Lecture 10 Chapter 8 Rotational Motion IIphysics.sfsu.edu/~lockhart/courses/Phys101/P101 F10 L10.pdf16-Sep-10 Physics 101 Chapter 8 Rotational Motion II Lecture 10 ... In such a case,

Physics 10116-Sep-10 Physics 101

Chapter 8Rotational Motion II

Lecture 10

Quiz -- Monday Sept. 20 (Chaps. 4-7)

Physics 10116-Sep-10

Center of Mass/Gravity

Average position of all the mass in an object is called the center of mass (CM) of object.

Average position of the weight distribution is called the center of gravity (CG).

When gravity is constant (usually the case), these two locations are the same.


Locating Center of Gravity

Balance an object to find center of gravity

Centerof

Gravity


Stability

Object is stable if CG is above the base.

CG CG

Wei

ght

Wei

ght

BASEAxis

AxisBASE

STABLE

UNSTABLE


Demo: Balance the CanIf a small amount of water is added to an

empty soda can then the can may be balanced on its bottom edge.

x CG

PEPS

I


Check Yourself

Three trucksare parked ona slope. Whichtruck(s) tipover?

CG

CG

CG

BASEBASEX

X

X

Physics 101

Balance & Ballet

On one foot

Feet flat on the floor

Balance is

OK anywhere

in here

Center of Gravitylocated above thedancer’s toe

The force of gravity and the support force of the floor can balance only when a dancer’s center of gravity is located above the base of support.

Physics 101

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


Demo: Balanced BirdWhere is the bird’s center of gravity?


Centripetal ForceCentripetal 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.

Physics 101

Centripetal Force• Any force directed toward a fixed center is

called a centripetal force.• Centripetal means “center-seeking” or

“toward the center.”

Example: To whirl a tin can at the end of a string, you pull the string toward the center and exert a centripetal force to keep the can moving in a circle.


Check Yourself

A

B C

D

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?


Centripetal Force Examples

Friction force (tires) is centripetal.

Tension force (string) is centripetal.

Gravity force (on satellite due to Earth) is centripetal


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).

SupportForce

Physics 101

Centripetal Force—Example• When a car rounds a

curve, friction provides the centripetal force needed to keep it from skidding off the road.

• If the road is wet, or if the car is going too fast, friction cannot provide enough centripetal force to prevent skidding off the road.


Magnitude of Centripetal Force

Amount of centripetal force needed is large when

• Speed is large• Radius is small• Mass is large

Physics 101

Centrifugal “Force”• Although centripetal force is center directed, an

occupant inside a rotating system seems to experience an outward force. This apparent outward force is called centrifugal force.

• Centrifugal means “center-fleeing” or “away from the center.”

Physics 101

Centrifugal “Force”– A Common Misconception

• It is a common misconceptionthat a centrifugal force pulls outward on an object.

• Example: – If the string breaks, the object

doesn’t move radially outward. – It continues along its tangent

straight-line path—because no force acts on it. (Newton’s first law)


Centrifugal “Force”

What we see

What theinsect feels

Insect inside a can rotating in a circleWhen an object is

moving in a circle, it appears to the object that there is an “outward” force. Call this apparentforce the centrifugal “force”.

Centripetal force


Demo: Bucket Overhead

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.

CentripetalForce

Centrifugal“Force”


Demo: Bucket Overhead

Throw a bowling ball overhead.

As long as the speed is fast enough, ball will sail overhead in a curved path.

Gravity by itself supplies the centripetal force.

Gravity


Simulated GravityCentrifugal “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


Demo: Spin Out

Everyday examples of “enhanced” gravity:

Salad spinner.Spin cycle in washer.Centrifuge.


Angular MomentumThere are two types of momentum

(Linear Momentum) = (Mass) x (Velocity)

and(Angular Momentum) =

(Rotational Inertia) x (Rotational Velocity)

Can have conservation of both types.Conservation of Angular Momentum: If there is

no external torque on a system, the angular momentum of the system remains constant.


Demo: Skater’s SpinBy moving her

outstretched arms and legs inward, an ice skater can decrease her body’s rotational inertia.

By conservation of angular momentum, she increases her angular velocity (spins faster)


Demo: Skater’s Spin

SlowRotation

FASTRotation

LARGE Rotational Inertia Small Rotational Inertia

Angular momentum is constant since(Rotational Inertia) x (Angular Velocity) remains constant.


Demo: Flip the Wheel

Counter-ClockwiseRotation


ClockwiseRotation

Similar tocollisions


Demo: Spin Up

ZeroRotation Clockwise

Rotation


Similar torecoil


Blades

Body

Helicopter’s TailWhen a helicopter’s 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.

Physics 101

Key Points of Lecture 10Key Points of Lecture 10

Before next lecture, read Hewitt through Chap.8

Homework Assignment #6 is due before 11:00 PM on Sunday, Sept. 19.

Quiz on Monday, Sept. 20 (Chaps. 4-7).

• Center of Mass/Gravity and Balance• Stability• Centripetal Acceleration and Force• Centrifugal “Force”• Angular Momentum• Conservation of Angular Momentum

Documents

Lecture 10 Chapter 8 Rotational Motion IIphysics.sfsu.edu/~lockhart/courses/Phys101/P101 F10 L10.pdf16-Sep-10 Physics 101 Chapter 8 Rotational Motion II Lecture 10 ... In such a case,