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Lecture 16 Chapter 6: Circular Motion Please sit in the first six rows Mid Grades 9 8 7 6 5 4 3 2 1 0 A B C D F Exam 2 9 8 7 6 5 4 3 2 1 0 A B C D F Quick Review of Last Friday • Last Friday • The kinematics of uniform circular motion • TODAY – The dynamics of uniform circular motion – Circular orbits of satellites – Newton’s law of gravity Uniform Circular Motion • Uniform is constant magnitude of velocity (speed) (t ) angular position d (t ) angular velocity t dt d (t ) angular acceleration t dt • Going from angular velocity to angular displacement: f i t 1 T period where f is frequency (rad/s) f 2 rad for uniform circular motion T Uniform Circular Motion • Uniform magnitude of velocity (speed) ω, is constant • But α is not zero because direction of velocity is changing. 2 v 2 r r Centrifugal Force • NOT A REAL FORCE • What supplies the force to make your acceleration such as to cause you to move in a circle? • Centripetal FORCE—towards the center. This is the real force involved. a v Vertical Circle • Ferris wheel—free body diagram when at top FNET nTOP FNET w=mg mv 2 FNET , y mg nTOP r mv 2 mv 2 nTOP mg w r r Ferris Wheel At the bottom nBOTTOM w=mg mv 2 FNET , y nBOTTOM w r mv 2 nBOTTOM w r “Apparent weight” = n is greater at bottom of cycle than at top Centrifuges • • • • Diameter = 18 cm Centripetal acceleration = 250,000 g What is the frequency? Rev/sec and rpm Apparent weight of a 3 mg mass in this machine? Workbook due today • Go to board and explain – 1a and c – 1b and d –2 –3 –4 –5 – 6a,b and c A cyclist goes around a circular track at constant speed. Since her speed is constant, her acceleration is zero 33% 33% 33% io n se m or e in fo rm at Fa l Ne ed Tr ue 1. True 2. False 3. Need more information 6.15 • A 1500 kg car drives around a flat 200m diameter circular track. What are the magnitude and direction of the net force on the car? What causes this force? d ar To w Ta ng en tt o th e th e ce n te c ir c le ro ,i ft n ... 1. Tangent to the circle, in the direction of the ball’s motion 2. Toward the center of the circle he ... When a ball on the end of a string is swung in a vertical circle: What is the direction of the acceleration of 50% 50% the ball?