Post on 03-Jan-2016
transcript
Rotation
In addition to side to side (linear) motion, rotation plays an important role in physics, engineering, and life.
Name some common phenomena or devices that show rotationTops, planets, bicycle, car wheels, gears, pulleys, fans
etc
Speed on a Wheel
Which horses on a carousel move the fastest, inner or outer?
Outer
v = radius x angular speed
v = r
Example
A person half way out from the center of a rotating carousel walks all the way to the edge. What happens to their linear speed?
It doubles
Application of v = radius x constant angular speed
Taper of train wheels allows wheels to have different linear speed on curve although angular speed is same fopr each wheel
Mass at the End of a String
What force must thestring exert on the mass?What is the direction of this force?
A force toward the center of the circle
Centripetal Force
Any force directed toward the center of a circle is called centripetal.
Centripetal forces have clear causes such as tension in a string, gravity, friction etc.
Some people call centripetal force a “pseudoforce.” (not real)
They say “a real force such as friction provides centripetal force.”
How Big is Centripetal Force?
Fc = mv2/r The faster the speed the more the
force The tighter (smaller) the radius the
more the force v2/r is called centripetal
acceleration
Is a mass moving at steady speed in a circle
accelerating? Yes. The direction is changing What is the direction of this
acceleration?
Toward the center of the circle
Car on a Curve
When auto rounds corner, sideways acting friction between tires and road provides centripetal force that holds car on road
Don’t Confuse Inertia With Force
Tub’s inner wall exerts centripetal force on clothes, forcing them into circular path
Water escapes through
holes because it tends to move by inertia in a straight line path
Clothes WasherPhoto courtesy HowStuffWorks.com
How Can Water Stay In The Bucket?
Bucket swung in a vertical circle What force pushes on the water?You have to swing the bucket fast enough for the bucket to fall as fast as the water
There must be a “normal” force exerted by the bottom of the bucket on the water, in addition to gravity
Weight and normal
force down
Centrifugal Force
The force ON THE PAIL is inward (centripetal)
The force ON THE STRING is outward (centrifugal)
If the string broke, which way would the can go? Tangent to the circle
Change Your Point of View
In rest frame of the can there appears to be a centrifugal force. This pseudoforce(or fictitious force) is a result of rotationUnlike real forces, centrifugal force is not part of an interaction
Book on a Car Seat
When a car goes around a curve to the left, a book slides
Which way does it slide? Why doesn’t it keep moving with
the car?There is not enough static friction force to keep it going in a circle. This friction must provide the necessary centripetal force.
The explanation in the rotating rest frame is different. How?
Banked Road
Is it possible for a car to “make” a curve on a road without friction?
Courtesy Doug Davis, Eastern Illinois University
Ff
A component of normal force (to the left) keeps the car moving in a circle (provides centripetal force)
Torque Produces rotation The rotational analog of force Depends on direction and where applied Equals force times lever arm times sine
of angle between them = rFsin Unit is meter Newton Lever arm is perpendicular distance of
axis of rotation to line of action of force
Balanced Torques
Net torque produces acceleration When torques are balanced we
have rotational equilibrium Torques act to rotate a system
clockwise or counterclockwise
Angular Momentum
Analog of linear momentum mv L = Ilike mv in linear motion) I is rotational inertia or moment of
inertia, measuring how difficult it is to rotate something
Angular momentum is conserved
What happens when the skater brings in her arms?
L = Iconstant
Her rotational inertia decreases
If I decreases and I stays the same what must happen to ?
Center of Mass
A point located at an objects average position of mass
Sometimes called center of gravity
An object won’t topple if its CG is below point of support
Stable vs. Unstable Equilibrium
In stable equilibrium a little rotation is corrected (lowers CG)
In unstable it leads to toppling (raises CG)
Challenge
Can you stand on tiptoes facing the wall with toes against the wall for at least several seconds?
Simulated Gravity
The wall of the space station applies a centripetal force to keep the person moving in a circle. In the rest frame of the person this force is centrifugal and is experienced as weight.
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