Chapter 8 Rotational Motion

1
Chapter 8 Rotational Motion
2
Rotational Motion

• In physics we distinguish two types of motion for
  objects
• Translational Motion (change of location)
• Rotational Motion (change of orientation)
• Weve mostly discussed translational motion
  today we consider rotation.

3
Circles

• Circumference is distance around the perimeter of
  the circle.
• Small circle is half the radius so half the
  diameter and half the circumference.

Radius
Diameter
Axis
Radius
Diameter
Axis
4
Circular Motion

• Rotational Speed Revolutions per second
• Tangential Speed Total distance per second

Same Rotational Speed Different Tangential Speeds
5
Check Yourself

• A pair of wheels are connected by a chain.
• Which wheel has higher
• rotational speed?
• By how much?
• Faster tangential speed on rim?

6
Bicycles
Notice how gears work on a modern bicycle
7
Simple Complex Objects

• Motion of simple objects Position
• Motion of complex objects Position Rotation

Axis of Rotation
COMPLEX
SIMPLE
8
Inertia

• Mass is a measure of inertia for linear motion.
• Rotational inertia is similar concept for
  rotation.

Gold brick
Normal brick
M
m
Easy to move
Difficult to move
Wood Bat
Plastic Pee-wee Bat
x
x
Difficult to Rotate
Easy to Rotate
9
Rotational Inertia

• Rotational inertia depends on
• Total mass of the object
• Distribution of the mass
• Farther the mass is from the axis of rotation,
  the larger the rotational inertia.
• Rotational inertia goes as (mass) x (distance)2

10
Demo Inertia Sticks

• Two metal pipes of the same mass

Rotate
11
Check Yourself

• Which dancer has greater rotational inertia?

Axis of Rotation
A
B
12
Demo Hammer Balance

• When is the hammer easier to balance on your
  finger?

13
Demo Drop the Stick

• Two meter sticks stand upright against a wall
  one has a hunk of clay on the end.
• Which stick will swing down and hit the floor
  first?
• Why?

14
Demo Long Legs

• Long legs have greater rotational inertia than
  short legs so long legged animals have a slow
  walking stride.

15
Demo Ramp Racing

• The two disks and rods have the same mass but one
  has connecting rods near the center while the
  other has rods near the rim.
• When rolled down a ramp, which wins the race?

16
Demo Hoop Disk Racing

• Roll a hoop and a disk down a ramp which wins
  the race?

17
Torque

• When a force causes a rotation, we identify this
  as a torque.
• Torque depends on
• Magnitude of Force
• Direction of Force
• Lever Arm
• (Torque) (Force) x (Lever Arm)

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Lever Arm
Lever arm is perpendicular distance from axis of
rotation to the direction of the force.
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Check Yourself

• Identify the lever arm for each wrench.

Force
Force
Which wrench design gives the most torque?
20
Torque for a Pirouette

• The farther the distance between the feet, the
  greater the lever arm so the greater the torque
  for creating the rotation.

Push on Floor
Reaction Force
Lever Arm
Feet apart
Feet together
21
Check Yourself

• In which case are you exerting more torque?

A
B
22
Balance of Torques

• Torques clockwise and counter-clockwise balance
  in both cases since
• (250 N) x (3 m) (500 N) x (1.5 m)

Her lever arm is 3 meters
23
Center of Mass/Gravity

• Average position of all the mass in an object is
  called the center of mass (CM).
• Average position of the weight distribution is
  called the center of gravity (CG).
• When gravity is constant these two locations are
  the same.

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Locating Center of Gravity

• Balance an object to find center of gravity

Center of Gravity
25
Demo Balance the Can

• If a small amount of water is added to an empty
  soda can then the can may be balanced on its
  bottom edge.

PEPSI
CG
x
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Stability

• Object is stable if CG is above the base.

STABLE
CG
CG
UNSTABLE
Weight
Weight
Axis
BASE
BASE
Axis
27
Check Yourself

• Three trucks
• are parked on
• a slope. Which
• truck(s) tip
• over?

CG
CG
CG
28
Balance Ballet
The force of gravity and the support force of the
floor can balance only when a dancers center of
gravity is located above the base of support.
Center of Gravity located above the dancers toe
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Balance Beam

• You tend to hold your arms out when on a balance
  beam for two reasons
• Increase your rotational inertia so as to slow
  your rate of tipping over.
• Allow rapid changes of your center of gravity, to
  regain balance

30
Demo Balanced Bird

• Where is the birds center of gravity?

31
Demo Mystery Wheel

• Wheel doesnt roll down hill. How is that
  possible?

32
Centripetal Force

• Centripetal means towards the center.

Whenever an object moves along a circular path
there must be a force on that object in the
direction of the center of the circle.
In such a case, the force is said to be
centripetal.
33
Check Yourself

• Object rotates in a circle on the end of a
  string. Is there a force on the object?
• What causes the force?
• In what direction is the force?

34
Centripetal Force Examples
35
Demo Around the Ring

• The support force exerted by the wall of the ring
  is centripetal.
• Ball moves in a straight line once the force is
  removed (ball leaves the ring).

Support Force
36
Magnitude of Centripetal Force

• Magnitude of centripetal force is large when
• Speed is large
• Radius is small
• Mass is large

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Hurricanes
Hurricanes strength (wind speed) depends on how
low the pressure gets in the center.
F
H
L
H High Pressure L Low Pressure F
Centripetal Force due to pressure difference
Rita, 9/22/05
38
Demo Loop-the-Loop
If the speed of the ball is large then the
support force of the track is required to keep it
moving in a circle.
Release
Velocity
This is also a good demo for conservation of
kinetic potential energy.
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Demo Loop-the-Loop
Ball could even circle a loop with a gap, if the
speed was just right so gravity was just the
right amount of centripetal force.
GAP
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Centrifugal Force
Insect inside a can rotating in a circle

• When a centripetal force acts on an object, it
  appears to the object that there is an outward
  force. Call this apparent force the centrifugal
  force.

What we see
What the insect feels
41
Demo Bucket Overhead
Centrifugal Force

• Can put a bucket full of water over my head
  without getting wet by rotating it fast enough.
• Forces exerted on the water by gravity plus
  support force of the bucket are centripetal.
• Apparent centrifugal force presses the water into
  the bucket.

Centripetal Force
42
Demo Bucket Overhead

• Throw a bowling ball or ball of water overhead.
• As long as the speed is fast enough it will sail
  overhead in a curved path.
• Gravity by itself supplies the centripetal force.

Gravity
43
Simulated Gravity

• Centrifugal force could be used to simulate
  gravity in a space station.
• With the right rate of rotation a person on the
  outer rim would feel as if they stood on the
  surface of Earth.
• Scientifically accurate in the movie 2001 A
  Space Odyssey (1968)

Rotation
44
Demo Spin Out

• Everyday examples of enhanced gravity
• Salad spinner.
• Spin cycle in washer.
• Centrifuge.

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Angular Momentum

• There are two types of momentum
• (Linear Momentum) (Mass) x (Velocity)
• and
• (Angular Momentum)
• (Rotational Inertia) x (Rotational Velocity)
• Principle of conservation for both types.

46
Demo Skaters Spin

• By moving their outstretched arms and legs inward
  an ice skater can decrease their bodys
  rotational inertia.
• By conservation of angular momentum, they
  increase their angular velocity (spin faster)

47
Demo Skaters Spin
LARGE Inertia
Small Inertia
FAST Rotation
Slow Rotation
Angular momentum is constant since (Rotational
Inertia) x (Angular Velocity) remains constant.
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Demo Flip the Wheel
Counter- Clockwise Rotation
Clockwise Rotation
Counter- Clockwise Rotation
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Demo Spin Up
Counter- Clockwise Rotation
Zero Rotation
Clockwise Rotation
50
Helicopters Tail
When a helicopters blades start turning in one
direction, by conservation of angular momentum
the body would spin in the opposite
direction. To compensate, the small rotor in the
tail exerts a torque to balance.
Blades
Body
51
Demo Mid-Air Twist

• Stand up and clear space around you.
• When I say Jump!, jump.
• In mid-air Ill point left or right and I want
  you to try to turn so you land facing that
  direction.

Jump! Turn Land
How can you rotate in mid-air without pushing off
of anything?
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Demo Mid-Air Twist
As you turn your legs 90 degrees, your arms and
torso rotate in the opposite direction. Sticking
your arms out as you turn helps by increasing the
rotational inertia of your upper body. A large
rotation of your legs is exactly cancelled by a
small rotation of your outspread arms and torso.
Your rotation stops as soon as you stop
rotating your upper body but by that time youve
landed with your feet turned to the side. Once on
the ground you can push off on the ground to
restore your arms and torso to a normal stance.
Jump! Turn Land