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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.
Physics 10116-Sep-10
Locating Center of Gravity
Balance an object to find center of gravity
Centerof
Gravity
Physics 10116-Sep-10
Stability
Object is stable if CG is above the base.
CG CG
Wei
ght
Wei
ght
BASEAxis
AxisBASE
STABLE
UNSTABLE
Physics 10116-Sep-10
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
Physics 10116-Sep-10
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
Physics 10116-Sep-10
Demo: Balanced BirdWhere is the bird’s center of gravity?
Physics 10116-Sep-10
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.
Physics 10116-Sep-10
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?
Physics 10116-Sep-10
Centripetal Force Examples
Friction force (tires) is centripetal.
Tension force (string) is centripetal.
Gravity force (on satellite due to Earth) is centripetal
Physics 10116-Sep-10
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.
Physics 10116-Sep-10
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)
Physics 10116-Sep-10
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
Physics 10116-Sep-10
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”
Physics 10116-Sep-10
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
Physics 10116-Sep-10
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
Physics 10116-Sep-10
Demo: Spin Out
Everyday examples of “enhanced” gravity:
Salad spinner.Spin cycle in washer.Centrifuge.
Physics 10116-Sep-10
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.
Physics 10116-Sep-10
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)
Physics 10116-Sep-10
Demo: Skater’s Spin
SlowRotation
FASTRotation
LARGE Rotational Inertia Small Rotational Inertia
Angular momentum is constant since(Rotational Inertia) x (Angular Velocity) remains constant.
Physics 10116-Sep-10
Demo: Flip the Wheel
Counter-ClockwiseRotation
Counter-ClockwiseRotation
ClockwiseRotation
Similar tocollisions
Physics 10116-Sep-10
Demo: Spin Up
ZeroRotation Clockwise
Rotation
Counter-ClockwiseRotation
Similar torecoil
Physics 10116-Sep-10
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