013
Problem 1 Consider the TinkerToy Rotator shown in Figure 1. Take
the angle of the rods to be 45 , the masses to be equal, and the length of each
rod to be 2 in some suitable units. Ignore the masses of the rods an
Physics 141
Problem Set 1
Due Monday, Oct. 7 (hand in in class).
September 28, 2013
H. J. Frisch; 702-7479
=
General: Organization, Web page, Labs, Syllabus: See the P141 Information Sheet handed out
on Monday and posted under Course Documents on Chalk
=
PHYSICS 141 PS3: SOLUTIONS
PAVEL MOTLOCH
Contents
1.
2.
3.
4.
5.
6.
Problem
Problem
Problem
Problem
Problem
Problem
1
2
3
4
5
6
(Morin,
(Morin,
(Morin,
(Morin,
Problem
Problem
Problem
Problem
1
1
2
2
3
5
3.1)
3.2)
3.8)
3.11)
1. Problem 1
Deriving the fami
Introduction to Classical Mechanics
With Problems and Solutions
This textbook covers all the standard introductory topics in classical mechanics,
including Newtons laws, oscillations, energy, momentum, angular momentum,
planetary motion, and special relat
HJF Draft Version 1.0
November 23, 2013
Physics 141
Chapter 20: The TinkerToy Rotator: L = I.
1
An Example Of a Simple Rigid Body Showing L Does
Not Generally Lie Along
Figure 1 shows a simple object consisting of 2 equal masses at the ends of a light ro
PHYS141
Fall 2013
Discussion - Week 7
November 19, 2013
Giordon Stark
Contents
1 Moment of Inertia Tensor
1.1 The Rigid Body . . . . . . . .
1.2 Total Kinetic Energy . . . . .
1.3 The moment of inertia tensor
1.3.1 In matrix form . . . .
.
.
.
.
2
2
3
3
5
PHYSICS 141 QUIZ 6: SOLUTIONS
PAVEL MOTLOCH
Contents
1.
2.
Problem 1
Problem 2
1
2
1. Problem 1
1) The gure is the same as in the Tinker Toy notes:
Figure 1: Drawing of the rotator.
2) We know the moment of inertia and the vector , which means we can easi
PHYS141
Fall 2013
Gradient Primer
December 6, 2013
1
Giordon Stark
The Geometry
(a) polar
(b) spherical
Converting between the two coordinate systems is by
r=
x2 + y 2 + z 2
x = r sin cos
= arctan
y = r sin sin
x2 + y 2
z
= arctan
y
x
z = r cos
The u
PHYSICS 141 PS8: SOLUTIONS
PAVEL MOTLOCH (MOSTLY REWRITING LAST YEARS SOLUTIONS)
Contents
1.
2.
3.
4.
5.
6.
Problem
Problem
Problem
Problem
Problem
Problem
1
2
3
4
5
6
1
2
2
3
3
3
1. Problem 1
Write the radial equation of motion for a planet moving aroun
HJF Draft Version 1.0
November 29, 2013
Physics 141
Chapter 26: Circular Orbits- Section on Stability
1
Stability
1.1
Expanding the Eective Potential in a Taylor Expansion
Vef f = k/r + L2 /(2mr2 )
(1)
The eective potential has a minimum at the radius of
Feynman's Preface
These are the lectures in physics that I gave last year and the year before to the
freshman and sophomore classes at Caltech. The lectures are, of course, not
verbatimthey have been edited, sometimes extensively and sometimes less so.
Th
Physics 141
Problem Set 9: Review Problems
Due in class Wed. Dec. 4
Monday, Nov. 25, 2013; H. J. Frisch; 702-7479
=
This is the 2nd installment of review problems (the rst was the review for the
midterm, Problem Set 5). The nal will be largely composed of
Phys141
Homework # 3
Due Monday October 21st at 9.30 in Class.
Reading: Chapter 3 and chapter 4 until 4.6 included
5 Problems: (50 points total)
3.4
3.12
3.18
3.19
3.26
Studying guideline: Before starting the assigned problems, read carefully through the
Phys141
Homework # 7
Due Wednesday December 3rd at 9.30 in Class.
Reading: Chapter 12
5 Problems: (50 points total)
1. Doppler effect: Consider two light pulses at (0,0) and (0,T) in a frame S moving at
speed v along x with respect to a fixed frame S. Usi
Phys141
Homework # 2
Due Monday October 13th at 9.30 in Class.
Reading: Chapter 2 and chapter 3 until 3.5
5 Problems: (50 points total)
2.2
2.4
2.11
3.5
3.6
Studying guideline: Before starting the assigned problems, read carefully through the
sample probl
Phys141
Homework # 4
Due Monday November 3rd at 9.30 in Class.
Reading: Chapter 7 and 6
5 Problems: (50 points total)
6.3
6.17
7.8
7.9
7.19
Studying guideline: Before starting the assigned problems, read carefully through the
sample problems in the chapte
Phys141
Homework # 6
Due Monday November 17th at 9.30 in Class.
Reading: Chapter 9 and 10
5 Problems: (50 points total)
9.4
9.12
10.4
10.7
10.10
Studying guideline: Before starting the assigned problems, read carefully through the
sample problems in the c
Phys141
Homework # 5
Due Monday November 10th at 9.30 in Class.
Reading: Chapter 8
5 Problems: (50 points total)
8.1
8.3
8.5
8.7
8.11
Studying guideline: Before starting the assigned problems, read carefully through the
sample problems in the chapters ass
PHYS 141A: Problem Set 2 Solutions
2.2 Two blocks and string
The tension of the string T ensures that M1 and M2 always move with the same speed
and acceleration. Note that theres no friction. Since M1 and M2 only moves in x and y
direction respectively, w
Phys141
Homework # 2
Due Monday October 12th at 9.30 in Class.
Reading: Chapter 2 and chapter 3 until 3.5
5 Problems: (50 points total)
2.2
2.4
2.11
3.5
3.6
Studying guideline: Before starting the assigned problems, read carefully through the
sample probl
PHYS 141: Problem Set 1 Solutions
1.11 Volume of a parallelepiped
We want to show that the volume of a parallelepiped with edges A, B, and C is V =
|A(BC)|. We want the absolute value because we could otherwise end up with a negative
sign if we dont pick
Physics 141
Problem Set 8
Due Tues, Nov. 24th
November 17, 2015
H. J. Frisch; 702-7479
=
General: See the P141 Info Sheet posted under Course Documents on Chalk.
=
Reading: Central force motion is hard, as its dominated by conservation of angular momentum