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PHY 2048C
General Physics I with lab
Spring 2011
CRNs 11154, 11161 & 11165
Dr. Derrick Boucher
Assoc. Prof. of Physics
Session 9, Chapter 8
Chapter 8 Homework
Due Saturday @ midnight
Chapter 8
Practice Problems
9, 11, 27, 29, 33, 39, 43
Unless otherwise indicated, all practice
material is from the “Exercises and Problems”
section at the end of the chapter. (Not
“Questions.”)
Chapter 8. Dynamics II: Motion in
a Plane
Topics in this Highlights lecture:
• Velocity and Acceleration in Uniform
Circular Motion
• Dynamics of Uniform Circular Motion
• Nonuniform Circular Motion
Uniform Circular Motion
Circular motion can be
simple or part of a more
complex motion.
As long as something is
going in a circular path (or
part of one) the ideas in this
chapter will apply.
Uniform Circular Motion
The acceleration of uniform
circular motion points to the
center of the circle. Thus the
acceleration vector has only
a radial component ar. This
acceleration is conveniently
written in the rtz-coordinate
system as
Example, Problem 8-12, p. 231
Dynamics of Uniform Circular
Motion
The usefulness of the rtzcoordinate system becomes
apparent when we write
Newton’s second law in
terms of the r-, t-, and zcomponents, as follows:
EXAMPLE 8.4 Turning the corner I
Banked curve:
A component
of the normal
force acts in
the radial
direction:
Not as much
friction
needed
OR
Faster speeds
for a given
amount of
friction!
Banked curve:
A component
of the normal
force acts in
the radial
direction:
Not as much
friction
needed
OR
Faster speeds
for a given
amount of
friction!
Example, Problem 8-14, p. 231
Example, Problem 8-28, p. 232
Circular Orbits
Circular Orbits
Newton
conceived
artificial satellites
almost 300 years
before they were
created.
Fictitious Forces
• If you are riding in a car that makes a sudden stop,
you may feel as if a force “throws” you forward
toward the windshield.
• There really is no such force.
• Nonetheless, the fact that you seem to be hurled
forward relative to the car is a very real experience!
• You can describe your experience in terms of what
are called fictitious forces.
• These are not real forces because no agent is
exerting them, but they describe your motion
relative to a noninertial reference frame.
Centrifugal Force
If the car you are in turns a
corner quickly, you feel
“thrown” against the door.
The “force” that seems to
push an object to the outside
of a circle is called the
centrifugal force. It
describes your experience
relative to a noninertial
reference frame, but there
really is no such force.
Why Does the Water Stay in the
Bucket?
• Imagine swinging a bucket of water over your head.
If you swing the bucket quickly, the water stays in.
But you’ll get a shower if you swing too slowly.
• The critical angular velocity ωc is that at which
gravity alone is sufficient to cause circular motion at
the top.
Don’t use as a primary equation: work out Sum of Forces ALWAYS!!!
Why Does the Water Stay in the
Bucket?
Why Does the Water Stay in the
Bucket?
Why Does the Water Stay in the
Bucket?
Nonuniform Circular Motion
Nonuniform Circular Motion
The frictional force
between the tires and
the pavement and the
normal force from the
banked track keep the
bike on the circle.
If the bike is
accelerating, there is
also a tangential
component of the
acceleration.
Nonuniform Circular Motion
• The force component (Fnet)r creates a
centripetal acceleration and causes the particle
to change directions.
• The component (Fnet)t creates a tangential
acceleration and causes the particle to change
speed.
• Force and acceleration are related to each
other through Newton’s second law.
Example, Problem 8-50, p. 233
Chapter 8. Clicker Questions
For uniform circular motion, the
net force
A. points toward the center of the circle.
B. points toward the outside of the circle.
C. is tangent to the circle.
D. is zero.
A car is rolling over the top of a
hill at speed v. At this instant,
A. n > w.
B. n < w.
C. n = w.
D.We can’t tell about n without knowing v.
A ball on a string is swung in a vertical circle.
The string happens to break when it is parallel
to the ground and the ball is moving up.
Which trajectory does the ball follow?