Chapter 9
Circular Motion
Did You Know?

Did You Know? The
tilt of the Earth on
its axis and the
Earth's revolution
cause the seasons
NOT the Earth's
proximity to the
Sun.
Rotations & Revolutions
An axis is the straight line around
which rotation takes place.

Rotation is a
spin about an
axis located
within the body
• a wheel
• a satellite
Revolution is a
spin about an axis
outside the body.
-a wheel rim
- a satellite
orbiting the
earth
Rotation and Revolution


The Ferris wheel
turns about an
axis.
The Ferris wheel
rotates, while the
riders revolve
about its axis.
Rotations & Revolutions

Does a tossed football rotate or
revolve?
• rotates (spins)

Does a ball whirled overhead at the
end of a string rotate or revolve?
• revolves about you
Rotation and Revolution

Earth undergoes both types of
rotational motion.
• It revolves around the sun once
every 365 ¼ days.
• It rotates around an axis passing
through its geographical poles once
every 24 hours.
Rotational Speed &
Tangential Speed

Merry-go-around
• Rotational speed is same anywhere on
the ride (same revolutions/second)
• Linear speed is tangent to the curved
path and different depending on where
you ride.
Linear speed is perpendicular to the radial
direction is called “tangential velocity.”
Conceptual Physics: Demo - Rotational Speed - YouTube
Speed

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
Which part of the turntable moves
faster—the outer part where the
ladybug sits or a part near the
orange center?
It depends on whether you are
talking about linear speed or
rotational speed.
Linear (tangential) speed depends
on rotational speed and the
distance from the axis of rotation.
Rotational Speed
All parts of the turntable rotate at the same rotational speed.
a. A point farther away from the center travels a longer path in the
same time and therefore has a greater tangential speed.
b. A ladybug sitting twice as far from the center moves twice as fast.
Circular Motion….
In symbol form,
v ~ r
where v is tangential speed and  (pronounced
oh MAY guh) is rotational speed.
• You move faster if the rate of rotation
increases (bigger ).
• You also move faster if you are farther from
the axis (bigger r).
Conservation of Angular
Momentum
DEMO: Conservation of angular momentum - YouTube

angular momentum = rotational inertia 
rotational velocity
L=I

Newton's first law for rotating systems:
• “A body will maintain its state of angular
momentum unless acted upon by an
unbalanced external torque.”

The linear speed is directly
proportional to both rotational
speed and radial distance.
v=r

What are two ways that you can
increase your linear speed on a
rotating platform?
• Answers:


Move away from the rotation axis.
Have the platform spin faster.
Tangential Speed

Rotational Speed & Tangential Speed
Two coins on turn table, one near center
and other near edge.
Outer coin has …
greater linear speed.
Both have same …
rotational speed – revolutions per second.
Examples:
See design on hub cap but not on the tire.
Crack-the-whip end person.
Tangential Speed
(Linear Velocity)
Swinging Meterstick:
How fast at any given moment is the
100-cm mark moving compared to
the 50-cm mark?
The 100-cm mark is twice as far from the center of
rotation than the 50-cm mark and has twice the
linear speed.

Why does a flyswatter have long
handle?
• Long handle amplifies the speed of your
hand.
Tapered Wheels of Rail Road Cars

Do “Doing Physics” pg. 125 & 126
Rotational Speed
A tapered cup rolls in
a curve because the
wide part of the cup
rolls faster than the
narrow part.
10.2 Rotational Speed
A pair of cups fastened together will stay on the tracks as
they roll.
• The cups will remain on the track.
• They will center themselves whenever they roll off
center.
Rotational Speed
When the pair rolls to the left of center, the wider part of
the left cup rides on the left track while the narrow part of
the right cup rides on the right track.
This steers the pair toward the center.
If it “overshoots” toward the right, the process repeats,
this time toward the left, as the wheels tend to center
themselves.
Rotational Speed
When a train rounds a curve, the wheels have different
linear speeds for the same rotational speed.
Rotational Speed
When a train rounds a curve, the wheels have different
linear speeds for the same rotational speed.
Centripetal Force
Centripetal means “toward the center.”
The force directed toward a fixed center that causes an
object to follow a circular path is called a
centripetal force.
Example: If you whirl a tin can on the end of a string, you
must keep pulling on the string—exerting a centripetal
force.
The string transmits the centripetal force, pulling the can
from a straight-line path into a circular path
Centripetal Force
The force exerted on a whirling can is toward the center.
No outward force acts on the can.
Remember…
v=r

Centripetal Acceleration and Centripetal
Force
Centripetal Acceleration (ac)- acceleration directed toward the
center of the circle

change in velocity per unit of time

rate at which velocity is changing

velocity is changing because the object is constantly changing
its direction as it follows a curved path
centripetal acceleration = (linear speed)2 ac = v2 symbol:ac
radius
r
unit: m/ s2
if mass is being accelerated toward the center of a circle, it must
be acted upon by an unbalance net force that gives it this
acceleration
Joe is sitting 2m from the center of a merry-go-round that has a
frequency of 1. 25 Hz (Hertz is one revolution per second).
What is Joe’s centripetal acceleration? What is the direction of
the centripetal acceleration?
Centripetal Force

Centripetal Force
Whirling Can at End of a String
 The string pulls radially inward on
the can. By Newton’s Third Law, the
can pulls outward on the string – so
there is an outward-acting force on
the string. This outward force does
not act on the can. ONLY inward
force on the can.
Spinning Washer

The tub wall exerts Fc on the clothes
forcing it into a circular path, but not
the water. Water escapes bcs no
Force acting on it….so water stays in
straight line path perpendicular or
tangent to the curve.
Centrifugal Force
Center-fleeing or Away from Center






An apparent outward force on a rotating or
revolving body.
It is fictitious in the sense that it is not part
of an interaction but is due to the tendency
of a moving body to move in a straight-line
path due to inertia
Is useful only in a rotating frame of
reference
The inward push “feels” like an outward pull
to the object in a rotating system (as if a big
mass were out there causing gravity)
Not a real force – there is no interaction
(there is no mass out there pulling on it).
There is no action reaction pair of forces
Misconception
BIG MISCONCEPTION: centrifugal force pulls
outward on an object in a circular path
fig 9.7 then string breaks....
misconception.....centrifugal force pulls can
from its circular path
reality....can goes off in a straight-line path
tangent to circle because
there is NO FORCE acting on can anymore
fig 9.8 only the force from the string acts on
the can to pull the can inward there is no
outward
force acting on the can
Centrifugal “Forces”
The only force that is exerted on the whirling can
(neglecting gravity) is directed toward the center of
circular motion. This is a centripetal force. No
outward force acts on the can.
The can provides the centripetal force necessary to
hold the ladybug in a circular path.
Centrifugal Force
A person in a spinning space habitat
feels a force like that of gravity and
does pushups just like on earth.
 Is the force centripetal or
centrifugal?
 How is it different than gravity?

Conceptual Physics: Simulated Gravity - YouTube
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
ladybug is the force of the can on its feet.
From our outside stationary frame of reference, we see
there is no centrifugal force exerted on the ladybug.
Rotational Inertia



An object rotating about an axis
tends to remain rotating unless
interfered with by some external
influence.
This influence is called torque.
Rotation adds stability to linear
motion.
• Examples:



spinning football
bicycle tires
Frisbee


The greater the distance between
the bulk of an object's mass and
its axis of rotation, the greater
the rotational inertia.
Examples:
• Tightrope walker
• Metronome
Torque


Torque is the product of the force
and lever-arm distance, which tends
to produce rotation.
Torque = force  lever arm
• Examples:


wrenches
see-saws
Center of Mass



The center of mass of an object is
the average position of mass.
Objects tend to rotate about their
center of mass.
Examples:


Meter stick
Rotating Hammer
Stability


For stability center of gravity must
be over area of support.
Examples:



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Tower of Pisa
Touching toes with back to wall
Meter stick over the edge
Rolling Double-Cone
Direction of
Motion
Centripetal
Force
Centrifugal
Force
Centripetal Force


…is applied by some object.
Centripetal means "center
seeking".
Centrifugal Force


…results from a natural
tendency.
Centrifugal means "center
fleeing".

What is that force that throws you to
the right if you turn to the left in
your car?


centrifugal force.
What is that force that keeps you in
your seat when you turn left in your
car?

centripetal force.
Examples
Centripetal
Force

water in bucket


moon and earth

car on circular
path

Road Friction
coin on a hanger

Hanger



jogging in a space
station

Bucket
Earth’s
gravity
Space Station
Floor
Centrifugal
Force
Example Question

Two ladybugs are sitting on a
phonograph record that rotates at 33
1/3 RPM.
1. Which ladybug has a great linear
speed?
A. The one closer to the center.
B. The one on the outside edge.
C. The both have the same linear
speed
Example Question

Two ladybugs are sitting on a
phonograph record that rotates at 33
1/3 RPM.
1. Which ladybug has a great linear
speed?
A. The one closer to the center.
B. The one on the outside edge.
C. The both have the same linear
speed
Example Question

Two ladybugs are sitting on a phonograph
record that rotates at 33 1/3 RPM.
2. Which ladybug has a great rotational
speed?
A. The one closer to the center.
B. The one on the outside edge.
C. The both have the same rotational
speed
Example Question
You sit on a rotating platform halfway
between the rotating axis and the
outer edge.
You have a rotational speed of 20 RPM
and a tangential speed of 2 m/s.
What will be the linear speed of your
friend who sit at the outer edge?
Example Question
You sit on a rotating platform halfway between
the rotating axis and the outer edge.
You have a rotational speed of 20 RPM and a
tangential speed of 2 m/s.
What will be the linear speed of your friend who
sit at the outer edge?
A. 4m/s
B. 2m/s
C. 20 RPM
D. 40 RPM
E. None of these
Example Question
You sit on a rotating platform halfway between
the rotating axis and the outer edge.
You have a rotational speed of 20 RPM and a
tangential speed of 2 m/s.
What will be the rotational speed of your friend
who sit at the outer edge?
A. 4m/s
B. 2m/s
C. 20 RPM
D. 40 RPM
E. None of these
End of Chapter