5/5/2016
Book on a Cylinder
Physics 321
Hour 9
Curvilinear Systems and Central Forces
Book on a Cylinder
Book on a Cylinder
=
+
r sin
+ cos
sin
r
(r+b)cos
1
5/5/2016
Book on a Cylinder
Examples
= + 2 cos
( ) sin
potentials4_7.nb
potentials4_7b.nb
r
r co
Physics 321
Manipulating the 2nd Law
It is often better to turn one 2nd order equation
Into two 1st order equations:
Hour 2
Applying Newtons Laws of Motion
Manipulating the 2nd Law
We can also express F in terms of spatial
derivatives:
1
= =
=
=
Physics 321
Hour 1
Course Introduction
Course Components
Course Outline
Prerequisites: ODEs, Mathematica
Reading: Due before lecture
HW: Due MWF - see schedule on Learning Suite
Take-home Tests: Due most Thursdays
Midterm Exams: In the Testing Center
Fina
Consequences of Relativity
Physics 321
Momentum becomes
= =
Kinetic energy becomes
=
Potential energy becomes hazy
Momentum is conserved asymptotically
Hour 3
Application of Newtons Laws/Drag Forces
Problem 1
A mass hangs from a string from the
ro
4/29/2016
Linear and Angular Relationships
Physics 321
Hour 6
Conservation of Angular Momentum
Angular Momentum in Linear Motion
P
We must
calculate angular
momentum
about a point P.
b
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
Central Force
The torque is ze
Lorentz Force
Physics 321
Hour 4
Lorentz Force
Lorentz Force
If is a constant, without loss of generality we can
choose = .
=
=
0
or
=
= ,
0
=
=
=
or
,
Mathematica
Lorentz.nb
4/29/2016
Physics 321
Hour 5
Linear Momentum and Its Conservation
Momentum Conservation
In what collisions can you apply momentum
conservation?
Always unless external forces accelerate
masses during the collision process.
What does that mean and why is
5/5/2016
Central Force
Physics 321
If a vector field is radial and depends only on r, what
is its curl?
1
=
+
+
1
Hour 10
Coordinate Systems and Multiparticle
Systems
Notes on Coordinates
A vector can be expressed as
=
+
+
or as
=
+
+
=
=
+
1 sin
Homework Solution 10
Physics 121, Section 1
Due 10/11/07
1. The loaded car of a roller coaster has mass m = 320 kg. It goes over the top of a `hill' with a speed v
of 20 m/s. The radius of curvature R of the hill is 15 m.
(a) What are the magnitude and di
Homework Solution 9
Physics 121, Section 1
Due 10/9/07
1. A block with a mass of M = 7.65 kg is initially moving up the incline and is increasing speed with
a = 1.44 m/s2 . The applied force F is horizontal. The coecients of friction between the block and
Homework Solution 8
Physics 121, Section 1
Due 10/4/07
1. A block starts from rest at the top of a d = 2.00-m long, = 38.0 frictionless incline.
(a) What is the acceleration of the block?
Solution: Let the x direction be down the incline. The y direction
Homework Solution 7
Physics 121, Section 1
Due 10/2/07
1. (a) Why do you fall backward when standing inside a bus which is accelerating from rest?
As the bus accelerates forward, your body tends to follow Newton's First Law and not
accelerate. Thus, in an
Homework Solution 6
Physics 121, Section 1
Due 9/25/07
1. Work out the physics of the Monkey Hunter demonstration we did in class on Tuesday, September 20.
Assume that a projectile is shot from a blow gun at the same time a monkey drops from rest by letti
Homework Solution 5
Physics 121, Section 1
Due 9/20/07
1. What is wrong with the physics in the following statement? The car rounds the turn at a constant
velocity of 50 km/h Rewrite it so that it conveys the correct meaning.
Solution: If the car is round
Homework Solution 4
Physics 121, Section 1
Due 9/18/07
1. Joan measures the distance across a straight river by the following method:
Starting directly across the river from a tree on the opposite bank, she
walks 106 m along the river bank to establish a
Homework Solution 3
Physics 121, Section 1
Due 9/13/07
1. Eric slams on the brakes when he sees a tree blocking the road. The
car slows uniformly with an acceleration of -5.12 m/s2 for 3.51 s, making
straight skid marks 61.4 m long ending at the tree. Wit
Homework Solution 2
Physics 121, Section 1
Due 9/11/07
1. Wilma I. Ball walks at a constant speed of 4.83 m/s from home to the pharmacy to pick up her
prescription. She then walks back home along the same route with a constant speed of 3.66 m/s;.
What is
Homework Solutions 1
Physics 121, Section 1
Due 9/6/07
In the rst two problems of this solution, I have included the full level of
detail I would expect to see in your solutions. In the nal problem and on
subsequent assignment, we will usually only includ