Lecture08

Centripetal Acceleration and Circular Motion ,[object Object],Physics 101: Lecture 08 Exam I http://www.youtube.com/watch?v=ZyF5WsmXRaI

Circular Motion Act A B C Answer: B v 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 (demo)?

Acceleration in Uniform Circular Motion a ave =  v /  t Acceleration inward Acceleration is due to change in direction, not speed. Since turns “toward” center, must be a force toward center. v 1 v 2  v v 2 v 1 R  R centripetal acceleration

Preflights ,[object Object],1% 24% 38% 23% 14% “ Friction, Gravity, & Normal” f W F N correct  F = m a = m v 2 /R a=v 2 /R R

Common Incorrect Forces ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Preflights ,[object Object],A. Zero B. Pointing radially inward C. Pointing radially outward 14% 81% 5% “ Centripetal acceleration (the net force) is always pointing INWARD toward the center of the circle you are moving in..” “ must be a net force drawing the vehicle inward otherwise the cars direction would not change, and so the car would drive off the track and crash and burn” f W F N  F = m a = m v 2 /R a=v 2 /R R correct

ACT ,[object Object],v  F = m a F N - mg = m v 2 /R F N = mg + m v 2 /R mg F N R a=v 2 /R correct

Roller Coaster Example ,[object Object],mg Y Direction: F = ma -N – mg = m a Let N = 0, just touching -mg = m a -mg = -m v 2 /R g = v 2 / R v = sqrt(g*R) = 9.9 m/s N

Circular Motion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Circular to Linear ,[object Object],[object Object],[object Object]

[object Object],[object Object],Merry-Go-Round ACT (a) the same as Bonnie’s (b) twice Bonnie’s (c) half Bonnie’s Klyde Bonnie Bonnie travels 2  R in 2 seconds v B = 2  R / 2 = 9.42 m/s Klyde travels 2  (R/2) in 2 seconds v K = 2  (R/2) / 2 = 4.71 m/s

Merry-Go-Round ACT II ,[object Object],[object Object],(a) the same as Bonnie’s (b) twice Bonnie’s (c) half Bonnie’s Klyde Bonnie ,[object Object],[object Object]

Angular Acceleration ,[object Object],[object Object],= 0.64 rad/s 2

Summary (with comparison to 1-D kinematics) ,[object Object],And for a point at a distance R from the rotation axis: ,[object Object]

CD Player Example ,[object Object], = 13.3 radians 1 Revolutions = 2  radians  = 13.3 radians = 2.12 revolutions

Summary of Concepts ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Lecture08

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