Rotation & Centripetal Force

How to Keep it Straight Without Getting Dizzy

                        

Coutesy Space.com

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)

Rotating Space Station from “2001, A Space Odyssey”

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

Torque = rFsin

F

r

Axis of rotation

Lever arm

How to get the most torque

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

wrench?

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

CM of Moving Object

What would this look like if we threw the wrench through the air?

Stable vs. Unstable Equilibrium

In stable equilibrium a little rotation is corrected (lowers CG)

In unstable it leads to toppling (raises CG)

Neutral Equilibrium

In neutral equilibrium the CG does not get raised or lowered

Challenge

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

Rotational Inertia

Why do tightrope walkers carry a long pole?

Examples of Rotational Inertia

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

Condition to experience normal Earth weight (as seen from outside

ship)

Fn = mg mg = mv2/R v = R is radius of

spacecraft Fn

mg

Rg