Chapter 8Chapter 8

Rotational Motion

1.1. CIRCULAR MOTIONCIRCULAR MOTION

• Which parts on a merry-go-round move fastest?

• Which have greater rotational speeds?

• Examples of rotational motion:

Earth rotates and revolves

2.2. ROTATIONAL INERTIAROTATIONAL INERTIA

• Law of inertia for rotating systemsAn object rotating about an axis tends to remain rotating at the same rate about the same axis unless interfered with by some external influence.

• Examples: bullet, arrow, and earth

• Demo – Football and Spinning BasketballDemo – Football and Spinning Basketball• Demo - Whirly Tube (Zinger)Demo - Whirly Tube (Zinger)• Demo – Whirly ShooterDemo – Whirly Shooter• Demo - Disc GunDemo - Disc Gun• Demo - Rubber Bands Demo - Rubber Bands

• Demo - Inertia BarsDemo - Inertia Bars

• Moment of inertia (rotational inertia)

The sluggishness of an object to changes in its

state of rotational motion

• Distribution of mass is the key.

• Example: Tightrope walker

• Demo - Ring and Disk on InclineDemo - Ring and Disk on Incline

• Demo – MetronomeDemo – Metronome

• Walking pendulumsWalking pendulums (bending knees)

Lecture Table

• Demo – Falling Meter SticksDemo – Falling Meter Sticks

3.3. TORQUETORQUE

• Rotational analog of force

• A torque changes the rotational state of motion.

• Torque = force x lever arm length

• It is a vector.

• Units - N.m or lb.ft

See-Saw

FD = FD

D D

FD = FD

50 lb150 lb

2 ftx

)ft(lbx)lb( 215050

ftx 6

ftlblb 300x)50(

Line of action of the force

FTorque = Fl

Torque = Fl

Torque = Fl

l l Cheater Pipe

l

F F

l

4.4. CENTER OF MASS AND CENTER OF MASS AND CENTER OF GRAVITYCENTER OF GRAVITY

Center of mass - average position of mass

Earth

..

Center of gravity - average position of weight

Very large meteor

Path of center of mass of a rotating object will

be a straight line if no external forces act on

the object.

Demo – Hammer TossDemo – Hammer Toss

Locating the Center of Gravity

• Demo – Meter StickDemo – Meter Stick• Demo - Map of TexasDemo - Map of Texas• Demo - Balancing EagleDemo - Balancing Eagle• Demo - Curious GeorgeDemo - Curious George• Demo – Picking Up CandyDemo – Picking Up Candy

• Center can be outside of the object.• Examples: high jump and pole vaulting

Stability

• Demo - Tower of PisaDemo - Tower of Pisa

• Demo - Touching ToesDemo - Touching Toes

• Demo - Standing on ToesDemo - Standing on Toes

• Demo - Object Rolling UphillDemo - Object Rolling Uphill

• Video – Dog Center of MassVideo – Dog Center of Mass

1/61/8

1/41/2

• Demo - Boards Over the EdgeDemo - Boards Over the Edge

Equilibrium - Unstable

If an object is displaced slightly from equilibrium and

released and the object moves to a new position, then

the object was in a state of unstable equilibrium.

Example: Ball on inverted bowl

Equilibrium - Stable

If an object is displaced slightly from equilibrium and

released and the object returns to its old position,

then the object was in a state of stable equilibrium.

Example: Ball in bowl

Equilibrium - Neutral

If an object is displaced slightly from equilibrium and

released and the object remains where it is, then it

was in a state of neutral equilibrium.

Example: Ball on horizontal surface

• Centripetal force - center seeking force

• Examples: tin can and string, sling, moon

and earth, car on circular path, flying cat

5.5. CENTRIPETAL FORCECENTRIPETAL FORCE

• Demo - Coin on Clothes HangerDemo - Coin on Clothes Hanger

• Demo - String, Ball, and TubeDemo - String, Ball, and Tube

• Demo - Loop the LoopDemo - Loop the Loop

6.6. CENTRIFUGAL FORCECENTRIFUGAL FORCE

• Centrifugal force - center fleeing force

• Often confused with centripetal

• Examples: sling and bug in can

• Demo - Walk the LineDemo - Walk the Line

• Centrifugal force is attributed to inertia.

7.7. CENTRIFUGAL FORCECENTRIFUGAL FORCE IN A ROTATING IN A ROTATING REFERENCE FRAMEREFERENCE FRAME

• A frame of reference can influence our view of

nature.

• For example: we observe a centrifugal force

in a rotating frame of reference, yet it is a

fictitious (pseudo) force.

• Centrifugal force stands alone (there is no

action-reaction pair) - it is a fictitious force.

• Another pseudo force - CoriolisAnother pseudo force - Coriolis

8.8. SIMULATED GRAVITYSIMULATED GRAVITY

• To get a = g, the proper rotation rate and the

proper radius must be determined.

• Gravity gradients

• Jogging in space

9.9. ANGULAR MOMENTUMANGULAR MOMENTUM

For a point object the angular momentum is

r

mv

J = mvr

Units - kg.m2/s or sl.ft2/s

It is a vector.

Here the vector is pointing toward you.

• How do you change the angular momentum of

an object?

• An external torque is required.

• Newton's first law for rotating systems:

An object or system of objects will maintain its

state of angular momentum unless acted upon by

an unbalanced external torque.

• The larger J is, the larger the torque must be

to change it.

• Demo - Bicycle WheelDemo - Bicycle Wheel

• Demo - GyroscopeDemo - Gyroscope

10.10. CONSERVATION OF CONSERVATION OF ANGULAR MOMENTUMANGULAR MOMENTUM

• If there are no external torques acting on a

rotating system then

angular momentum is conserved.

• This means the final angular momentum is

equal to the initial angular momentum.

• Examples: ice skater spin, diving, tides and

moon

• Demo - "Ice Skater“Demo - "Ice Skater“

• Movie – Ice SkaterMovie – Ice Skater

• Movie – SFA CheerleadersMovie – SFA Cheerleaders

• Demo - Bicycle Wheel and Rotating PlatformDemo - Bicycle Wheel and Rotating Platform

• Movie - J in Sky LabMovie - J in Sky Lab

• Movie - More J in Sky LabMovie - More J in Sky Lab

II

Chapter 8 Review QuestionsChapter 8 Review Questions

In walking, people normally bend their knees. Why?

(a) it is easier to swing their legs because bending lowers the rotational inertia of their legs

(b) it is easier to swing their legs because bending increases the rotational inertia of their legs

Which is harder to stop? A rotating rod with its mass predominantly at the

(a) middle of the rod

(b) ends of the rod

(c) neither of the above

A ball is at rest on a horizontal table. It is in a state of equilibrium.

(a) neutral

(b) stable

(c) unstable

(d) both (a) and (b)

(e) both (a) and (c)

Which of the following forces is a

pseudo force?

(a) tension in a rope

(b) force of gravity

(c) centripetal

(d) friction

(e) centrifugal

What is the angular momentum of a 6 kg mass traveling with a speed of 6 m/s in a circle of radius of 12 m?

(a) 432 kg·m2/s

(b) 12 kg·m2/s

(c) 24 kg·m2/s

(d) 144 kg·m2/s

(e) 36 kg·m2/s