Rotation

1
Rotation Centripetal Force
Coutesy Space.com

• How to Keep it Straight Without Getting Dizzy

2
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
  rotation

Tops, planets, bicycle, car wheels, gears,
pulleys, fans etc
3
Speed on a Wheel

• Which horses on a carousel move the fastest,
  inner or outer?

Outer v radius x angular speed v rw
Way Cool Carousel Applet
4
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
5
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

6
Mass at the End of a String

• What force must the
• string exert on the mass?
• What is the direction of
• this force?

A force toward the center of the circle
7
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.

8
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

9
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
10
Car on a Curve

• When auto rounds corner, sideways acting friction
  between tires and road provides centripetal force
  that holds car on road

11
Dont Confuse Inertia With Force

• Tubs 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 Washer Photo courtesy HowStuffWorks.com
12
How Can Water Stay In The Bucket?

• Bucket swung in a
• vertical circle
• What force pushes on the
• water?

Weight and normal force down
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
13
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
14
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 rotation

Unlike real forces, centrifugal force is not part
of an interaction
15
Book on a Car Seat

• When a car goes around a curve to the left, a
  book slides
• Which way does it slide?
• Why doesnt 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?
16
Banked Road

• Is it possible for a car to make a curve on a
  road without friction?

Ff
Courtesy Doug Davis, Eastern Illinois University
17
A component of normal force (to the left) keeps
the car moving in a circle (provides centripetal
force)
18
Rotating Space Station from 2001, A Space
Odyssey
19
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 t rFsinq
• Unit is meter Newton
• Lever arm is perpendicular distance of axis of
  rotation to line of action of force

20
Torque t rFsinq
Lever arm
r
Axis of rotation
q
F
21
How to get the most torque

• What angle gives the most torque?
• Where should you hold the wrench?

22
Balanced Torques

• Net torque produces acceleration
• When torques are balanced we have rotational
  equilibrium
• Torques act to rotate a system clockwise or
  counterclockwise

23
Angular Momentum

• Analog of linear momentum mv
• L Iw (like mv in linear motion)
• I is rotational inertia or moment of inertia,
  measuring how difficult it is to rotate something
• Angular momentum is conserved

24
What happens when the skater brings in her arms?

• L Iw constant

Her rotational inertia decreases
If I decreases and Iw stays the same what must
happen to w?
25
Center of Mass

• A point located at an objects average position of
  mass
• Sometimes called center of gravity

An object wont topple if its CG is below point
of support
26
CM of Moving Object
What would this look like if we threw the wrench
through the air?
27
Stable vs. Unstable Equilibrium

• In stable equilibrium a little rotation is
  corrected (lowers CG)
• In unstable it leads to toppling (raises CG)

28
Neutral Equilibrium

• In neutral equilibrium the CG does not get raised
  or lowered

29
Challenge

• Can you stand on tiptoes facing the wall with
  toes against the wall for at least several
  seconds?

30
Rotational Inertia

• Why do tightrope walkers carry a long pole?

31
Examples of Rotational Inertia
32
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.

R
33
Condition to experience normal Earth weight (as
seen from outside ship)

• Fn mg
• mg mv2/R
• v
• R is radius of spacecraft

Fn