Physics 101: Lecture 8, Pg 1 Centripetal Acceleration and Circular Motion Physics 101: Lecture 08 l Today’s lecture will cover Chapter 5

Physics 101: Lecture 8, Pg 2 A B C Answer: B v Circular Motion Act 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?

Physics 101: Lecture 8, Pg 3 Acceleration in Uniform Circular Motion vv1vv1 vv2vv2 vvvv vv2vv2 vv1vv1 R RRRR Centripetal acceleration Centripetal force: F c = mv 2 /R a  v a ave =  v /  t Acceleration inward

Physics 101: Lecture 8, Pg 4

Physics 101: Lecture 8, Pg 5 Preflights Consider the following situation: You are driving a car with constant speed around a horizontal circular track. On a piece of paper, draw a Free Body Diagram (FBD) for the car. How many forces are acting on the car? A) 1 B) 2 C) 3 D) 4 E) 5

Physics 101: Lecture 8, Pg 6 Preflights Consider the following situation: You are driving a car with constant speed around a horizontal circular track. On a piece of paper, draw a Free Body Diagram (FBD) for the car. The net force on the car is A. Zero B. Pointing radially inward C. Pointing radially outward

Physics 101: Lecture 8, Pg 7ACT 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 F N exerted on you by the car seat as you drive past the bottom of the hill A. F N mg v R

Physics 101: Lecture 8, Pg 8

Physics 101: Lecture 8, Pg 9 Roller Coaster Example What is the minimum speed you must have at the top of a 20 meter diameter roller coaster loop, to keep the wheels on the track.

Physics 101: Lecture 8, Pg 10 Circular Motion Angular displacement  =  2 -  1 è How far it has rotated Angular velocity  =  t è How fast it is rotating  Units radians/second 2  = 1 revolution Period =1/frequency T = 1/f = 2  è Time to complete 1 revolution

Physics 101: Lecture 8, Pg 11 Circular to Linear Displacement  s = R  in radians) Speed |v| =  s/  t = R  /  t |v| = R  l Direction of v is tangent to circle

Physics 101: Lecture 8, Pg 12

Physics 101: Lecture 8, Pg 13 l Bonnie sits on the outer rim of a merry-go-round with radius 3 meters, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every two seconds. è Klyde’s speed is: (a) (a) the same as Bonnie’s (b) (b) twice Bonnie’s (c) (c) half Bonnie’s Klyde Bonnie Merry-Go-Round ACT

Physics 101: Lecture 8, Pg 14 Merry-Go-Round ACT II l Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go- round makes one complete revolution every two seconds. è Klyde’s angular velocity is: (a) (a) the same as Bonnie’s (b) (b) twice Bonnie’s (c) (c) half Bonnie’s Klyde Bonnie

Physics 101: Lecture 8, Pg 15 Angular Acceleration Angular acceleration is the change in angular velocity  divided by the change in time. l If the speed of a roller coaster car is 15 m/s at the top of a 20 m loop, and 25 m/s at the bottom. What is the car’s average angular acceleration if it takes 1.6 seconds to go from the top to the bottom?

Physics 101: Lecture 8, Pg 16

Physics 101: Lecture 8, Pg 17 Constant angular acceleration summary (with comparison to 1-D kinematics) AngularLinear And for a point at a distance R from the rotation axis: x = R  v =  R  a =  R

Physics 101: Lecture 8, Pg 18 CD Player Example l The CD in your disk player spins at about 20 radians/second. If it accelerates uniformly from rest with angular acceleration of 15 rad/s 2, how many revolutions does the disk make before it is at the proper speed?

Physics 101: Lecture 8, Pg 19 Summary of Concepts l Uniform Circular Motion è Speed is constant è Direction is changing è Acceleration toward center a = v 2 / r è Newton’s Second Law F = ma l Circular Motion   = angular position radians   = angular velocity radians/second   = angular acceleration radians/second 2  Linear to Circular conversions s = r  l Uniform Circular Acceleration Kinematics è Similar to linear!

Physics 101: Lecture 8, Pg 20