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Lesson 11
Newton IV - Circular Motion and Friction
I.
Circular Motion Problems
A.
Circular motion problems are NO Different than any other Newton II problem.
We draw free body diagrams and inventory forces just like any other problem.
B.
Coordinate Axis Trick
Choose your coordinate axis so that ONE of the Axis lies along the
_______________ of the __________________. The _____________________
in this direction is then the ______________________ __________________ !
C.
Centripetal Force
The _________________________ force is ANY force or
_________________________ of __________________________ that cause
____________________________ _________________________. It is NOT
a NEW Force!!
There is NO C in WANTf
Example: At a carnival ride, a small airplane of mass m is suspended by a 5.00 m rod as
shown below. During the ride, the airplane revolves with constant speed v in a horizontal
circle of radius r. If during the ride, the rod make a 30 angle with respect to the vertical,
what is the speed of the airplane and its period of rotation.

r
Solution:
L
II.
Friction and Sliding Friction
A.
Introduction
The study of friction is an important and complicated field of engineering and
physics. There is no comprehensive theory for friction at the microscopic level.
Instead, we have several different macroscopic equations and approximations
depending on the type of friction. Tire companies spend considerable amount of
money researching new designs to improve friction between the tires and the road
while the automotive industry attempts to develop new fluids and manufacturing
processes to reduce frictional wear. One interesting frictional process involves
your knees. In order for you to stand, it is necessary that the friction between
bones of the knee be very large otherwise you would wobble like a newborn colt.
However, you require a much smaller frictional force between the knee joints in
order to walk. The knee changes its frictional force by secreting and absorbing a
liquid (you have a self-oilier!). Maybe now you will appreciate why knee injuries
are so serious for athletes.
Two Common Misconceptions About Friction
1)
Friction is a bad thing!
2)
Friction always causes an object to slow down!
It is friction that allows your car to speed up and to make turns! Without friction,
you couldn't stay in your seat when you wiggle or even leave the classroom when
class was dismissed. Without friction, you car wouldn't come to a stop when you
hit the brakes and you couldn't jack up your car to change a flat.
II.
Static Friction
Leonard de Vinci developed the theory of sliding and static friction that is still
used today. Consider a stationary block resting on a table. If we begin pulling on
the block using a spring balance, the block will remain stationary until we reach
some maximum force upon which time the block will begin to accelerate.
4
3
2
1
F
Free Body Diagram of the Block
Newton II Equations for Stationary Block
Thus, when we plot a graph of the friction force f versus the applied force F we obtain the
following graph:
fs
F
Microscopic Picture
If we look at the block and table surfaces under a microscope, we would see
millions of small sharp points. Sharp points on the table interact with sharp points
on the block by applying normal forces that are perpendicular to each surface of
contact. When the block is stationary, the sharp points on the block can reside in
valley on the surface of the table and vice versa. When the force becomes too
great the surface begin to move with respect to each other.
A.
There is ____________ _____________________ ___________________
for the MAGNITUDE of the STATIC FRICTION FORCE! Its value is whatever
value is required to prevent _______________________ and must be found by
applying __________________________ .
B.
The direction of the STATIC FRICTION FORCE is such that it
__________________ motion.
C.
Special Case - Maximum Static Friction Force
The magnitude of the maximum static friction force is ___________________
______________________ to the magnitude of the normal force acting at the
surface. The ______________________ ____________________ depends on the
physical properties of the two objects (material, smooth/rough, etc.) and is called
the _____________________ of _____________________ _________________.
The magnitude of the static friction force is always greater or equal to the
magnitude of the sliding friction force.
Example: A block is at rest on an inclined plane as shown below. The angle of
inclination is slowly increased. Assuming that the block just starts to slide when the angle
of inclination reaches 40 degrees, what is the coefficient of static friction between the
block and the plane?

Solution:
III. Sliding (Kinetic) Friction
A.
Once an object begins sliding the frictional force becomes constant with a
magnitude that is ________________________ to the __________________
_____________________.
B.
The magnitude of the sliding friction force _______________________ of the
relative _________________________ of the two surfaces!
C.
The _______________________ of ______________________
__________________________ contains ALL information about the nature of the
two surfaces (rough, etc.)
D.
The direction of the sliding friction force is in the direction that
________________________ ________________________.
Example: A block of mass 10.0 kg is initially at rest on an inclined plane with a 40.0
degree angle of inclination. Find the speed of the block after it has slide 5.00 m down the
incline assuming that the coefficient of kinetic friction between the block and plane is
0.15 m.
Example: Consider a circular racetrack of radius 5000 m. If the coefficient of static
friction between the race track and the car's tires is 0.450, what is the maximum speed
that a car of mass 1000 kg can have before sliding assuming that
A) Race track is level
radius
B) Race track is inclined by 20 degrees
radius
20