PHYS 230
Fall 2007
Assignment 6
1. French 3.6 The space and time co-ordinates of two events as measured in a frame S are as follows: Event 1: x1 = x0 , t1 = x0 /c, (y1 = z1 = 0). Event 2: x2 = 2x0 , t2 = x0 /2c, (y2 = z2 = 0). (a) There exists a fr
Physics 230 MidTerm Examination Tuesday October 23rd, 2007
Each question is worth 10 points. Try all three, if you wish, but you will get points only for your best two. If you do not have time to finish a problem, but know how to do it, you can get p
2.5 Solutions
39
distance the rightmost point on the top block can hang out beyond the :x:<)~ table') How docs your answer bcha\e for S
Solutions
I, Hanging rope Let T(l'l bc the 1elbi(>ll ,b 2 timctiol1 of hc'lghL Con,ider a smail ple<.:e of the rope bcl
Chapter 1 Ordinary Differential Equation
Page 1
Chapter 1 Ordinary Differential Equation
1.1 Differential Equation
Equation, which involves the solving of an unknown variable or function, is a
very important topic in mathematics and physics. For example,
Phys 230 Midterm Info
Our midterm exam will be on Oct. 19, Tuesday, 8:35-9:55am, in class. Here are some
information about the exam.
1. Students with last name starting with A to M: please write the exam in our classroom (room
118 of Physics Building). Th
PHYS2626 Introductory Classical Mechanics
Suggested Solutions for Assignment 1
September 2008
1. Problem 3.34
Refer to the gure for the symbols used.
Only forces used to solve the problem
are shown.
The equations:
= ma.
3
(N2 N3 ) cos
= ma.
3
(N2 + N3 ) s
PHYS2626 Introductory Classical Mechanics
Suggested Solutions for Assignment 2
October 2009
1. Problem 4.19
Method I: Initially,
x(t) = d cos
2k/m t + ,
x(t) = d 2k/m sin
2k/m t + .
At t = 0, when x(0) = d/2,
cos
2k/m t +
1
=
, sin
2
2k/m t + =
3
.
2
|x
PHYS2626 Introductory Classical Mechanics
Suggested Solutions for Assignment 3
November 2008
1. Problem 8.51
Let f be the friction between the plank and the coin,
A and a be the accelerations of the plank and coin respectively, and
be the angular acceler
ANGULARMOMENTUMAGENERALAPPROACH
9.1Somebasictheorems
Theorem1(ChaslesTheorem)
Themotionofarigidbodycanbedescribedbythetranslationmotionofapoint
P in the body and the rotational about an axis (which may change with time)
passingthroughP.
Theorem2
S1,S2andS
CHAPTER 1 NEWTONIAN MECHANICS FOR SINGLE PARTICLE
1.1 Frame of Reference
Before we can discuss the physical laws, we have to talk about the concepts of the
reference frame. Indeed, before we make any description of the motion of a single
particle, firstly
CHAPTER 2 OSCILLATIONS
2.1 Quick Review of Simple Harmonic Motion (SHM)
2.1.1 Equation of Motion for SHM
The equation of motion for the SHM is:
or
where
(2.1)
.
The general solutions of this equation of motion are :
(1) x(t) = A cos (t + );
(2) x(t) = A s
CHAPTER 3 MOTION OBSERVED IN A ROTATING FRAME
3.1 Pseudo-force in the Rotating Frame
z
z'
x'
y
y'
x
Consider that we have an inertia
frame S with coordinate system xyz
fixed to it and another frame S' (with
coordinate system x'y'z' attached to it).
S' is
CHAPTER 4 MOTION OF MANY BODY SYSTEM
4.1 Newtonian Mechanics for Many Particle System
In the previous chapters, we have studied the motion of single particle and the
laws which govern the dynamics of single particle under the influence of a force field. I
CENTRAL FORCES
Definition:
(1) The potential is only dependent on the distance from source.
i.e.
(2) From (1):
, i.e. the central force is radical in
direction and its magnitude is only dependent on the distance from the source.
Theorem 1:
conserved.
If a
1
Phys 230 - Midterm I
October 1st, 2015
Answer all questions, on the two sides of the page
1. Math preparations
(a) Vectors - Two vectors in the two dimensions are given. The first is given in
Cartesian coordinates ~v1 = (1, 3) and the second is given in
1
Phys 230 - Midterm II
November 5th, 2015
1. Balancing Torques (20 points)
A ball is held up by a string, as shown in the Figure below, with the string tangent
to the ball. If the angle between the string and the wall is , show that the minimum
coefficie
1
Final practice questions
1. Gravity
Two equal masses m are moving under the influence of their gravitational attraction.
(a) The distance between the masses is constant, r0 . Show that the kinetic energy is minus half of the potential
energy.
(b) We now
1
Conservative Forces & Stokes Theorem
Figure 1: Two integrations paths along the contour of an infinitesimal rectangle in the x-y plane. Both paths have
the same initial and final points, (x, y) and (x + dx, y + dy) respectively.
(A)
(x+dx,y+dy)
We assu
Phys 230 - Solutions to Assignment 2
~ = (1, 3, 1).
1. Given A
a)
~ =
A = |A|
p
1+9+1=
p
11 ' 3.317 .
b) You can see this either by drawing the vector and using geometry to find the angle,
cos =
Az
A
= arccos
Az
A
= arccos
1
3.317
= 107.55 .
Another meth