PHYS 16 Lecture 21 Circular Motion October 27

PHYS 16 – Lecture 21 Circular Motion October 27, 2010

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

Where have we been… • • • Position, Velocity, and Acceleration 1 D and 2 D Motion – Kinematics Force – Newton’s laws Momentum Energy http: //www. teachengineering. org/collection/cub_/lessons/cub_images/cub_rockets_lesson 02_figure 3. jpg

Where we are going… • Applications – Circular Motion and Rotation – Static Equilibrium – Gravitation and Movement of Planets – Fluids • Mechanical waves http: //www. ux 1. eiu. edu/~cfadd/1350/06 Cir. Mtn/Images/loop. gif

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

Angular displacement, velocity, and acceleration

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

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?

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/250 px-Polar_coordinates_. png

Discussion Questions • Which way does ball on string go? Tangentially • 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? Ang. Velocity is the same for any point on wheel Lin. Velocity is greatest at edge

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

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

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

Angular Kinematics

Angular kinematics – same as linear • Assume α=constant

Centripetal Force

Centripetal Force • Force keeping an object moving in a circle http: //astronomy. swin. edu. au/cms/imagedb/albums/scaled_cache/centripedal-316 x 300. png