Chasing your tail for Chasing your tail for science.science.

MovingMoving

Stand up.Stand up. Walk in a perfectly round path to Walk in a perfectly round path to

your left.your left. Which way do you have to push with Which way do you have to push with

your foot to walk in the circle?your foot to walk in the circle? Answer :Answer : Toward the center of your path.Toward the center of your path.

PushingPushing

Using the ball at the front of the room.Using the ball at the front of the room. Make the ball travel counterclockwise Make the ball travel counterclockwise

in a circle around a pen at the lab in a circle around a pen at the lab tables.tables.

Which way do you have to push to get Which way do you have to push to get the ball to go in a circle?the ball to go in a circle?

Answer :Answer : Toward the pen.Toward the pen.

Circular motionCircular motion

You have just studied circular motion.You have just studied circular motion. It has 2 dimensions.It has 2 dimensions. Speed can be constant but velocity will Speed can be constant but velocity will

always change.always change. Moving in a circle causes velocity to Moving in a circle causes velocity to

constantly change. constantly change. But which way?But which way? Lets study!!!!!!!!!!!!!!!!!!!!!!!!Lets study!!!!!!!!!!!!!!!!!!!!!!!!

VocabVocab Circumference Circumference

distance around a circle.distance around a circle. C = 2C = 2r r Units : meters (m)Units : meters (m)

Period Period time to complete one revolution along a time to complete one revolution along a

circular or repeating path.circular or repeating path. Symbol: TSymbol: T Unit : seconds (s)Unit : seconds (s)

Frequency Frequency number of rotations per second.number of rotations per second. Symbol : Symbol : ff Unit : Hertz (Hz)Unit : Hertz (Hz)

Calculate speedCalculate speed To find speed, need to know distance and To find speed, need to know distance and

time.time. Time for once around is the period, TTime for once around is the period, T Distance for once around is circumference. Distance for once around is circumference.

C=2C=2rr So, So,

Units are m/sUnits are m/s This is when moving at a constant speed.This is when moving at a constant speed.

T

r

T

Cv

2

Speed calculationSpeed calculation

A merry-go-round has a radius of 6.0 m A merry-go-round has a radius of 6.0 m and takes 60 s to complete one revolution.and takes 60 s to complete one revolution.

How fast is an ant traveling that is sitting How fast is an ant traveling that is sitting at the outer edge of the merry-go-round?at the outer edge of the merry-go-round?

Give : T = 60 s, r = 6.0mGive : T = 60 s, r = 6.0m

v = 0.628 m/sv = 0.628 m/s

s

m

T

r

T

Cv

60

)0.6(22

Acceleration?Acceleration?

What happens to the What happens to the velocity vector as velocity vector as you move in a circle?you move in a circle?

It changes direction. It changes direction. You have zero You have zero displacement for displacement for each round trip.each round trip.

Changing velocity Changing velocity means, acceleration.means, acceleration.

Which way is it Which way is it changing?changing?

AccelerationAcceleration

Velocity changes toward Velocity changes toward the center.the center.

Acceleration points toward Acceleration points toward center of circular path.center of circular path.

Called Called Centripetal Centripetal AccelerationAcceleration

Always toward center of Always toward center of curved path for constant curved path for constant speed.speed.

Centripetal AccelerationCentripetal Acceleration

Found by equation :Found by equation :

Where :Where :v = speedv = speedr = radiusr = radius

Acceleration Acceleration depends on both depends on both speed and radius of speed and radius of path.path.

r

vac

2

Centripetal AccelerationCentripetal Acceleration Find acceleration for merry-go-round.Find acceleration for merry-go-round. v = 0.628 m/s, r = 6.0 mv = 0.628 m/s, r = 6.0 m So aSo acc= (0.628 m/s)= (0.628 m/s)22/6.0m = 0.066 /6.0m = 0.066

m/s/sm/s/s How would aHow would acc change if the velocity change if the velocity

was constant and the antwas constant and the ant Moved toward center? Moved toward center? Acceleration will increase.Acceleration will increase. Moved away from center?Moved away from center? Acceleration will decrease. Acceleration will decrease. Moved to center?Moved to center? No acceleration. r = 0No acceleration. r = 0

True ForceTrue Force

When you move in a circle, Which way are When you move in a circle, Which way are you accelerating?you accelerating?

Toward the center.Toward the center. Which way are you being pushed?Which way are you being pushed? Toward the center.Toward the center. What object is doing this?What object is doing this? The surface.The surface. What is the sum of the forces?What is the sum of the forces?

Centripetal ForceCentripetal Force

Unbalanced force responsible for Unbalanced force responsible for circular motion.circular motion.

Always exerted toward center of path.Always exerted toward center of path. There is no object pushing you outward.There is no object pushing you outward. THERE IS NO CENTRIFUGAL FORCE THERE IS NO CENTRIFUGAL FORCE

EVER.EVER. What makes you feel the fake effect?What makes you feel the fake effect? Inertia.Inertia.

Centripetal ForceCentripetal Force Found by using 2Found by using 2ndnd Law. Law. ΣΣF=maF=ma ΣΣFFcc=ma=macc

This is the total sum of the forces which This is the total sum of the forces which causes circular motion.causes circular motion.

r

vmF

c

2

ExampleExample

Find the centripetal force exerted on Find the centripetal force exerted on you when standing at the edge of the you when standing at the edge of the merry-go-round.merry-go-round.

aacc = 0.066m/s/s , m = 50 kg = 0.066m/s/s , m = 50 kg ΣΣFFcc=ma=macc

ΣΣFFcc=(50 kg)(0.066 m/s/s) = 3.3 N=(50 kg)(0.066 m/s/s) = 3.3 N Which way is this force exerted?Which way is this force exerted? Toward Center of merry-go-round.Toward Center of merry-go-round.

Why don’t I fall?Why don’t I fall?

Gravitron – centripetal force exerted Gravitron – centripetal force exerted by the wall keeps you moving in a by the wall keeps you moving in a circle. Friction between body and circle. Friction between body and wall balances the force exerted by wall balances the force exerted by Earth and you don’t fall.Earth and you don’t fall.

Rollercoaster loop – at top you do not Rollercoaster loop – at top you do not fall because track pulls the cars fall because track pulls the cars toward center at g.toward center at g.