Circular Motion Physics Mrs Coyle

Earth rotates about its axis Satellite revolves about the earth

Cup on string Car on string Kick ball in circle Barf machine hoop and ball Accelerometer

Part I-Intro to Circular Motion Tangential Speed and Velocity Frequency and Period Centripetal Force Centripetal Acceleration

Characteristics of Circular Motion Tangential (linear) Velocity Frequency Period

Frequency, f : #revolutions per unit time f = # rev / time Units: (1/sec)=sec-1=Hertz (Hz) rpm (#rev/min) rps (#rev/sec) r

Period Period T : time for 1 revolution Relating Frequency and period Unit: sec, min, h Relating Frequency and period f= 1 T

Tangential (Linear) Velocity The tangential velocity vector is tangent to the circle at the point of study. v v

Average Tangential (Linear) Speed v= d t Unit: m/s Circumference= 2pr Linear speed= 2pr/T = 2prf

Uniform Circular Motion Linear(tangential speed is constant) v=constant

Problem 1 A biker travels once around a circular track of radius 20.0m in 3s. Calculate: the average tangential speed the frequency the period Answers: 41.9m/s, f=0.33Hz, T=3s 2.09rad/sec 41.89m/s f=0.33Hz T=3s

Record Player

Problem 2 A coin sits 0.10m from the center of a record player spinning at 45rpm. What is the frequency in Hertz? What is the period? What is the linear speed? Answer: 0.75Hz, 1.33s, 0.47m/s

Merry-go-Round

How does the v vary with r? The linear speed increases as r increases. Example: How does your linear speed change when you are on a merry-go-round and you move away from the center?

Centripetal Acceleration, ac= v2 r Has same direction as centripetal force.(Always points to the center). Is perpendicular to the tangential velocity at any given instant.

Centripetal Force, Fc= m v2 r Is a center seeking force. (Always points to the center.) Is perpendicular to the tangential velocity at any given instant. It is not an extra force. An existing force represents the centripetal force.

What forces represent the centripetal force in these examples? Car on bend of road. Coin on record player. Child on merry-go-round. Ball tied on a string.

How does the f vary with r? Angular velocity= angles /second How does your frequency/period change when you are on a merry-go-round and you move away from the center?

Centripetal Force Fc=mac

Problem 3 A child on a merry-go-round sits 1.5m from the center. They spin 3 times in one min. The mass of the child is 40kg. Find the friction(centripetal force) acting on the child. Answer: 5.9N

Part II More Centripetal Force Problems Car Rounding a Curve Loop-the- loop Rotor

What force plays the role of the centripetal force when a car rounds a curve?

Car Rounding a Bend

Example 1: Car Rounding a Curve A car is travelling with a speed of 45km/h on a circular horizontal track of radius 50m. What is the minimum coefficient of friction, so that the car stays on the track? Answer: 0.3

What force plays the role of the centripetal force when a ball is on the top of a loop-the-loop?

Loop the Loop

Example 2: Loop-the-loop What is the critical velocity of a ball at the top of the loop of radius .3m so that it completes the loop? Answer: 1.7m/s

Rotor Ride

Rotor Ride http://www.youtube.com/watch?v=J7k8Oz_73mw&feature=player_embedded#

What force plays the role of the centripetal force in the rotor ride? http://upload.wikimedia.org/wikipedia/commons/7/7d/Rotormidcyclelunapraksyd.JPG

Example 3: Rotor A brave student rides in a rotor of radius 5m whose floor drops when it reaches a speed of 20mi/h. What is the coefficient of friction between the student and the wall of the rotor, so that the student does not fall? Answer: 0.6

Recap