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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

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

- 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

- Examples:

- 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 mass and its axis of rotation, the greater the

- 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.”

Direction of mass and its axis of rotation, the greater the

Motion

Centripetal

Type of

Force

Centrifugal

Type of

Force

Centripetal mass and its axis of rotation, the greater the

- …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 mass and its axis of rotation, the greater the

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 mass and its axis of rotation, the greater the

- 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.

- Answers:

Centripetal Acceleration mass and its axis of rotation, the greater the

- “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.

- Answers:

Moments of Inertia mass and its axis of rotation, the greater the Table 21.2

Hoop or Ring

Solid Cylinder

Moments of Inertia mass and its axis of rotation, the greater the Table 21.2

Short Barbell

Long Barbell

Moments of Inertia mass and its axis of rotation, the greater the Table 21.2

Rectangular Parallelepiped

b

c

a

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

Moments of Inertia mass and its axis of rotation, the greater the Table 21.2

Solid Sphere

Problem 21.6

Problem 21.9 mass and its axis of rotation, the greater the

Problem 21.10 mass and its axis of rotation, the greater the

FN

Free

Body

Diagram

H2O

Fg

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

What if you ran in a spinning space station? mass and its axis of rotation, the greater the

What if you ran in a spinning space station? mass and its axis of rotation, the greater the Would you feel heavier or lighter or no different?

What if you ran the other way? mass and its axis of rotation, the greater the

You’d lose “weight”!

Project Two Update mass and its axis of rotation, the greater the

- 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 Update mass and its axis of rotation, the greater the

- Week 1
- Piston and Pressure Vessel Construction

- Week 2
- Crankshaft and Flywheel Construction

- Week 3
- Final Adjustments and Testing

Project Two Update mass and its axis of rotation, the greater the

- 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

- Examples: mass and its axis of rotation, the greater the
- 1. ice skater spin
- 2. cat dropped on back
- 3. Diving
- 4. Collapsing Stars (neutron stars)

Torque mass and its axis of rotation, the greater the

- Torque is the product of the force and lever-arm distance, which tends to produce rotation.
- Torque = force ´ lever arm
- Examples:
- wrenches
- see-saws

- Examples:

Center of Mass mass and its axis of rotation, the greater the

- 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 mass and its axis of rotation, the greater the

- 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 Motion mass and its axis of rotation, the greater the

- 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 mass and its axis of rotation, the greater the Equation 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

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