Download Centripetal Force

Centripetal Force
I CAN …
explain the forces that cause circular motion
determine the motion of an object when the centripetal force
is removed.
differentiate between centripetal force, centripetal
acceleration and tangential velocity.
compare and contrast the directions of the centripetal force,
centripetal acceleration, and tangential velocity.
calculate centripetal force and centripetal acceleration.
compare universal gravitational force between objects with
different distances using the inverse square law.
calculate orbital velocity using centripetal force and universal
gravitation equations.
calculate torque from forces perpendicular to a lever arm.
calculate the torque or force necessary for an object to be in
rotational equilibrium.

Academic Vocabulary:
Centripetal force
Centripetal acceleration
Circular motion
Tangential velocity
Inverse square law
Gravitational constant
Universal gravitational force
Weightlessness
Torque
Center of mass
Lever arm
Rotational Equilibrium
Equations:
ac 
vt2
r
Fc  mac
FG  G
m1 m 2
r2
  rF
Inertia vs. Force
When a car accelerates, you feel as
if you are flung backward.
Your inertia (mass) resists
acceleration.
There is no force pushing you
backward; your body wants to remain
at rest as the car accelerates
forward.
The Normal Force of the car seat
pushes you forward, but your brain
interprets this feeling as a force
pushing you back into the seat.
Inertia vs. Force
When a car quickly stops, you feel as if you
are flung forward.
Your inertia (mass) resists the negative
acceleration.
There is no force pushing you forward; your
body wants to remain in motion at constant
velocity as the car accelerates backwards.
Your brain interprets the absence of the
Normal Force of the car as a force pushing
you forward. In reality, the only reason you
do not fly through the windshield is
because of the force of friction and normal
force from the seatbelt pushing you
backward.
Inertia vs. Force
When a car turns, you feel as if you are flung to the
outside. Your inertia resists acceleration.
There is no force pushing you to the outside of the
turn; your body simply wants to keep moving in straight
line motion!
In every case, the REAL force is in the opposite
direction of what your brain interprets.
The “Real” Force required to
turn a car
• The car wants to continue its
current motion.
• At location 1, the car wants to
continue to move forward (up).
• The force required to make a
turn (or circle) must be
directed toward the center of
the turn.
3
2
1
Uniform Circular Motion
2 Conditions:
Uniform (constant) speed
 Circle has a constant radius.

Caused by a force
Centripetal Force:
Force responsible for uniform circular motion.
v
Always toward
center of circle!
v
Fc
Fc
Tangential velocity:
Fc
v
Speed and direction of the object at any given time.
Always tangent to the circle!
(perpendicular to the Centripetal Force)
Centripetal Force
•ALWAYS points toward the center of the circle.
•NEVER changes an object’s speed.
•ALWAYS changes the object’s direction.
•ALWAYS perpendicular to the velocity.
•If centripetal force is removed, the object will
follow its tangential velocity.
v
Fc
v
Fc
Fc
v
Concept Check:
An object moves in a circular path with
a constant speed.
a. Is the object’s velocity constant?
No, direction of v is changing… but the
speed IS constant
b. Is its Fc constant?
No, direction of Fc is changing… but the
magnitude of Fc is constant
Concept Check
Cause of Centripetal Force
Centripetal force is not a new type of force.
You can always identify the real force which is
causing the centripetal acceleration.
Nearly any kind of force can act as a centripetal
force.
Friction as Fc
As a car makes a turn,
the force of friction
acting upon the turned
wheels of the car
provide the centripetal
force required for
circular motion.
Tension as Fc
As a bucket of water is
tied to a string and
spun in a circle, the
force of tension acting
upon the bucket
provides the centripetal
force required for
circular motion.
Normal Force as Fc
Centripetal force on
a spinning carnival
ride is from the
normal force of wall
or seat on you.
Gravity as Fc
As the moon orbits the
Earth, the force of
gravity acting upon the
moon provides the
centripetal force
required for circular
motion.
Combination of Forces as Fc
Centripetal force on
a roller coaster is
from the normal
force and gravity
combined.
If a hobo steals your truck keys and does donuts in the
Wal-Mart parking lot, what is the centripetal force?
The frictional force that exists between your tires and
the ground while turning causes the truck to maintain
the circular motion necessary to generate a donut.
Could the hobo do donuts in a hockey rink if he stole a
zomboni?
No, without friction, there is no Centripetal Force
Centripetal Acceleration:
Acceleration responsible for
uniform circular motion.
v
ac
v ac
ac
v
Centripetal Acceleration
2
t
v
aC 
r
 ac: centripetal acceleration in m/s2
 v: tangential speed in m/s
 r: radius in meters
Centripetal Force
Fc = m ac
2
t
v
FC  m
r
Fc: centripetal force in N
vt: tangential speed in m/s
r: radius in meters
Example 1
A 0.5 kg object moves in a circular path with a radius of
0.25 m at a constant speed of 4.0 m/s. What is the
magnitude of the object’s acceleration?
vt2
aC 
r
(4.0 m ) 2
s
aC 
0.25m
2
m
16
2
s
aC 
0.25m
aC  64 m
s2
Example 2
A 5 kg bucket of water is being swung in a horizontal
circle at a constant speed of 2.0 m/s. If the force
required to keep the bucket moving in a circle is 25 N,
What is the radius of the circular motion?
vt2
FC  m
r
(2.0 m ) 2
s
25 N  (5kg)
r
2
m
20kg
2
s
25 N 
r
2
m
(25N )r  20kg
r  0.8m
s2