PHY 113 C General Physics I 11 AM – 12:15 PM TR Olin 101 Plan for Lecture 17:

1. PHY 113 C General Physics I 11 AM – 12:15 PM TR Olin 101 Plan for Lecture 17: Review of Chapters 9-13, 15-16 Comment on exam and advice for preparation Review Example problems PHY 113 C Fall 2013 -- Lecture 17

2. PHY 113 C Fall 2013 -- Lecture 17

3. Webassign questions – Assignment #15 Consider the sinusoidal wave of the figure below with the wave function y = 0.150 cos(15.7x − 50.3t) where x and y are in meters and t is in seconds. At a certain instant, let point A be at the origin and point B be the closest point to A along the x axis where the wave is 43.0° out of phase with A. What is the coordinate of B? PHY 113 C Fall 2013 -- Lecture 17

4. Webassign questions – Assignment #15 A transverse wave on a string is described by the following wave function. y = 0.115 sin ((π/9)x+ 5πt) where x and y are in meters and t is in seconds. Determine the transverse speed at t = 0.150 s for an element of the string located at x = 1.50 m. (b) Determine the transverse acceleration at t = 0.150 s for an element of the string located at x = 1.50 m. PHY 113 C Fall 2013 -- Lecture 17

5. Webassign questions – Assignment #15 A sinusoidal wave in a rope is described by the wave function y= 0.20 sin (0.69πx + 20πt) where x and y are in meters and t is in seconds. The rope has a linear mass density of 0.230 kg/m. The tension in the rope is provided by an arrangement like the one illustrated in the figure below. What is the mass of the suspended object? T mg PHY 113 C Fall 2013 -- Lecture 17

6. Comment about exam on Tuesday 10/29/2013 PHY 113 C Fall 2013 -- Lecture 17

7. iclicker question • What is the purpose of exams? • Pure pain and suffering for all involved. • To measure what has been learned. • To help students learn the material. • Other. PHY 113 C Fall 2013 -- Lecture 17

8. Advice on how to prepare for the exam • Review lecture notes and text chapters 9-13,15-16 • Prepare equation sheet • Work practice problems • Topics covered • Linear momentum • Rotational motion and angular momentum • Gravitational force and circular orbits • Static equilibrium • Simple harmonic motion • Wave motion PHY 113 C Fall 2013 -- Lecture 17

9. What to bring to exam: • Clear head • Calculator • Equation sheet • Pencil or pen PHY 113 C Fall 2013 -- Lecture 17

10. iclicker question: Have you looked at last year’s exams? A. Yes B. No PHY 113 C Fall 2013 -- Lecture 17

11. Linear momentum • What is it? • When is it “conserved”? • Conservation of momentum in analysis of collisions • Notion of center of mass PHY 113 C Fall 2013 -- Lecture 17

12. Linear momentum -- continued Physics of composite systems PHY 113 C Fall 2013 -- Lecture 17

13. Example – completely inelastic collision; balls moving in one dimension on a frictionless surface PHY 113 C Fall 2013 -- Lecture 17

14. Examples of two-dimensional collision; balls moving on a frictionless surface PHY 113 C Fall 2013 -- Lecture 17

15. The notion of the center of mass and the physics of composite systems PHY 113 C Fall 2013 -- Lecture 17

16. Finding the center of mass PHY 113 C Fall 2013 -- Lecture 17

17. Rotational motion and angular momentum • Angular variables • Newton’s law for angular motion • Rotational energy • Moment of inertia • Angular momentum q PHY 113 C Fall 2013 -- Lecture 17

18. Review of rotational energy associated with a rigid body PHY 113 C Fall 2013 -- Lecture 17

19. Moment of inertia: PHY 113 C Fall 2013 -- Lecture 17

20. CM CM PHY 113 C Fall 2013 -- Lecture 17

21. iclicker exercise: Three round balls, each having a mass M and radius R, start from rest at the top of the incline. After they are released, they roll without slipping down the incline. Which ball will reach the bottom first? C B A PHY 113 C Fall 2013 -- Lecture 17

22. q How can you make objects rotate? Define torque: t = r x F t = rF sin q r F sin q q F PHY 113 C Fall 2013 -- Lecture 17

23. Example form Webassign #11 • iclicker exercise • When the pivot point is O, which torque is zero? • A. t1? • B. t2? • C. t3? t3 X t2 t1 PHY 113 C Fall 2013 -- Lecture 17

24. Vector cross product; right hand rule PHY 113 C Fall 2013 -- Lecture 17

25. From Newton’s second law – continued – conservation of angular momentum: PHY 113 C Fall 2013 -- Lecture 17

26. Example of conservation of angular momentum PHY 113 C Fall 2013 -- Lecture 17

27. Summary – conservation laws we have studied so far PHY 113 C Fall 2013 -- Lecture 17

28. Fundamental gravitational force law and planetary motion • Newton’s gravitational force law • Gravity at Earth’s surface • Circular orbits of gravitational bodies • Energy associated with gravitation and orbital motion PHY 113 C Fall 2013 -- Lecture 17

29. Universal law of gravitation  Newton (with help from Galileo, Kepler, etc.) 1687 PHY 113 C Fall 2013 -- Lecture 17

30. Gravitational force of the Earth RE m Note: Earth’s gravity acts as a point mass located at the Earth’s center. PHY 113 C Fall 2013 -- Lecture 17

31. REM F Stable circular orbit of two gravitationally attracted objects (such as the moon and the Earth) v a PHY 113 C Fall 2013 -- Lecture 17

32. m2 R2 R1 m1 Circular orbital motion about center of mass v2 CM v1 PHY 113 C Fall 2013 -- Lecture 17

33. m2 R2 R1 m1 v2 L1=m1v1R1 L2=m2v2R2 L = L1 + L2 v1 Note: More generally, stable orbits can be elliptical. PHY 113 C Fall 2013 -- Lecture 17

34. Gravitational potential energy Example: PHY 113 C Fall 2013 -- Lecture 17

35. Analysis of static equilibrium Meanwhile – back on the surface of the Earth: Conditions for stable equilibrium PHY 113 C Fall 2013 -- Lecture 17

36. PHY 113 C Fall 2013 -- Lecture 17

37. X ** T Mg mg PHY 113 C Fall 2013 -- Lecture 17

38. Some practice problems PHY 113 C Fall 2013 -- Lecture 17

39. PHY 113 C Fall 2013 -- Lecture 17

40. From webassign: A 100-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.800 rev/s in 2.00 s? (State the magnitude of the force.) view from top: F R PHY 113 C Fall 2013 -- Lecture 17

41. From webassign: A 10.3-kg monkey climbs a uniform ladder with weight w = 1.24  102 N and length L = 3.35 m as shown in the figure below. The ladder rests against the wall and makes an angle of θ = 60.0° with the ground. The upper and lower ends of the ladder rest on frictionless surfaces. The lower end is connected to the wall by a horizontal rope that is frayed and can support a maximum tension of only 80.0 N. PHY 113 C Fall 2013 -- Lecture 17