1. PHYS16 – Lecture 21 Circular Motion October 27, 2010

2. Administration Test – Th/F 1-4 pm – Merrill 200 – Same Format Remember 4 assignments due Sunday or Monday

3. Where have we been… Position, Velocity, and Acceleration 1D and 2D Motion – Kinematics Force – Newton’s laws Momentum Energy http://www.teachengineering.org/collection/cub_/lessons/cub_images/cub_rockets_lesson02_figure3.jpg

4. Where we are going… Applications – Circular Motion and Rotation – Static Equilibrium – Gravitation and Movement of Planets – Fluids Mechanical waves http://www.ux1.eiu.edu/~cfadd/1350/06CirMtn/Images/loop.gif

5. Circular Motion and Rotation Angular disp., velocity, and acceleration Circular motion kinematics Centripetal force Angular momentum Torque and inertia Simple Machines II – gears, belts, and levers

6. Angular displacement, velocity, and acceleration

7. Polar Coordinates http://en.citizendium.org/images/thumb/1/18/Polar_coordinates_.png/250px-Polar_coordinates_.png

8. Angular displacement Angular displacement – the angular difference between final and initial angle Arc length – angular equivalent of distance, how long the arc is that the angle sweeps out Scalar or vector?

9. Angular velocity Angular velocity or angular frequency (ω) – how much an object’s angular coordinate changes with time Related to frequency (f) and period (T) http://en.citizendium.org/images/thumb/1/18/Polar_coordinates_.png/250px-Polar_coordinates_.png

10. Discussion Questions Which way does ball on string go? If you have a rotating wheel and I want to velcro a marble to it, where should I velcro to get max ang. velocity? Where should I velcro to get max lin. velocity? Tangentially Ang. Velocity is the same for any point on wheel Lin. Velocity is greatest at edge

11. Angular vs. linear velocity http://edubuzz.org/blogs/advhigherthings/files/2008/09/circle-diagram.jpg

12. Angular acceleration Angular acceleration (α) – how the angular velocity changes in time Related to the tangential acceleration (a T )

13. Angular vs. linear acceleration Uniform circular motion – α = 0, only centripetal accel. (a C ) Non-uniform circular motion – both a T and a C http://upload.wikimedia.org/wikipedia/commons/thumb/2/22/Nonuniform_circular_motion.svg/293px-Nonuniform_circular_motion.svg.png aCaC aTaT

14. Angular Kinematics

15. Angular kinematics – same as linear Assume α=constant

16. Centripetal Force

17. Force keeping an object moving in a circle http://astronomy.swin.edu.au/cms/imagedb/albums/scaled_cache/centripedal-316x300.png