Transcript Circular Motion

Aim: How can we describe
circular motion?
Circular Motion
How can we describe circular speed?
Objects traveling
How do we
in define
circular
SPEED?
motion have SPEED
Velocity is TANGENT to the
What ‘t’
‘d’are
arewe
we talking
talkingabout?
about?
d at ALL POINTS
circle
v
t
CIRCUMFERENCE
PERIOD (T)
Time C
for= one
2πr revolution
= πd
If this is true, why does ANYTHING
move in a circle?
2r
vc 
T
How can we define 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?
Can you explain what is really happening?
As the Gravitron starts to spin,
friction between your body and the ride
start you moving
Fc
vc
Once you are moving, your body wants
to go STRAIGHT
… but you can’t…
The WALLS push you back in toward
the center of the ride!
What is it you feel?
• centrifugal (center fleeing) force
– A ‘fictitious’ or ‘inertial’ force that is
experienced from INSIDE a circular motion
system
• centripetal (center seeking) force
– A true force that pushes or pulls an object
toward the center of a circular path
How can we calculate Centripetal
Acceleration?
Centripetal force provides an unbalanced, net force
toward the center of a circular path
Unbalanced forces cause ACCELERATION
v , Fc , and ac constantly
CHANGE DIRECTION, but not MAGNITUDE
2
v
ac 
r
Example #1
Determine the centripetal acceleration
of a toy ball swinging with a speed of
12 meters per second on the end of
a 1.44 meter long string.
ac = v2 / r
ac = (12 m)2 / (1.44 m)
ac = 100 m/s2
Example #2
Determine the velocity of a car that
experiences a centripetal acceleration
of 6 meters per second2 as it moves through a
turn with a radius of 5 meters.
ac = v2 / r
6 m/s2 = v2 / (5 m)
v = 5.48 m/s
Calculating Fc
Newton’s 2nd Law?
F = ma
2
v
ac 
r
Fc  mac
mv
Fc 
r
2
Example #3
What is the centripetal force on a
2000 kilogram airplane making a
turn with a radius of 1000 meters
if it is moving at 300 meters per second?
Fc = mv2 / r
Fc = (2000 kg) (300 m/s)2 / (1000 m)
Fc = 180,000 N
Example #4
How far from the center of a merry-go-round
is a 500 kilogram horse that is traveling
at 3 meters per second if it experiences
a force of 3000 newtons?
Fc = mv2 / r
3000 N = (500 kg) (3 m/s)2 / r
r = 1.5 m