Physics 1A: Classical Mechanics Fall 2015
Concept Lecture 1-3: Circular Motion
The molecular motor that drives the paramecium flagellum Credit: Protonic NanoMachine Project, ERATO:
http://www.fbs.osaka-u.ac.jp/labs/namba/npn/movies/MotorReversal.mpeg
Ballet Piroutte Credit: Jim Lamberson CC BY-SA 4.0
https://en.wikipedia.org/wiki/Turn_(dance_and_gymnastics)#/media/File:Pirouette.gif
Simulation of interacting galaxies Credit: NASA https://www.youtube.com/watch?v=BwhUl1qvG4k
Hurricane Gonzalo imaged by the NASA GOES satellite Credit: NASA http://www.nasa.gov/downloadable/videos/satellites_see_powerful_hurricane_gonzalo_hit_bermuda.mp4
= arclength
Angular displacement is a dimensionless quantity with units of radians, where 2π radians = 360º
= angular displacement
A
B
units = = 1 meters meters
angular rate
angular speed
angular velocity
A
B
polar coordinate unit vector for angular motion
A → B in time Δt
radial velocity
angular acceleration
A
B
angular acceleration
Constant Circular Motion
x
y
Constant Circular Motion
x
y
Constant angular speed but NOT constant angular velocity
Constant Circular Motion
x
y
Circular motion requires a centripetal acceleration for the change in velocity direction
change in orientation
Children on a roundabout Credit Jayhawksean CC BY-SA 3.0
https://en.wikipedia.org/wiki/File:Merry-go-round.jpg
Acceleration parallel to velocity speeds up or slows down objects
Acceleration perpendicular to velocity turns an object toward a new direct of motion
Helical motion Uploaded by Pieter Kuiper, CC AY-SA 2.0 Generic
https://commons.wikimedia.org/wiki/File:Rising_circular.gif
Deltoid motion Created by Sam Derbyshire, CC AY-SA 3.0
https://commons.wikimedia.org/wiki/File:Deltoid2.gif
Epicycloid motion Created by Sam Derbyshire, CC AY-SA 3.0
https://commons.wikimedia.org/wiki/File:EpitrochoidOn3-generation.gif
Summary
Kinematic quantities of circular motion: angular displacement: Δφ in radians arclength: L = RΔφ angular rate: ω = Δφ/Δt angular speed & velocity: vφ = RΔφ/Δt = Rω
tangent to circle
angular acceleration: α = Δω/Δt, aφ = Rα centripetal acceleration: ac = Rω2 = vφ2/R
Summary
Circular motions are often easier to write in polar coordinates r(t), φ(t) Convert to rectangular using Complex motions seen in nature arise when circular and linear motions are combined
Top Related