Summary: All about relating velocities using basic Kinematics
1). The translational velocity of an object (the speed at
which the centre-of-mass of the object moves) is
given by r where r is the radius from the centre
to the point it is rolling on.
C
r
P

Introduction.
So far we have only dealt with objects that slide or fall in a linear fashion. We
have more or less ignored rotations (other than centripetal acceleration and
kinematics).
Rotations add another twist (pardon the pun) to our collection of too

Vectors
Please read Chapter 1.1 to 1.6 for basic material we assume you are familiar
with(units, conversions, sig figs, uncertainties etc.)
The next couple of lectures cover the material in chapter 1, sections 1.7 to 1.10.
Not everything can be done in cl

Review of Previous Class on Work-Energy
W FNet x FNet x cos
K mv
1
2
The general
definition of work.
The Kinetic Energy of an
object in translation.
2
W K mv mv
1
2
2
f
1
2
2
i
Derived from general
definition of work.
APSC 111 Work and Energy
Page 4.16
E

One last problem.
Lara Croft and YoginiMon are trying to save the world from
the toxic effects related to genetically modified seeds. They
have stolen and hidden the DNA code for the seeds inside a thin
walled sphere. They are being chased and need to hid

Review of Previous Class
WNC = K + U
E = K +U
Work done by Non
Conservative Forces
Energy lost to heat etc.
Total Mechanical Energy
Kinetic + Potential
WNC E f Ei
=
APSC 111 Work and Energy
Page 4.109
Example 5.10
A 61.0 kg bungee-cord jumper is on a brid

What about the relationship between Work and
Energy for non-constant force?
This was covered in class for the 1-D case. We wont cover
the 3-D case in class, it is here for reference only. It is
completely analogous to the 1-D case, with just longer lines

Review of Previous Classes on Work-Energy
WNet = K
Conservative
Gravity
Elastic Spring
Work is change in
kinetic energy.
Conservative forces lead
to potential energy
U =WC
U g = mgh
We can classify work
by whether force is
conservative or not.
Non-conse

Power
We may write the instantaneous power in terms of the
net force applied to an object and its velocity.
dW
F d d
P=
=
=F
= F v
dt
dt
dt
APSC 111 Work and Energy
Page 4.62
Example Problem
The resistance to motion of a 1000 kg car consists of rolling

Example 6.8 : Totally inelastic collision in two dimensions.
Car 1: moving north at speed 15 m/s collides with Car 2 moving
east at speed 10 m/s
= 1000 kg, v1 15 m/s y
m1 =
= 2000 kg, v2 10 m/s x
m2 =
After the collision, the cars couple together and move

In addition to using work energy to solve rotational
dynamics, we can use torque.
(This is just as when we were doing linear
dynamics we could apply either Newtons laws or
use work-energy.)
APSC 111
Rotational Kinematics and Dynamics of Rigid Bodies.
Page

Topic 5: Linear Momentum
Chapter 8: Linear Momentum
Momentum and Impulse
Material to
Conservation of Momentum
appear on
Conservation of Energy and Momentum in
midterm
Collisions
Center of Mass (CM)
Systems of Variable Mass; Rocket Propulsion
APSC 111 Line

Relative Velocity
We have already considered relative speed in one
dimension:
5 km/h (relative to train)
80 km/h
85 km/h (relative to ground)
APSC 111 Kinematics
Page 2.125
Relative Velocity
Each velocity is labeled first with the object, and second with

Friction while Rolling
v
a
f
When rolling at constant speed,
wheel has no tendency to slide so
there is no frictional force.
(Idealized rigid body and rigid
surface)
APSC 111 Static Equilibrium and Stability
P
When a motor drives the wheel to
create accel

Summary so far
r r2 r1
Displacement:
Average Velocity:
vave
r
t
r2 r1
t 2 t1
r dr
Instantaneous Velocity: v lim
t 0 t
dt
v2 v1
Average Acceleration:
a
t2 t1
dv
Instantaneous Acceleration:
a
dt
APSC 111 Kinematics
Page 2.26
This lecture:
- Some questi

Equations of Motion at Constant Acceleration
v f= vi + at
Summary
Distance is unknown
x f xi = vi t + at
1
2
2
v v 2a ( x f xi )
=
2
f
2
i
v=
v f + vi
Final velocity is unknown
Time is unknown
Acceleration is unknown
2
Kinematic equations for constant acc

Thursday Lecture: Introduction of main concepts
Application of Newtons Laws with Friction
Drag Forces
Friction in Circular Motion
Friday Lecture: Example problems
Worked Examples with friction and lots of sliding blocks
Drag
Circular motion examples

Free-Body Diagrams:
Summary of Important Concepts
For each object, draw a free-body diagram, showing all the
forces acting on the object. Do not include any forces which
do not act on the object. For example a person pulling: the
pulling force does not a

Example
A rescue plane flies at 198 km/h at an elevation of h = 500 m toward a
point directly over a boating victim in the water. The pilot wants to
release a rescue capsule so that it hits the water very close to the victim.
What should the angle , the p

End of projectile motion:
The only way to get good at these sorts of questions is
practice. There are lots of example questions in the text
book, in the workbook (both examples in the relevant
section, or as tutorial questions), or old exam questions,
or

Mechanics:
Branch of physics that deals with the study of the motion of objects,
and the related concepts of force and energy.
It is usually divided into two parts:
Kinematics: Description of HOW objects move
(velocity, acceleration, projectiles, circular

Mechanics:
Branch of physics that deals with the study of the motion of objects,
and the related concepts of force and energy.
It is usually divided into two parts:
Kinematics: Description of HOW objects move
(velocity, acceleration, projectiles, circular

Summary of rotational variables
We introduced the basic
variables for rotations:
, ,
,
angle
angular velocity
angular acceleration
s = r
v = r
at = r
Which are related to
instantaneous linear
variables as:
same every
where in object
v, at
,
r
And whic

Tutorial 1:
Review of Vector Methods.
This special tutorial set is designed to provide an opportunity to review the basic concepts
concerning vector manipulation (components, addition, subtraction, scalar (dot) and vector
(cross) products).
1) A boy on a

Tutorial set week 9 2012
M58. A spring is provided at the bottom of an elevator shaft to reduce the shock if the elevator
cable breaks. The elevator has a mass of 104 kg and the spring is compressed 0.40 m when the
elevator rests on it. As the result of a

aC
v
r
FC
FC
m
r
maC
v
r
Stopper on a string
Car going around a corner
Hot wheels car on loop
Airplane turning
v
m
l
r
l
g
l
m
Highway Curves: Banked and Unbanked
v
v
r
r
v
r
N
r
T
mg
T
N
T
FC
mg
ac
T
maC
r
mg
mg
rmax
rmin

Types of Friction
Sliding Friction: Friction arising from the interactions when one
object slides (or attempts to slide) over another.
Static Friction: Friction that resists slipping when a force is
applied but the object is not yet slipping.
Kinetic Fric

Wnet
yf -
mv f
mvi
KE f
vi
yi -
K
KEi
mvi
K
K
K
U
WC
K
U
WC
Consider the ball
WG
no net work
(no change in K)
UG
Ws
Consider a hippo pulled along the table and back to the start
Us
U
mgy f
mgyi
mgy
kx f
kxi
kx
x=0
Next term we will add electric potential

r F
F
Fx
Fy
r
r
F
Torque can be about any point.
Pick point to take torque about such that the line of
action of at least one unknown force goes through the
point (produces no torque about the point)
F
F
F
r
r
rF
rF
y
x
N1
Mg
mg
N2
Fy
N1
N2
Pick point to

ROTATIONS
Ch. 10 of Text
Well cover Sections 10.1 to 10.5 in weeks 3 and 4.
ANGULAR QUANTITIES
The figure depicts a rigid object rotating about a fixed axis to the page. (The
axis of rotation need not pass through the CM.)
The angle is defined as the
dime

Centre of Mass
Physicists love to look at something complicated and
find in it something simple and familiar. Here is an
example: if you flip a baseball bat in the air, its motion
as it turns is more complicated than that of, say, a
tossed stone. Every pa

POTENTIAL ENERGY AND ENERGY CONSERVATION
Well discuss the following:
Potential Energy
Mechanical Energy and Its Conservation
Problem Solving Using Conservation of Mechanical Energy
Conservative and Nonconservative Forces
The Law of Conservation of Energy

MOMENTUM, IMPULSE, AND COLLISIONS
When an 18-wheeler collides head-on with a compact car, which way does the wreckage go after
the collision? Why are the occupants of the car much more likely to be injured? Questions such as
these can't be answered by dir

NEWTON'S LAWS
If you see the velocity of a body change in either magnitude or direction, you
know that some agent must have caused that change (i.e. the acceleration). The
agent is called a FORCE. The relation between a force and the acceleration it
cause