Determine the moment produced by the force F in Fig. 4—14a about
point 0. Express the result as a Caltesian vector.
SOLUTION
As shown in Fig. 4—14a, either r A or ['3 can be used to determine the
moment about point 0.These position vectors are
rA = {12k}

At t = I], a wheel rotating about a fixed axis at a constant angular aeeeleration has an angular 1velocityr of 2.1]
radr's. Two seconds later it has turned through 5.13 complete revolutions. What is the angular acceleration
of this wheel?
a. 1? ranlfs2
h.

CHAPTER 14:
POLYMER STRUCTURES
ISSUES TO ADDRESS.
What are the basic microstructural features?
How are polymer properties effected by
molecular weight?
How do polymeric crystals accommodate the
polymer chain?
Chapter 14 - 1
Chapter 14 Polymers
What is

Chapter 12: Structures &
Properties of Ceramics
ISSUES TO ADDRESS.
Structures of ceramic materials:
How do they differ from those of metals?
Point defects:
How are they different from those in metals?
Impurities:
How are they accommodated in the lattic

Chapter 9: Phase Diagrams
ISSUES TO ADDRESS.
When we combine two elements.
what equilibrium state do we get?
In particular, if we specify.
-a composition (e.g., wt% Cu - wt% Ni), and
-a temperature (T )
then.
How many phases do we get?
What is the compo

Chapter 3: The Structure of Crystalline Solids
ISSUES TO ADDRESS.
How do atoms assemble into solid structures?
(for now, focus on metals)
How does the density of a material depend on
its structure?
When do material properties vary with the
sample (i.e.

Chapter 5: Diffusion in Solids
ISSUES TO ADDRESS.
How does diffusion occur?
Why is it an important part of processing?
How can the rate of diffusion be predicted for
some simple cases?
How does diffusion depend on structure
and temperature?
Chapter 5

Mathematical Methods I Dr Gordon Ogilvie Example Sheet 2 1. Dene (x) for > 0 by (x) = (a) Evaluate
Natural Sciences Tripos, Part IB Michaelmas Term 2008
x 1 sin x
.
(x) dx given that
0
sin x dx = . x 2
(b) Argue that for a good functio

Mathematical Methods I Dr Gordon Ogilvie Example Sheet 4
Natural Sciences Tripos, Part IB Michaelmas Term 2008
1. Dene the circle of convergence of a power series of a complex variable z. Find the radii of convergence of the three series
nz ,
n

Mathematical Methods I Dr Gordon Ogilvie Example Sheet 3
Natural Sciences Tripos, Part IB Michaelmas Term 2008
1. Use the CauchySchwarz inequality and the properties of the inner product to prove the triangle inequality |x + y| |x| + |y|
for a com

Mathematical Methods I Dr Gordon Ogilvie Example Sheet 1
Natural Sciences Tripos, Part IB Michaelmas Term 2008
1. (a) To what quantities do the following expressions in sux notation (using the summation convention) correspond? Simplify where approp

Mathematical Methods I Dr Gordon Ogilvie Example Sheet 0
Natural Sciences Tripos, Part IB Michaelmas Term 2008
This is a revision sheet. If you did NST Mathematics A or B last year you should be able to do the questions already (let me know if I ha