Chasing your tail for science.

Moving Stand up. Walk in a perfectly round path to your left. Which way do you have to push with your foot to walk in the circle? Answer : Toward the center of your path.

Pushing Using the ball at the front of the room. Make the ball travel counterclockwise in a circle around a pen at the lab tables. Which way do you have to push to get the ball to go in a circle? Answer : Toward the pen.

Circular motion You You have just studied circular motion. It It has 2 dimensions. Speed Speed can be constant but velocity will always change. Moving Moving in a circle causes velocity to constantly change. But But which way? Lets Lets study!!!!!!!!!!!!!!!!!!!!!!!!

Vocab Circumference Circumference distance around a circle. distance around a circle. C = 2  r Units : meters (m) C = 2  r Units : meters (m) Period Period time to complete one revolution along a circular or repeating path. time to complete one revolution along a circular or repeating path. Symbol: TUnit : seconds (s) Symbol: TUnit : seconds (s) Frequency Frequency number of rotations per second. number of rotations per second. Symbol : f Unit : Hertz (Hz) Symbol : f Unit : Hertz (Hz)

Calculate speed To find speed, need to know distance and time. Time for once around is the period, T Distance for once around is circumference. C=2r So, Units are m/s This is when moving at a constant speed.

Speed calculation A merry-go-round has a radius of 6.0 m and takes 60 s to complete one revolution. How fast is an ant traveling that is sitting at the outer edge of the merry-go-round? Give : T = 60 s, r = 6.0m v = m/s

Acceleration? What happens to the velocity vector as you move in a circle? What happens to the velocity vector as you move in a circle? It changes direction. You have zero displacement for each round trip. It changes direction. You have zero displacement for each round trip. Changing velocity means, acceleration. Changing velocity means, acceleration. Which way is it changing? Which way is it changing?

Acceleration Velocity changes toward the center. Acceleration points toward center of circular path. Called Centripetal Acceleration Always toward center of curved path for constant speed.

Centripetal Acceleration Found by equation : Where : v = speed r = radius Acceleration depends on both speed and radius of path.

Centripetal Acceleration Find acceleration for merry-go-round. v = m/s, r = 6.0 m So ac= (0.628 m/s)2/6.0m = m/s/s How would ac change if the velocity was constant and the ant Moved toward center? Acceleration will increase. Moved away from center? Acceleration will decrease. Moved to center? No acceleration. r = 0

True Force When you move in a circle, Which way are you accelerating? Toward the center. Which way are you being pushed? Toward the center. What object is doing this? The surface. What is the sum of the forces?

Centripetal Force Unbalanced force responsible for circular motion. Always exerted toward center of path. There is no object pushing you outward. THERE IS NO CENTRIFUGAL FORCE EVER. What makes you feel the fake effect? Inertia.

Centripetal Force Found by using 2nd Law. ΣF=ma ΣFc=mac This is the total sum of the forces which causes circular motion.

Example Find the centripetal force exerted on you when standing at the edge of the merry- go-round. ac = 0.066m/s/s, m = 50 kg ΣFc=mac ΣFc=(50 kg)(0.066 m/s/s) = 3.3 N Which way is this force exerted? Toward Center of merry-go-round.

Why don’t I fall? Gravitron – centripetal force exerted by the wall keeps you moving in a circle. Friction between body and wall balances the force exerted by Earth and you don’t fall. Rollercoaster loop – at top you do not fall because track pulls the cars toward center at g.