Chapter 6: Circular Motion Summary Motion in a vertical circle Apparent Weight Extending beyond Physics 151 Rotational a

1. Week 16 Day 3 - Last day of Class • Chapter 6: Circular Motion • Summary • Motion in a vertical circle • Apparent Weight • Extending beyond Physics 151 • Rotational analog to translational motion • Moment of Inertia • Angular Momentum • Center of Mass Slide 15-37

2. Week 16 Day 3 - Last day of Class • Announcements • Exam 3 grades will post and exams will be in boxes by noon tomorrow – An email will be sent out • Last Worksheet may be turned in Monday by 5 PM w/o late penalty. Solution will post by 6 PM • Exam 2 make-up exam will start at 1:30 PM on Tuesday, 12/14 in RH 115. • You will have a few minutes to look the exam over. • Once you start writing, you will get the average of the two exam scores • Final Exam will be next Wednesday from 7:00 - 9:45 AM • Final Exam notes for this semester will post tomorrow - last year’s final exam notes are already posted • Exam Prep Session will be Monday from 2 – 4 PM in RH 114/116 Slide 15-37

3. Checking Understanding • When a ball on the end of a string is swung in a vertical circle, the ball is accelerating because • the speed is changing. • the direction is changing. • the speed and the direction are changing. • the ball is not accelerating. Slide 6-13

4. Answer • When a ball on the end of a string is swung in a vertical circle, the ball is accelerating because • the speed is changing. • the direction is changing. • the speed and the direction are changing. • the ball is not accelerating. Slide 6-14

5. Checking Understanding • When a ball on the end of a string is swung in a vertical circle: • What is the direction of the acceleration of the ball? • Tangent to the circle, in the direction of the ball’s motion • Toward the center of the circle Slide 6-15

6. Answer • When a ball on the end of a string is swung in a vertical circle: • What is the direction of the acceleration of the ball? • Tangent to the circle, in the direction of the ball’s motion • Toward the center of the circle Slide 6-16

7. Checking Understanding: Circular Motion Dynamics • For the ball on the end of a string moving in a vertical circle: • What is the direction of the net force on the ball? • tangent to the circle • toward the center of the circle • there is no net force Slide 6-19

8. Answer • For the ball on the end of a string moving in a vertical circle: • What is the direction of the net force on the ball? • tangent to the circle • toward the center of the circle • there is no net force Slide 6-20

9. Checking Understanding: Circular Motion Dynamics • For the ball on the end of a string moving in a vertical circle: • What force is producing the centripetal acceleration of the ball? • gravity • air resistance • normal force • tension in the string Slide 6-17

10. Answer • For the ball on the end of a string moving in a vertical circle: • What force is producing the centripetal acceleration of the ball? • gravity • air resistance • normal force • tension in the string Slide 6-18

11. Loop the Loop • Consider a ball on a string making a vertical circle. • Draw a free-body diagram of the ball at the top and bottom of the circle • Rank the forces in the two diagrams. Be sure to explain the reasoning behind your rankings • Find the minimum speed of the ball at the top of the circle so that it keeps moving along the circular path • What would happen if the speed was less than the minimum? • What would happen if the speed was more than the miniumum? Slide 6-12

12. Keep the Water in the Bucket Slide 6-12

13. Roller Coaster and Circular Motion • A roller-coaster car has a mass of 500 kg when fully loaded with passengers as shown on the right. • 1. If the car has a speed of 20.0 m/s at point A, what is the force exerted by the track at this point?What is the apparent weight of the person? • 2. What is the maximum speed the car can have at point B and stay on the track? Slide 15-37

14. Every quantity we studied has a rotational analog • We have mainly discussed particle motion • This describes motion of the center of mass • What about rotational motion about the center of mass • Every motion quantity we have looked at in kinematics, Forces, momentum, and Energy has an analogous quantity in Rotation. • Every equation has an analog too • Rotational equations look exactly the same • Examples • Position => theta • Force => torque • Kinetic Energy => Rotational Kinetic Energy • Momentum => Angular momentum • Mass => Moment of Inertia Slide 15-37

15. Additional Example Problems At Talladega, a NASCAR track, the turns have a 370 m radius and are banked at 33°. At what speed can a car go around this corner with no assistance from friction? The Globe of Death is a spherical cage in which motorcyclists ride in circular paths at high speeds. One outfit claims that riders achieve a speed of 60 mphin a 16 ft diameter sphere. What would be the period for this motion? What would be the apparent weight of a 60 kg rider at the bottom of the sphere? Given these two pieces of information, does this high speed in this small sphere seem possible? Slide 6-51