Lecture 22: Harmonic Waves. Physics 2210 Fall Semester 2014

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1 Lecture 22: Harmonic Waves Physics 2210 Fall Semester 2014

2 Announcements Unit 21 Simple and Physical Pendula (Nov 24th ) HW Due 11/25 th as usual No new material Wednesday November 26th. In-class discussion of problems for last midterm, final exam. Unit 22 Harmonic Waves Monday Dec 1st HW due Sunday December 7 th at midnight Exam 3 (covering thru unit 19) December 3rd Unit 23 Standing Waves and Superposition, Monday December 8th HW Due Tuesday 9 th Course Review December 10th Final Exam (December 16 th )

3 Announcements Final exam time is Tues Dec 16th, 3:30-5:30 PM. Room JFB 101 US Source -

4 Prelecture Feedback How does this tie in with earlier material? It seems to be its own thing. Can you review energy per unit length? Homework and exam type problems.

5 How to make a Function Move Suppose we have some function y = f (x): y 0 y x f (x a) is just the same shape moved a distance a to the right: 0 x = a x Let a = vt Then y f (x vt) will describe the same shape moving to the right with speed v. 0 x = vt v x Mechanics Lecture 22, Slide 5

6 Harmonic Wave

7 Harmonic Wave

8 Example: A wave moving in the +x direction has amplitude 15.0 cm, wavelength 40.0 cm, frequency 8.00 Hz. At t = 0, x = 0; y = 15.0 cm. Find the wave number k, the period P, the angular frequency and the speed v.

9 Example: A wave moving in the +x direction has amplitude 15.0 cm, wavelength 40.0 cm, frequency 8.00 Hz. At t = 0, x = 0; y = 15.0 cm. Find the wave number k, the period P, the angular frequency and the speed v. Follow-up: If y = 0 at x = t = 0, what changes and why?

10 Checkpoint

11 Checkpoint 2

12 Mechanics Lecture 22, Slide 12

13 Example: A uniform string has mass kg and length of 6.00 m. The string passes over a pulley and supports a 2 kg object. Find the speed of a pulse traveling on the string.

14 Follow-up: What about mass of string hanging from pulley? What if mass and string were hanging from the ceiling? Example: A uniform string has mass kg and length of 6.00 m. The string passes over a pulley and supports a 2 kg object. Find the speed of a pulse traveling on the string.

15 Energy Mechanics Lecture 22, Slide 15

16 Checkpoint

17

18 Homework Problem Mechanics Lecture 22, Slide 18

19 Homework Problem Mechanics Lecture 22, Slide 19

20 Homework Problem f 2 Mechanics Lecture 22, Slide 20

21 Homework Problem f 2 Mechanics Lecture 22, Slide 21

22 Review for Exam #3

23 Details When: Wednesday December 3rd, 3PM. Where: This room. Sit every other seat. Time: 3:00 PM 4:30 PM. Allowed materials: Formula sheet (provided) Blue/black pen. Indicate errors by strikethrough Hand held calculator. Not the one on your cellphone. Straightedge to make neat diagrams

24 Details Coverage: Units (but cumulative...) Rotational kinematics and moment of inertia Parallel axis theorem and torque Rotational dynamics Rotational statics Angular momentum Angular momentum vector and torque Types of problems: Short answer and workout. Study recommendations: Review homework See practice exam on course webpage Solve problems, problems, problems...

25 Formula Sheet: Note that this is posted to course web page under supplemental reading

26 Exam 3 Topic: Rotational Kinematics What is the moment of inertia of each rod? What is the moment of inertia of the disk? What is the moment of inertia of entire fan? Compute angular acceleration from time to full speed.

27 You will be given I for basic shapes.

28 Exam 3 Topic: Torque What magnitude of torque about z-axis from F 1? F 2? F 3? What is total torque about x, y, and z axes? What is angular acceleration of disk?

29 Exam 3 Topic: Rotational Dynamics What is linear acceleration of the hoop? What is linear acceleration of the sphere? What is angular acceleration of pulley? What is angular acceleration of the sphere? What is tension in string between sphere and pulley? How long does it take hoop to fall a distance h? Given masses and dimensions of sphere, disk pulley, and hoop. Orange sphere rolls without slipping.

30 Exam 3 Topic: Rotational Statics What is tension in the wire? What is net force of hinge on beam? Given max tension in wire, what is maximum mass of sign? Given masses, lengths, angles.

31 Exam 3 Topic: Angular Momentum What is total moment of inertia about the center of the disk when person is at rim? What is final moment of inertia, when person stands 2/3 of way to the center of the disk? What is final angular velocity of the disk? What is the change in kinetic energy?

32 Exam 3 Topic: Vector Angular Momentum d Given: dimensions of gyroscope, Frequency in revolutions/second. What is AM of spinning disk? What is torque due to gravity on disk? What is period of precession? What is direction of AM at time shown? What is the direction of precession?

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