PHSX213 class

1. PHSX213 class • Class stuff • MidTerm Exam 2 • Wed. March 16th 8:00 – 9:30 PM • Chapters 7-11 • Budig 120 (same area as before) • Practice Exam • Answers on web • No classes next Wed., Fri. • Problem Solving Session. • Today: 4:30 – 6:00 PM Malott 3005 • Projects • Torque and Angular Momentum

2. Project Choices for PHSX213 Spring 2005 Student   Suggested Topic   Approved (Y/N) ? 1. Christina C.   Physics of Mediaeval Jousting   Y 2. Laura S.   Physics of Gymnastics   Y 3. Venkatesh S.   Physics of Formula 1 Racing   Y 4. Stephen P.   Physics of Rocket Motion   Y 5. Lake W.   Aerospace related Physics (specific topic to be defined)   Y 6. Jennifer G.   Physics of the Cello   Y 7. Fran G.   Physics of Dirt-Biking   Y 8. Brent F.   Physics of Earthquakes   Y 9. Michael M.   Physics of Phonographs   Y 10. Travis L.   Orbital Mechanics: Slingshot trajectories   Y 11. Chris B.   Golf-ball trajectories   Y 12. Becky H.   Physics of Surfing   Y 13. Jake F.   Pyrotechnics and Rocketry   Y 14. Brett H.   Baseball Pitching   Y 15. Brent E.   Physics of Running   Y 16. Abby P. Tsunamis Y 17. Jessica S. Foucault Pendulum YYour name here   Putting: "Ideal" Line vs Green Slope, Speed and Elevation   Y Your name here   Physics of tornadoes   Y Another name   General relativity   N Another name   An experimental test of special relativity   Y Your name here   Physics of hot-air balloons   Y Your name here   Physics and investigating car accidents   Y Last updated by GWW Mar. 11th 2005 4 students still to choose.

3. Timing Test of Clicker System • I want to measure how long it takes to receive all responses. • Please refrain from clicking once you’ve given some response. • GO

4. 2nd Timing Test of Clicker System • I want to double-check the measurement of how long it takes to receive all responses. • Please refrain from clicking once you’ve given some response. • GO AGAIN • Thanks.

5. Check-Point I • Two uniform cylinders have different masses and different rotational inertias. They simultaneously start from rest at the top of an inclined plane and roll without sliding down the plane. The cylinder that gets to the bottom first is: • A. the one with the larger mass • B. the one with the smaller mass • C. the one with the larger rotational inertia • D. the one with the smaller rotational inertia • E. neither (they arrive together)

6. Let’s verify that

7. What’s going on here ??

8. Forces in Rolling • Rolls smoothly down the ramp without sliding/slipping. • How much torque about the CoM does each force produce ? • How big is fS ? • How big is the acceleration ? Note : I’ll define +x down the incline

9. One can derive that : fS = I a/R2 = [b/(1+b)] mg sinq And that, a = g sinq/(1 + I/(MR2)) = g sinq/(1+b) Where we have defined b, via I = b M R2 bhoop = 1, bcylinder = 0.5, bsolid sphere = 0.4 Rolling

10. Discuss rolling in terms of KE • From energy conservation considerations. • Note the frictional force in this case doesn’t oppose the angular motion, and the work done by this non-conservative force is transformed into rotational kinetic energy. • W = ∫ t dq • And we find that K = ½ m v2 + ½ I w2 • = ½ m (1+b) v2 ( = mg h) Since the contact point doesn’t move, there is no translational displacement.

11. Another way to look at this • Stationary observer sees rotation about an axis at point P with w = v/R. • Using the parallel axis theorem, IP = ICoM + mR2 • So, K = ½ IPw2 • = ½ ICoMw2 +½ m v2 • just as before.

12. Torque Definition for a Particle t = r F Vector product means that the torque is directed perpendicular to the plane formed by (r, F). Whether it is up or down is from the right-hand rule convention NB Only makes sense to talk about the torque wrt or about a certain point

13. Torque Demo

14. Angular Momentum Definition for a Particle l = r p = r m v NB Only makes sense to talk about the angular momentum wrt or about a certain point

15. Angular Momentum Definition for a Rigid Body About a Fixed Axis L = Sli = I w In analogy to P = M v

16. Newton II for Rotation • S F = dp/dt ( the general form of Newton II) • St = dl/dt • It is the net torque that causes changes in angular momentum.

17. Angular Momentum Conservation • Just as for Newton II for linear motion where if the net force was zero, dp/dt =0 => p conserved. • For rotational motion, if the net torque is zero, dl/dt =0, so l conserved.

18. Angular Momentum Conservation Iiwi = Ifwf

19. Angular Momentum Demo

20. Two buckets spin around in a horizontal circle on frictionless bearings. Suddenly, it starts to rain. As a result, Check-Point 2 • The buckets continue to rotate at constant angular velocity because the rain is falling vertically while the buckets move in a horizontal plane. • The buckets continue to rotate at constant angular velocity because the total mechanical energy of the bucket + rain system is conserved. • The buckets speed up because the potential energy of the rain is transformed into kinetic energy. • The buckets slow down because the angular momentum of the bucket + rain system is conserved. • None of the above.

21. Notes • When dealing with torque and angular momentum, it is very important, that each one is defined with respect to the same point.

22. Check-Point 3 • A rod rests on frictionless ice. Forces that are equal in magnitude and opposite in direction are then simultaneously applied to its ends as shown. The quantity that vanishes is its: • A. angular momentum • B. angular acceleration • C. total linear momentum • D. kinetic energy • E. rotational inertia F F

23. Angular Momentum Conservation Problems

24. Kepler’s Second Law Each planet moves so that a line drawn from the Sun to the planet sweeps out equal areas, A, in equal periods of time. ie. dA/dt = 0

25. Runner on circular platform

26. Clutch design

27. Check-Point 4 • The angular momentum vector of Earth about its rotation axis, due to its daily rotation, is directed: • A. tangent to the equator toward the east • B. tangent to the equator toward the west • C.north • D. south • E. toward the Sun

28. Why does a rolling sphere slow down ?

29. Turnstile problem