Rotation & Centripetal Force Coutesy Space.com                          How to Keep it Straight Without Getting Dizzy

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

Speed on a Wheel Which horses on a carousel move the fastest, inner or outer? Outer v = radius x angular speed v = rw

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 the string 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 Washer Photo courtesy HowStuffWorks.com

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

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 rotation Unlike 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? Ff Courtesy Doug Davis, Eastern Illinois University

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 t = rFsinq Unit is meter Newton Lever arm is perpendicular distance of axis of rotation to line of action of force

Torque t = rFsinq Lever arm r Axis of rotation q F

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 = 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

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?

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