Circular (Rotational) Motion Angular Speed and Angular Acceleration Centripetal (Radial) Acceleration Radial Forces

Arc Length, s, and Angular Position,  s subtends angle  at ___________ radius r  measured in _______ counterclockwise from x-axis Fig. 7.1, p. 191

Angular Displacement Difference between final and initial angular positions Units are radians (rad) Positive if __________________ Fig. 7.3, p. 191

Angular Speed Divide angular displacement by time interval Units are _________ Fig. 7.3, p. 191

Angular Acceleration Divide angular speed by time interval Units are _________ Fig. 7.4, p. 193

Angular Kinematics w/  = const Draw analogy with linear motion ( a = const ) Rotational MotionLinear Motion

Relating Linear to Angular _________ of v related to  Called _________ velocity v t Also have tangential accleration a t Fig. 7.5, p. 196 All points have ______ angular speed & acceleration; points further from origin have ______ linear speed & acceleration

Centripetal Acceleration v always _____________ to r If Δt small then Δs and Δ  small  v points toward _______ Use similar triangles (a) and (b): Fig. 7.7, p. 200

Centripetal Acceleration Put it all together: Total acceleration:

Centripetal Forces Can be any of our familiar forces Tension, friction, normal, gravitational Apply Newton’s 2 nd Law to radial, tangential, and perpendicular directions Net centripetal force is:

Typical Applications Vehicle making a turn on an unbanked curve (friction only) Vehicle making a turn on a banked curve (no friction) The Gravitron amusement ride Vertical circular motion – Ferris Wheels – Loop-the-loops (roller coasters)