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Chapter 21. Angular Momentum. Definitions. P = period in seconds (sec) f = frequency in Hertz (Hz or rev/sec) w = angular speed ( rad /sec) P=1/f w = 2 p f. I = Rotational Inertia.

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chapter 21

Chapter 21

Angular Momentum

definitions
Definitions
  • P = period in seconds (sec)
  • f = frequency in Hertz (Hz or rev/sec)
  • w = angular speed (rad/sec)
  • P=1/f
  • w = 2 p f
i rotational inertia
I = 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
slide4
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
conservation of angular momentum
Conservation of Angular Momentum
  • angular momentum = rotational inertia ´ rotational velocity
  • L = I w
  • Newton's first law for rotating systems:
    • “A body will maintain its state of angular momentum unless acted upon by an unbalanced external torque.”
slide6

Direction of

Motion

Centripetal

Type of

Force

Centrifugal

Type of

Force

centripetal
Centripetal
  • …is applied by some object.
  • Centripetal means "center seeking".

Centrifugal

  • …results from a natural tendency.
  • Centrifugal means "center fleeing".
  • This is a fictitious force. Why?
examples
Examples

Centripetal

Type of Force

CentrifugalType of Force

  • Bucket
  • Earth’s gravity
  • Road Friction
  • Hanger
  • Space Station Floor
  • Nature
  • Nature
  • Nature
  • Nature
  • Nature
  • water in bucket
  • moon’s orbit
  • car on circular path
  • coin on a hanger
  • jogging in a space station
circular motion
Circular Motion
  • The linear speed is directly proportional to both rotational speed and radial distance.

v = w 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.
centripetal acceleration
Centripetal Acceleration
  • “Turning acceleration”

ac = v2/r = w2 r

  • What are two ways that you can increase the “false gravity” in a spinning space station?
    • Answers:
      • Move away from the rotation axis.
      • Have the space station spin faster.
moments of inertia table 21 2
Moments of Inertia Table 21.2

Hoop or Ring

Solid Cylinder

moments of inertia table 21 213
Moments of Inertia Table 21.2

Short Barbell

Long Barbell

moments of inertia table 21 214
Moments of Inertia Table 21.2

Rectangular Parallelepiped

b

c

a

Which axis of a book has the highest moment of inertia?

moments of inertia table 21 215
Moments of Inertia Table 21.2

Solid Sphere

Problem 21.6

problem 21 9
Problem 21.9

Ff

Free

Body

Diagram

FN

Fg

problem 21 917
Problem 21.9

Ff

Free

Body

Diagram

FN

Fg

[maximum]

problem 21 10
Problem 21.10

FN

Free

Body

Diagram

H2O

Fg

Note: “Minimum angular speed” means that FN=0.

what if you ran the other way
What if you ran the other way?

You’d lose “weight”!

project two update
Project Two Update
  • We will now have meetings outside of class time to work on Project Two.
  • We will meet in room 315A for these meetings. Be sure to sign in when you arrive.
  • We will attempt to build 2 engines per team, rather than 1 for each person.
project two update27
Project Two Update
  • Week 1
    • Piston and Pressure Vessel Construction
  • Week 2
    • Crankshaft and Flywheel Construction
  • Week 3
    • Final Adjustments and Testing
project two update28
Project Two Update
  • Take 3 minutes to select a meeting time for your team for this week.
  • Select an alternate time from the list below as well.

Tuesday

    • 12:00
    • 4:00
    • 5:00

Wednesday

    • 2:30
    • 3:30
    • 4:30
    • 5:30

Thursday

    • 11:00
    • 12:00
    • 5:00

Friday

    • 12:00
    • 1:00
    • 2:00
    • 3:00
    • 4:00
slide29
Examples:
    • 1. ice skater spin
    • 2. cat dropped on back
    • 3. Diving
    • 4. Collapsing Stars (neutron stars)
torque
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
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
      • Rolling Double-Cone
stability
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
circular motion33
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).
linear versus rotational motion equation sheet for exam 4
Linear versus Rotational MotionEquation Sheet for Exam 4
  • Momentum and Impulse
  • Conservation of Momentum
  • Newton’s Second Law
  • Distance
  • Speed
  • Acceleration
  • vf = vi + at
  • xf = xi +vit + ½ at2