Download 9.5 Centrifugal Force in a Rotating Reference Frame

Unit 2C: Circular Motion
Centripetal force keeps an
object in circular motion.
Which moves faster on a carousel, a horse near the
outside rail or one near the inside rail?
We begin by first discussing the difference between
rotation and revolution.
9.1 Rotation and Revolution
axis:
line around which rotation takes place
• rotation: (spinning)
object turns about an internal axis
(axis within object’s body)
• revolution: (circling)
object turns about an external axis
9.1 Rotation and Revolution
A Ferris wheel
rotates (spins)
about an axis
(at the center).
Each rider
revolves (circles)
about its axis.
axis
9.1 Rotation and Revolution
Earth undergoes both types
of rotational motion.
• It revolves (orbits)
around the sun once
every 365 ¼ days.
(1 year)
• It rotates around its own
axis through its poles
once every 24 hours.
(1 day)
9.2 Rotational Speed
The record rotates around its axis while the
bug sitting at its edge revolves around the
same axis.
Which part moves faster—the outer part where the
ladybug sits or a part near the orange center?
It depends: do you mean linear or rotational speed?
9.2 Rotational Speed
linear velocity:
distance traveled per unit of time
• A point on the edge travels further in one
rotation than a point near the center, so…
• linear speed is greater on the edge of a
rotating object than it is closer to the axis.
tangential velocity: (linear)
speed of object moving along a circular path
(the direction is always tangent to the circle)
9.2 Rotational Speed
rotational velocity: (angular velocity)
number of rotations per unit of time
• All parts of the record have the same rate
of rotation, or the same number of
rotations per unit of time.
• commonly express rotational velocity in
revolutions per minute (RPM).
9.2 Rotational Speed
All parts of the record rotate at the same rpm.
a. A point further from the center travels a longer
path in the same time and therefore has a
greater tangential velocity.
9.2 Rotational Speed
All parts of the record rotate at the same rpm.
a. A point further from the center travels a longer
path in the same time and therefore has a
greater tangential velocity.
b. A ladybug sitting twice as far from the center
moves twice as fast.
9.2 Rotational Speed
Tangential and Angular Velocity
Tangential velocity is directly proportional to
the angular velocity and the radial distance
from the axis of rotation.
v ~ r
tangential velocity ~ radial distance × angular velocity
proportional
radial distance: (radius)
distance from the
center axis of rotation
9.2 Rotational Speed
think!
At a playground, you and a friend stand on a
merry-go-round. You stand at the edge and
have a rotational velocity of 4 RPM and a
linear velocity of 6 m/s. Your friend stands
halfway to the center.
What is his rotational velocity?
What is his linear velocity?
His rotational velocity is 4 RPM (same), but …
his linear velocity is 3 m/s (half as much)
9.2 Rotational Speed
Railroad Train Wheels
How do the wheels of a train stay on the tracks?
The train wheels stay on the tracks because their
rims are slightly tapered.
A curved path occurs
when a tapered cup
rolls. The wider part of
the cup travels a
greater distance per
revolution.
A tapered cup
rolls in a curve
because the wide
part of the cup
rolls faster than
the narrow part.
9.2 Rotational Speed
Fasten a pair of cups together at their wide ends
and roll the pair along a pair of parallel tracks.
• The cups will remain on the track.
• They will center themselves whenever they
roll off center.
9.2 Rotational Speed
The wheels of trains are similarly tapered. This shape
is essential on the curves of railroad tracks.
• On any curve, the distance along the outer part is
longer than the distance along the inner part.
• The outer wheels travel faster than inner wheels.
9.2 Rotational Speed
When a train rounds
a curve, the wheels
have different
linear velocities for
the same angular
velocity.
Quick Quiz!
1. Rotation takes place about an axis that is
internal. Revolution takes place about an
axis that is…
A. outside the object.
B. at the center of gravity.
C. at the center of mass.
D. inside the object.
Quick Quiz.
2. When you roll a tapered cup across a table,
the path of the cup curves because the
wider end rolls …
A. slower.
B. at the same speed as the narrow part.
C. faster.
D. in an unexplained way.
9.3 Centripetal Force
When the can moves in a circle at a constant speed,
does it accelerate? Yes!
• speed is constant but direction changes so
velocity changes (acceleration).
• change in direction must be due to a net force
(or the can would continue to go in a straight line).
What applies this force?
centripetal force:
inward force directed
toward the center
causing any object to
have a circular path
9.3 Centripetal Force
Centripetal force is not a basic force of nature,
but is the name given to any force that is
directed toward a fixed center.
Centripetal force is exerted in different ways:
• gravitational forces hold planets and
moons in orbit.
• electrical forces act between an orbiting
electron and the atomic nucleus in an atom.
• friction force keeps a car on a curved path.
• tension force in a rope keeps a tethered
ball in a circle around a pole.
9.3 Centripetal Force
Anything that moves in a circular path is
acted on by a centripetal force perpendicular
(at a right angle) to the object’s path.
9.3 Centripetal Force
a. For a car to go around a curve, there must be
enough friction to provide the required centripetal
force to change its direction.
9.3 Centripetal Force
a. For a car to go around a curve, there must be
enough friction to provide the required centripetal
force to change its direction.
b. If the force of friction is not great enough, skidding
occurs as the car’s inertia keeps it going in a
straight line.
9.3 Centripetal Force
The clothes in a washing machine are forced into a
circular path, but the water is not, and it flies off in a
straight line tangent to the circle.
Video Clips
of Circular Motion
http://www.teachersdomain.org/resource/psu10phy.sci.centripetal/
http://www.teachersdomain.org/resource/lsps07.sci.phys.maf.circmotio
n/
http://www.teachersdomain.org/resource/phy03.sci.phys.mfw.roller/
http://safari4.volusia.k12.fl.us/SAFARI/montage/playlistedit.php?Search
Type=my&Action=MakeActive&playlistkeyindex=12563&location=local
9.4 Centripetal and Centrifugal Forces
Sometimes it seems like there’s an outward
force caused by circular motion.
centrifugal force:
outward “force” directed away from the
center of a circular path
9.4 Centripetal and Centrifugal Forces
It’s a common misconception to state that a
centrifugal force pulls outward on the can, BUT…
when the string breaks the can goes off in a tangent
straight-line path because no force acts on it.
So when you swing an object around, there is actually
no force pulling it outward.
When the string breaks
(centripetal force stops)
the object’s inertia keeps it
moving in a straight line,
tangent to—not outward
from the center of—its
circular path.
9.4 Centripetal and Centrifugal Forces
The can presses against
the bug’s feet and provides
the centripetal force that
holds it in a circular path.
The ladybug in turn
presses against the
floor of the can.
Neglecting gravity, the only force exerted on the bug
is the force of the can on its feet. (centripetal)
From our outside stationary frame of reference, we
see there is no centrifugal force exerted on the bug.
Quick Quiz!
1. When you whirl a can in a horizontal circle
overhead, the force that holds the can in
the path acts …
A. in an inward direction.
B. in an outward direction.
C. in either an inward or outward direction.
D. parallel to the force of gravity.
Quick Quiz.
2. Anything that moves in a circular path must
be acted on by a centripetal force that is
_______________ the object’s path.
A. in the same direction as
B. in the opposite direction of
C. parallel to
D. perpendicular to
Quick Quiz.
3. When you whirl a can in a horizontal circle
overhead, the force that the can exerts on
the string acts …
A. in an inward direction.
B. in an outward direction.
C. in either an inward or outward direction.
D. parallel to the force of gravity.
9.4 Centripetal and Centrifugal Forces
The can presses against
the bug’s feet and provides
the centripetal force that
holds it in a circular path.
The ladybug in turn
presses against the
floor of the can.
Neglecting gravity, the only force exerted on the bug
is the force of the can on its feet. (centripetal)
From our outside stationary frame of reference, we
see there is no centrifugal force exerted on the bug.
9.5 Centrifugal Force in a Rotating Reference Frame
BUT…
from the frame of reference of the ladybug
inside the whirling can, the ladybug is being held
to the bottom of the can by a force that is
directed away from the center of circular motion.
9.5 Centrifugal Force in a Rotating Reference Frame
From a stationary frame of reference outside the
whirling can, we see there is no centrifugal force
acting on the ladybug inside the whirling can.
We do see centripetal force acting on the can,
producing circular motion.
centripetal force
centrifugal force
In the rotating frame of reference of the whirling can,
both centripetal force and centrifugal force act on
the ladybug.
9.5 Centrifugal Force in a Rotating Reference Frame
centripetal force
centrifugal force
9.5 Centrifugal Force in a Rotating Reference Frame
centripetal
force
centrifugal
force
9.5 Centrifugal Force in a Rotating Reference Frame
The centrifugal force appears to
be a force as real as the pull of
gravity, BUT…
there is a difference between
the gravity-like centrifugal force
and actual gravitational force.
Gravitational force is always an
interaction between two
masses. The gravity we feel is
due to the interaction between
our mass and the mass of Earth.
centripetal
force
centrifugal
force
feels like
“gravity”
9.5 Centrifugal Force in a Rotating Reference Frame
The centrifugal force is an
effect of rotation, but it is not
part of an interaction and is
not a true force.
For this reason, physicists refer
to centrifugal force as a
fictitious force.
But to observers in a rotating
system, centrifugal force is very
real. Just as gravity is ever
present at Earth’s surface,
centrifugal force is ever present
within a rotating system.
centripetal
force
centrifugal
force
feels like
“gravity”
http://www.teachersdomain.org/
resource/phy03.sci.phys.mfw.rol
ler/
ROLLER COASTER
9.6 Simulated Gravity
9.6 Simulated Gravity
http://www.youtube.com/watch?
v=H9fe_4QB7Uk&safety_mode
=true&persist_safety_mode=1&
safe=active
SIMULATED GRAVITY
9.5 Centrifugal Force in a Rotating Reference Frame
think!
Which observer sees the ball being pulled outward,
stretching the spring?
Which sees the
spring pulling the
ball into circular
motion?
From inside the rotating reference frame, centrifugal
force pulls outward on the ball, stretching the spring.
From the rest frame, only centripetal force from the
stretched spring pulls the ball into circular motion.
Quick Quiz!
1. A bug inside a can whirled in a circle feels a
force of the can on its feet. This force acts…
A. in an inward direction.
B. in an outward direction.
C. in either an inward or outward direction.
D. parallel to the force of gravity.
Quick Quiz.
2. Imagine a rotating (spinning) space station
designed to simulate gravity. If the radius of
the station was ______, then it would have to
spin _______ to simulate the same gravity.
A. larger, faster
B. larger, slower
C. smaller, faster
D. smaller, slower
Quick Quiz.
3. You weigh slightly less at Earth’s equator
than at either pole. Why?
1 rev per day
v ~ rω
more
centrifugal
“force”