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Chapter 21

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Chapter 21

Angular Momentum

- 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

- 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

- 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

Motion

Centripetal

Type of

Force

Centrifugal

Type of

Force

- …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?

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

- 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:

- “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:

Hoop or Ring

Solid Cylinder

Mass on a Rod

m

R

Short Barbell

Long Barbell

Rectangular Parallelepiped

b

c

a

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

Solid Sphere

Problem 21.6

Ff

Free

Body

Diagram

FN

Fg

Ff

Free

Body

Diagram

FN

Fg

[maximum]

FN

Free

Body

Diagram

H2O

Fg

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

You’d lose “weight”!

- 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.

- Week 1
- Piston and Pressure Vessel Construction

- Week 2
- Crankshaft and Flywheel Construction

- Week 3
- Final Adjustments and Testing

- 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:
- 1. ice skater spin
- 2. cat dropped on back
- 3. Diving
- 4. Collapsing Stars (neutron stars)

- 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:

- 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

- 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

- 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).

- Momentum and Impulse
- Conservation of Momentum
- Newton’s Second Law
- Distance
- Speed
- Acceleration
- vf = vi + at
- xf = xi +vit + ½ at2