Fall 2015 ph106 Problem Set 5 Solutions
Zachary Mark
November 30, 2015
Problem 1
HF 4.12 (Center of Mass). 10 Points
A projectile in outer space subjected to no external forces suddenly explodes into three pieces, which have Cartesian coordinates
r1 , r2
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Problem Set 7
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Problem 4
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Problem 4
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Problem 8
Fall 2005 Ph106a/196a
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Problem 8
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Physics 106a Midterm: Solutions
Ke (Kevin) Ye,
kye AT caltech.edu
October 23, 2015
3. Constrained Motion [15 Points]
Let us set up our coordinate system. Take the origin at the center of large cylinder, and let x and z
be the horizontal and vertical axis.
Physics 106a Problem Set 1: Solutions
Ke (Kevin) Ye,
kye AT caltech.edu
October 10, 2015
1. Momentum and Angular Momentum [10 Points]
From the given trajectory we can compute the momentum using elementary derivative in Cartesian
coordinate:
r = (x0 + at2
Physics 106a, Caltech 29 September, 2016
Lecture 2: Variational Approach
Example
We looked at a simple example of applying Newtons laws of motion, a block sliding on an inclined
plane. This is discussed in Hand and Finch 1.1, and will be used as a recurri
Physics 106a, Caltech 27 September, 2016
Course Organization
Most of the information here is on the course website:
https:/labcit.ligo.caltech.edu/ajw/ph106/ph106a 2016.html
Please read the course policies below!
Acknowledgement: Much of the material for
Physics 106a: Assignment 3
14 October, 2016; due 5pm Friday, 21 October in the Ph106 In Box in East Bridge mailbox.
Constrained dynamics and small oscillations
Reading
Constrained dynamics: HF 2.6-8, T 7.3,7.10. You should work through some problems on
th
Physics 106a, Classical Mechanics Fall Term, 2016
Final Exam
Do not read beyond this page until you are ready to start the exam!
Due date: Due by 4pm in Physics 106 In Box in East Bridge on Friday 9 December.
Late exams will require extenuating circumstan
Physics 106a: Assignment 1
30 September, 2016; due 5pm Friday, 7 October in the Ph106 In Box in East Bridge
mailbox.
Remember: only identify your solution set with your class id number, not your name.
Variational Approach and Lagrangian Dynamics
Reading
I
Physics 106a: Assignment 2
7 October, 2016; due 5pm Friday, 14 October in the Ph106 In Box in East Bridge mailbox.
Constraints, Virtual Work, and Lagrangian Dynamics
Reading
You can now read the complete chapters 1 and 2 in Hand and Finch or 6 and 7 in Ta
Physics 106a, Classical Mechanics
Midterm Exam, Fall Term, 2016
Do not read beyond this page until you are ready to start the exam!
Material: The exam covers the material of Lectures 1-8.
Due date: Due by noon in Ph106 box, East Bridge, on Monday October
Physics 106a: Assignment 5
4 November, 2016; due 5pm Friday, 11 November in the Ph106 In Box in East Bridge mailbox.
Canonical Transformations etc.
Reading
Hand and Finch Chapter 6. Taylor does not cover these topics. The discussion in Goldstein et al. is
Physics 106a: Assignment 6
11 November, 2016; due 5pm Friday, 18 November in the Ph106 In Box in East Bridge mailbox.
Reading
Hand and Finch Chapter 7 (see the lecture notes for a coordinate-free derivation of the results in section 7.5 and
7.6 of H&F). T
Physics 106a: Assignment 7 Rotational Motion
25 November, 2016; due 5pm Friday, 2 December in the Ph106 In Box in East Bridge
mailbox. This set is a bit longer than usual. You have two weeks to work on it, but take some
time to relax during Thanksgiving b
Physics 106a: Assignment 4
28 October, 2016; due 5pm Friday, 4 November in the Ph106 In Box in East Bridge mailbox.
Hamiltonian Formulation
Reading
Hand and Finch Chapter 5. Also review Chapter 4 on central forces.
Problems
Problems 1 and 4 are longer, an