Chapter 8
Rotational
Motion
Forces and circular motion
Circular motion =
accelerated motion
(direction changing)
Centripetal acceleration
present
Centripetal force must be
acting
Centrifugal force apparent outward tug as
direction changes
Centripetal force ends:
motion = straight line
v
ac = r
2
v
Fc =ma c = m r
2
Direction of
Motion
Centripetal
Force
Centrifugal
Force
Centripetal Force
…has different origin (friction,
tension, gravity, etc.).
Centripetal means "center seeking".
Centrifugal Force
(not a real force)
…results from a natural tendencyto
keep a state of motion (inertia).
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 Centrifugal
Force
Force
water in bucket
Bucket
Inertia
moon and earth
Earth’s
gravity
Inertia
car on circular
path
Road Friction
Inertia
coin on a hanger
Hanger
Inertia
jogging in a space
station
Space
Station Floor
Inertia
Circular Motion
Linear speed - the distance moved per
unit time. Also called simply speed.
Rotational speed - the number of
rotations or revolutions per unit time.
Rotational speed is often measured in
revolutions per minute (RPM).
Angular Position, Velocity, and
Acceleration
Angular Position, Velocity, and
Acceleration
Degrees and revolutions:
Angular Position, Velocity, and
Acceleration
Arc length s,
measured in
radians:
Connections Between Linear and
Rotational Quantities
Connections Between Linear and
Rotational Quantities
The linear speed is directly
proportional to both rotational speed
and radial distance.
v=wr
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.
Connections Between Linear and
Rotational Quantities
Connections Between Linear and
Rotational Quantities
This merry-go-round
has both tangential and
centripetal
acceleration.
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
Map of Texas
Rotating Hammer
Center of Mass and Balance
If an extended object is to be balanced, it must
be supported through its center of mass.
Center of Mass and Balance
This fact can be used to find the center of mass
of an object – suspend it from different axes and
trace a vertical line. The center of mass is where
the lines meet.
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
– Inertia Bars
– Ring and Disk on an Incline
– Metronome
Torque
From experience, we know that the same force
will be much more effective at rotating an
object such as a nut or a door if our hand is not
too close to the axis.
This is why we
have long-handled
wrenches, and
why doorknobs
are not next to
hinges.
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
We define a quantity called torque:
The torque increases as the force increases,
and also as the distance increases.
Only the tangential component of force causes
a torque:
Stability
For stability center of gravity must be
over area of support.
Examples:
Tower of Pisa
Touching toes with back to wall
Meter stick over the edge
Rolling Double-Cone
Conservation of Angular
Momentum
angular momentum = rotational inertia  rotational velocity
L=Iw
Newton's first law for rotating systems:
– “A body will maintain its state of angular momentum
unless acted upon by an unbalanced external
torque.”
Conservation of Angular Momentum
If the net external torque on a system is zero,
the angular momentum is conserved.
The most interesting consequences occur in
systems that are able to change shape:
Examples:
– 1.
– 2.
– 3.
– 4.
ice skater spin
cat dropped on back
Diving into water
Collapsing Stars (neutron stars)
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