PHYS 211 Lecture 26 - Torque-free rotation - body-fixed axes
26 - 1
Lecture 26 - Torque-free rotation - body-fixed axes
Text:Fowles and Cassiday, Chap. 9
Demo: gyroscope, tennis racket, old CD
We now want to consider how the angular momentum L and the ang
PHYS 211 Lecture 25 - Principal axes
25 - 1
Lecture 25 - Principal axes
Text: Fowles and Cassiday, Chapter 9
Demo: tennis racket
We formally introduced the principal axes in Chap. 9 as the set of eigenvectors that
diagonalize the inertia tensor. It is not
PHYS 211 Lecture 24 - Rotation about an arbitrary axis
24 - 1
Lecture 24 - Rotation about an arbitrary axis
Text: Fowles and Cassiday, Chap. 9
In the previous lecture, we saw that L and need not be parallel, but are related to
each other through the inert
PHYS 211 Lecture 22 - Rolling objects
22 - 1
Lecture 22 - Rolling objects
Text: Fowles and Cassiday, Chap. 8
We now apply our knowledge of rotational dynamics to several systems, at least two of
which have been discussed lightly in first year mechanics.
P
PHYS 211 Lecture 23 - Inertia tensor
23 - 1
Lecture 23 - Inertia tensor
Text: Fowles and Cassiday, Chap. 9
Just when we thought that we understood everything about rotation, consider the
following simple problem. A conical pendulum is mechanically like an
PHYS 211 Lecture 21 - Moments of inertia
21 - 1
Lecture 21 - Moments of inertia
Text: similar to Fowles and Cassiday, Chap. 8
As discussed previously, the moment of inertia I for a single mass m executing a circle
of radius r about an axis is
I = mr 2.
Fo
PHYS 211 Lecture 20 - Rigid-body motion
20 - 1
Lecture 20 - Rigid-body motion
Text: similar to Fowles and Cassiday, Chap. 8
We began our discussion of the mechanics of extended objects by introducing the
concept of centre-of-mass, and by showing how aspec
PHYS 211 Lecture 18 - Many-particle systems
18 - 1
Lecture 18 - Many-particle systems
Text: similar to Fowles and Cassiday, Chap. 7
Kinematic variables and the form of Newtons equations for many-particle
systems were introduced in first-year mechanics. He
PHYS 211 Lecture 17 - Orbital Stability
17 - 1
Lecture 17 - Orbital Stability
Text: same material as Fowles and Cassiday, Chap. 6, but with different method
There is more to understanding the motion of an object than just solving a set of force
equations.
PHYS 211 Lecture 19 - Collisions and conservation of momentum
19 - 1
Lecture 19 - Collisions and conservation of momentum
Text: similar to Fowles and Cassiday, Chap. 7
In first year physics, if not high school, the idea was introduced that some quantities
PHYS 211 Lecture 16 - Orbital energetics
16 - 1
Lecture 16 - Orbital energetics
Text: Fowles and Cassiday, Chap. 6
What we want to do next is find the velocities and energies given the orbital equation
r( ). Recall from Lecture 1 that the velocity in 2D p
PHYS 211 Lecture 15 - Keplers Laws
15 - 1
Lecture 15 - Keplers Laws
Text: Fowles and Cessiday, Chap. 6
One of the major successes of Newtons law of universal gravitation in the late
1600s was that it (along with conservation of angular momentum) was able
PHYS 211 Lecture 11 - Rotating coordinate systems
11 - 1
Lecture 11 - Rotating coordinate systems
Text: similar to Fowles and Cassiday, Chap. 5
We start our discussion of rotating coordinate systems with the case of pure rotation
about a common origin. Th
PHYS 211 Lecture 14 - Central forces
14 - 1
Lecture 14 - Central Forces
Text: Fowles and Cassiday, Chap. 6
Both Newtons law of gravity and Hookes law for springs are examples of central
forces in which the direction of the force is along the line of separ
PHYS 211 Lecture 10 - Accelerated coordinate systems
10 - 1
Lecture 10 - Accelerated coordinate systems
Text: Fowles and Cassiday, Chap. 5
Most of our intuition about mechanics comes from our experience on Earth: we
describe projectile motion, spring osci
PHYS 211 Lecture 8 - Forces in three dimensions
8-1
Lecture 8 - Forces in three dimensions
Text: Fowles and Cassiday, Chap. 4
We now revisit some aspects of force in three dimensions. Forces are classified as
conservative or nonconservative according to w
PHYS 211 Lecture 9 - Examples of 3D motion
9-1
Lecture 9 - Examples of 3D motion
Text: Fowles and Cassiday, Chap. 4
In one dimension, the equations of motion to be solved are functions of only one
position variable, namely x. In three dimensions, there ar
PHYS 211 Lecture 13 - Projectile motion on the Earth's surface
13 - 1
Lecture 13 - Projectile motion on the Earths surface
Text: Fowles and Cassiday, Chap. 5
As one last example of motion in a rotating reference frame, we consider projectile
motion, inclu
PHYS 211 Lecture 12 - The Earth's rotation
12 - 1
Lecture 12 - The Earths rotation
Text: Fowles and Cassiday, Chap. 5
Demo: basketball for the earth, cube for Cartesian frame
A coordinate system sitting with fixed orientation on the Earths surface (i.e.,
PHYS 211 Lecture 7 - Forced harmonic motion
7-1
Lecture 7 - Forced harmonic motion
Text: Fowles and Cassiday, Chap. 3
Demo: driven spring
There are many situations in which a system may be driven by a regular or irregular
external force. For example, mach
PHYS 211 Lecture 6 - Damped harmonic motion
6-1
Lecture 6 - Damped harmonic motion
Text: Fowles and Cassiday, Chap. 3
Simple harmonic motion is an idealization of most physical systems: in general
there is some dissipative force present that robs the syst
PHYS 211 Lecture 5 - Oscillations: simple harmonic motion
5-1
Lecture 5 - Oscillations: simple harmonic motion
Text: Fowles and Cassiday, Chap. 3
Consider a power series expansion for the potential energy of an object
V(x) = Vo + V1x + V2x 2 + .,
where x
PHYS 211 Lecture 4 - Velocity-dependent forces - II
4-1
Lecture 4 - Velocity-dependent forces - II
Text: Fowles and Cassiday, Chap. 2
Having established experimentally one form of the drag force in the previous lecture,
here we determine analytically the
PHYS 211 Lecture 3 - Velocity-dependent forces - I Lecture 3 - Velocity-dependent forces - I Text: Fowles and Cassiday, Chap. 2 Demo: coffee filters, ball bearings in oil.
3-1
Most examples of force in first year physics are position-dependent [V(x) or F(
PHYS 211 Lecture 2 - Newtonian mechanics
2-1
Lecture 2 - Newtonian Mechanics (Fowles and Cassiday, Chap. 2)
Students who have completed first-year physics are already familiar with
Newtons laws of motion, which we restate here as
1st Law
2nd Law
3rd Law
E
PHYS 211 FINAL EXAMINATION
Thursday, 12 August, 2004
Time: 3 hours
Name_
Student # _
Calculator and one formula sheet permitted.
Please show complete solutions to problems 4-8 and explain your reasoning (this requires words, not
just equations). State any
PHYS 211 FINAL EXAMINATION
Tuesday, 5 August, 2003
Time: 3 hours
Name_
Student # _
Calculator and one formula sheet permitted.
Please show complete solutions to problems 4-8 and explain your reasoning (this requires words, not
just equations). State any p
PHYSICS 211
FINAL EXAMINATION
16 August, 2002
Name _
Time: 3 hours
Signature _
Student number _
Calculator and one formula sheet permitted. Circle your answers to questions 1 to 3 on these sheets.
Provide detailed solutions to questions 4 to 7 in the exam
PHYS 211 FINAL EXAMINATION
Friday, 10 August, 2001
Time: 3 hours
Calculator and one formula sheet permitted.
Please show complete solutions to problems and explain your reasoning (this requires
words, not just equations). State any principles that you use