Physics 101: Lecture 08 Exam 2 Centripetal Acceleration and Circular Motion Exam 1 Review session Tuesday 9-10AM 144Loomis

Circular Motion B C A v Use this to motivate circular motion involves acceleration. A ball is going around in a circle attached to a string. If the string breaks at the instant shown, which path will the ball follow? 10

Acceleration in Uniform Circular Motion v2 v1 R R centripetal acceleration Acceleration is due to change in direction, not speed. Since turns “toward” center, must be a force toward center. 12

Acceleration in Uniform Circular Motion Draw in forces. v1 12

Common Incorrect Forces Acceleration: SF = ma Force of Motion (Inertia not a force) Centrifugal Force (wrong object!) Centripetal Force (tension, gravity, friction, normal)

Example: ball in vertical circle A ball of mass 2kg is being swung in a vertical circle with a speed of 10m/s. What is the tension in the rope at the top of the circle? Draw in forces. v1=10m/s g 12

Example: ball in vertical circle A ball of mass 2kg is being swung in a vertical circle with a speed of 10m/s. What is the tension in the rope at the bottom of the circle? Draw in forces. g v1=10m/s 12

Clicker Question Suppose you are driving through a valley whose bottom has a circular shape. If your mass is m, what is the magnitude of the normal force FN exerted on you by the car seat as you drive past the bottom of the hill A. FN < mg B. FN = mg C. FN > mg v mg FN R a=v2/R 20

Example: roller coaster What is the minimum speed you must have at the top of a 20 meter roller coaster loop, to keep the wheels on the track. Y Direction: F = ma Let N = 0, just touching N mg 25

Circular Motion Angular displacement Dq = q2-q1 How far it has rotated Units radians 2p = 1 revolution Angular velocity w = Dq/Dt How fast it is rotating Units radians/second 2p = 1 revolution Angular acceleration is the change in angular velocity w divided by the change in time. α = Dw/Dt How much is it speeding up or slowing down Units radians/second2 Rotate ruler 90 degrees ask students how far rotated. Motivate meters bad unit, use angles. Also w/ record player 27

Comparison to 1-D kinematics Angular Linear And for a point at a distance R from the rotation axis: x = Rv = R a = R

Example: 48x cd-rom A 48x cd-rom spins at about 9600 rpm. If it takes 1.5 sec. to get up to speed, what is the angular acceleration? How many revolutions does the disk make before it is at the proper speed? 48

Summary of Concepts Uniform Circular Motion Speed is constant Direction is changing Acceleration toward center a = v2 / r Newton’s Second Law F = ma 50