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Welcome back to Physics 211

Welcome back to Physics 211. Today’s agenda Motion along curved paths, circles Tangential and radial components of acceleration. Current homework assignments. WHW3: In blue Tutorials in Physics homework book HW-21 #3, HW-21 #4, HW-22 #5, HW-23 #6 due Wednesday Sept 19 th in recitation

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Welcome back to Physics 211

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  1. Welcome back to Physics 211 Today’s agenda Motion along curved paths, circles Tangential and radial components of acceleration

  2. Current homework assignments • WHW3: • In blue Tutorials in Physics homework book • HW-21 #3, HW-21 #4, HW-22 #5, HW-23 #6 • due Wednesday Sept 19th in recitation • NoFHW this week (FHW2 will be assigned tomorrow and due 2 weeks later) • Finish 2D Motion worksheets from yesterday and discuss with TAs and coaches on Friday

  3. Exam 1: next Thursday (9/20/07) • Seating arrangement will be posted outside Stolkin • Material covered: • Textbook chapters 1, 2, and 3 • Lectures up to 9/18 (slides online) • Tutorials on Velocity, Acceleration in one dimension, and Motion in two dimensions • Problem Solving Activities 1, 2, and 3 (on Graphs,Vectors, and Problems on motion in two dimensions) • Homework assignments

  4. Preparing for exam • Review homework problems and worksheets from recitation workshops • Work through practice exam problems (posted on website) • Work on more practice exam problems next Wednesday in recitation workshop • Try extra end-of-chapter problems in textbook • Solve problems on Mastering Physics website (not required!) -- use course ID = MPPLOURDE0001 • Society of Physics Students (SPS) review session: Wednesday (Sept. 19) 5:30-6:30, location TBA

  5. Velocity is tangent to path Ds sI sF O v = Ds/Dt lies along dotted line. As Dt  0 direction of v is tangent to path

  6. Motion on a curved pathat constant speed

  7. For an object moving at constant speed along a curved path, the acceleration is not zero.

  8. A child is riding a bicycle on a level street. The velocity and acceleration vectors of the child at a given time are shown. Which of the following velocity vectors may represent the velocity at a later time? a 1. 2. 3. 4.

  9. A biker is riding at constant speed clockwise on the oval track shown below. Which vector correctly describes the acceleration at the point indicated?

  10. Biker moving around oval at constant speed As point D is moved closer to C, angle approaches 90°.

  11. Summary • For motion at constant speed, instantaneous acceleration vector is perpendicular to velocity vector • Points ``inward’’ • What is the magnitude of the acceleration vector?

  12. Acceleration vectors for ball swung in a horizontal circle at constant speed v v1 v2 R q v1 q v2 What is the magnitude of the acceleration?a = v2/R

  13. Acceleration of object moving at constant speed on a circular path: Acceleration depends on radius of circle.

  14. Two cars are moving at different constant speeds on a curved road. One after the other, they are passing the same point on the road: Car A at 18 mph; car B at 36 mph. If car A’s acceleration is 2 m/s2, car B’s acceleration is: 1. 1 m/s2 2. 2 m/s2 3. 4 m/s2 4. 8 m/s2

  15. A ball is rolling counter-clockwise at constant speed on a circular track. One quarter of the track is removed. What path will the ball follow after reaching the end of the track?

  16. What is the magnitude of the acceleration of an object moving at constant speed if the path is curved but not a circle? “r” is theradius of curvatureof the path at a given point

  17. Radius of curvature • The radius of a circle which just touches the curved path at that point. r Radius of curvature r

  18. Acceleration vectors for object moving around oval at constant speed

  19. Acceleration vectors for car moving on peanut-shaped track at constant speed

  20. What if the speed is changing? • Consider acceleration for object on curved path starting from rest • Initially, v2/r = 0, so no radial acceleration • But a is not zero! It must be parallel to velocity

  21. Acceleration vectors for object speeding up:Tangential and radial components(or parallel and perpendicular)

  22. A Ferris wheel with diameter 14.0 m, which rotates counter-clockwise, is just starting up. At a given instant, a passenger on the rim of the wheel and passing through the lowest point of his circular motion is moving at 3.00 m/s and is gaining speed at a rate of 0.500 m/s2. (a) Find the magnitude and the direction of the passenger’s acceleration at this instant. (b) Sketch the Ferris wheel and passenger showing his velocity and acceleration vectors. Sample problem

  23. Components of acceleration vector: • Parallel to direction of velocity: • (Tangential acceleration) • “How much does speed of the object increase?” • Perpendicular to direction of velocity: • (Radial acceleration) • “How quickly does the object turn?” Summary

  24. Acceleration vector for object speeding up from rest at point A ?

  25. Car going through loop-the-loop

  26. Reading assignment • Relative motion • 3.5 in textbook • Review for Exam 1 !

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