Download Circular Motion

Round and Round
2-2-3 Circular Motion
Uniform Circular Motion
How in
do circular
we define motion
VELOCITY?have constant
Objects traveling
Velocity
is
TANGENT
to
the
speed and constantlyWhat
CHANGING
velocity
–
‘t’ are
‘d’
are we
we talking
talking
about?
about?
dcircle at all points
changing
notPERIOD
magnitude
v  in direction but CIRCUMFERENCE
(T)
t
2r
vc 
T
Time for
C = one
2πr revolution
= πd
If this is true, why does ANYTHING
move in a circle?
Centripetal Force
• Inertia causes objects to travel STRAIGHT
• Paths can be bent by FORCES
• CENTRIPETAL FORCE bends an object’s path
into a circle - pulling toward the CENTER
Misconception
The doors to the “Gravitron” close and it starts to spin.
You are pushed against the outside edge of the ride and
pinned there, You must be experiencing “centrifugal
force” throwing you outward from the ride! Right?
What is really happening?
As the Gravitron starts to spin, friction
F between your body and the
ride start you moving
v
Once you are moving, your
body wants
to go STRAIGHT
… but you can’t…
The wall keeps pushing you back in toward
the center of the ride!
What is the sensation that you feel?
• centrifugal (center fleeing) force
– A ‘fictitious’ or ‘inertial’ force that is
experienced from INSIDE a circular motion
system – WHAT YOU FEEL
• centripetal (center seeking) force
– A true force that pushes or pulls an object
toward the center of a circular path – WHAT
ACTUALLY HAPPENS
Centripetal Acceleration
• Centripetal force is a NET FORCE
• Causes ACCELERATION
• In the SAME DIRECTION AS NET FORCE
2
v
ac 
r
Example #1
• What is the centripetal acceleration of a
toy ball on the end of a 1.44 meter long
string if it is moving at 12 meters per
second?
ac = v2/r
ac = (12 m/s)2/1.44 m
ac = 100 m/s2
Centripetal Force
2
Fnet
v
Fc  maFcanet  maac 
m
r
mv
Fc 
r
2
Example #2
• What is the centripetal force acting on a
2000 kilogram airplane if it turns with a
radius of 1000 meters while moving at 300
meters per second?
ac = v2/r
Fc = mac
ac = (300 m/s)2/1000 m
Fc = (2000 kg)(90 m/s2)
ac = 90 m/s2
Fc = 1.8 x 105 N
Example #3
• Is it possible for a 1000 kilogram car to
make a turn with a radius of 50 meters
while moving at 15 meters per second
with rubber tires on dry asphalt?
Fc = 4500 N
Ff = 8339 N
2/r
F
F
=
=
mv
μF
f
N F ≥F
Yes, asc long
as
f
c
2/ 50 m
Fc = (1000
Ff = (0.85)(9810
kg)(15 m/s)N)
Fcf = 8339
4500 N
End of 2.2.3 - PRACTICE