1. 1 Physics 7B - AB Lecture 7 May 15 Recap Angular Momentum Model (Second half of Chap 7) Recap Torque, Angular Momentum Rotational Inertia (new concept!) Intro to Newtonian Model (start Chapter 8)

2. 2 Re-evaluation Request Due Quiz 2 May 22 (next Thursday) Quiz 3 May 29 Quiz 4 graded, solution up on the web, rubrics will follow Quiz 3 average 7.75 (C+)

3. 3  gentleman bug is Recap Rotational (Angular) Motion Ladybug Gentleman bug

4. 4  gentleman bug is Recap Rotational (Angular) Motion B)The two bugs each travel the same angle (ie. one revolution or 2  radians or any other angle) in the same amount of time so they have the same angular velocity Ladybug Gentleman bug

5. 5  ladybug points along the Recap Rotational (Angular) Motion Ladybug

6. 6  ladybug points along the Recap Rotational (Angular) Motion E)Use your right hand to show that the angular velocity points along the +z axis. Ladybug

7. 7 Recap Rotational (Angular) Motion the pivot point. What is the direction of this torque  ? A)Torque vector  pointing into the slide (clockwise rotation) B) Torque vector  pointing out of the slide (counterclockwise rotation) C)Torque is zero. F

8. 8 Recap Rotational (Angular) Motion the pivot point. What is the direction of this torque  ? A)Torque vector  pointing into the slide (clockwise rotation) B) Torque vector  pointing out of the slide (counterclockwise rotation) C)Torque is zero. F B)You should see that pushing this way will tend to rotate the wheel counterclockwise about its axle and that the right hand rule give you a torque vector pointing toward you.

9. 9 Recap Rotational (Angular) Motion v tablecloth F / /table cloth on the goblet (friction) F  table cloth on the goblet F Earth on the goblet

10. 10 B)Very similar to the previous question. If the goblet tips over, it will tip over counterclockwise. Recap Rotational (Angular) Motion v tablecloth F / /table cloth on the goblet (friction) F  table cloth on the goblet F Earth on the goblet

11. 11 Force is exerted tangentially on the rim, the rim is at a distance r (moment arm) from the pivot point. F tangential r Direction of Torque Force and Torque are two different physical quantities! Torque - rotational force that can change the rotational motion Rotation this way Direction of  is given by the RHR Torque this way

12. 12 F tangential r Magnitude of Torque  = r  F tangential = r F tangential Force and Torque are two different physical quantities! Rotational motion is changed by applying forces, But where the force is applied is Just as important as the size of the force

13. 13 Recap Extended Force Diagram F string on Plank

14. 14 Recap Extended Force Diagram F string on Plank

15. 15 F fulcrum on Plank Recap Extended Force Diagram

16. 16 F fulcrum on Plank Recap Extended Force Diagram

17. 17 F Earth on Plank Recap Extended Force Diagram

18. 18 F Earth on Plank Recap Extended Force Diagram

19. 19 Recap Rotational (Angular) Motion

20. 20 F Earth on Plank = – Mg F fulcrum on Plank F string on Plank = – (M/2)g F ??

21. 21 Angular analogue to Impulse is Angular Impulse Angular Impulse Is related to the net external torque in the following way: Net Angular Impulse ext = ∆ L = ∫  ext (t)dt If the torque is constant during a time interval ∆t Net Angular Impulse ext = ∆ L =  ave.ext x ∆ t If the net torque is zero, the plank will stay stationary…

22. 22 F Earth on Plank = – Mg F fulcrum on Plank F string on Plank = – (M/2)g F

23. 23 F Earth on Plank = – Mg F fulcrum on Plank F string on Plank = – (M/2)g F = (M/6)g  ave.ext = (L/4)(M/2)g + (0)(M/2)g – (L/4)Mg + (3L/4) F = 0 (L/4)(M/2)g – (L/4)Mg + (3L/4) F = 0 (3L/4) F = (L/4)(M/2)g 3 F = (M/2)g F = (M/6)g

24. 24 Define Angular Momentum L Think of rotational inertia I kind of like mass for now. rotating like this with  Magnitude of Angular Momentum L = I 

25. 25 Define Angular Momentum L Think of rotational inertia I kind of like mass for now. rotating like this with  Magnitude of Angular Momentum L = I  Rotation This way Direction of L is given by the RHR

26. 26 Rotational Inertia Depends not only on the amount of mass in the object but also on how the mass is distributed about the axis of rotation : I can change! Formula not really important, but the idea is that the further mass is from the axis of rotation, the greater I Example: Same mass, same volume but arranged differently r1r1 r2r2 rotates this way I1I1 I2I2 > What do you mean by rotational analog to mass?

27. 27 Rotational Inertia the idea is that the further mass is from the axis of rotation, the greater I r What do you mean by rotational analog to mass? r r Point mass m Thin ring of mass m Disk of mass m

28. 28 Rotational Inertia the idea is that the further mass is from the axis of rotation, the greater I r What do you mean by rotational analog to mass? r r Point mass m Thin ring of mass m Disk of mass m I = mr 2

29. 29 Rotational Inertia the idea is that the further mass is from the axis of rotation, the greater I r What do you mean by rotational analog to mass? r r Point mass m Thin ring of mass m Disk of mass m I = mr 2

30. 30 Rotational Inertia the idea is that the further mass is from the axis of rotation, the greater I r What do you mean by rotational analog to mass? r r Point mass m Thin ring of mass m Disk of mass m I = mr 2 I = (1/2)mr 2

31. 31 Question

32. 32 Question

33. 33 Why does a figure skater start spinning faster when she pulls her arms in? Initial  initial Final  final <

34. 34 Assume ice surface is frictionless, the net torque on the skater is zero… Net Angular Impulse ext = ∆ L =  ave.ext x ∆ t = 0 Angular Momentum L skater is conserved! Initial L initial, skater = I initial, skater  initial Final L final, skater = I final, skater  final I initial, skater  initial = I final, skater  final Remember I initial, skater > I final, skater So when the rotational inertia decreases (which it does when she pulls her arms in), angular velocity must increase in order to conserve the angular momentum Spin control is nothing but invoking Conservation of Angular momentum!

35. 35 Newtonian Model Ouch… Umm why does an apple fall ?? I tried to understand the force on an apple and its relation to apple’s motion. It is all summarized in Newton’s Laws of Motion. Sir. Isaac Newton

36. 36 Newtonian Model Newton’s Laws of Motion Newton’s first law: If the momentum changes, there is a net force on the system. If the momentum is not changing, there is no net force on the system. Newton’s second law: Quantitatively relates instantaneous change in momentum (or velocity) to net force Net Impulse ext = ∆ p = ∑ F ave.ext x ∆ t ( ∑ F ave.ext = ∆ p /∆ t ) in terms of instantaneous time rate change of momentum… ∑ F ext = d p /dt = m dv/dt = ma An unbalanced force (∑ F ext  0) causes a change in motion of an object,i.e.time rate change of velocity (acceleration)

37. 37 Newtonian Model Newton’s Laws of Motion Newton’s first law: If the momentum changes, there is a net force on the system. If the momentum is not changing, there is no net force on the system. Newton’s second law: Quantitatively relates instantaneous change in momentum (or velocity) to net force Net Impulse ext = ∆ p = ∑ F ave.ext x ∆ t ∑ F ext = d p /dt = m dv/dt = ma An unbalanced force (∑ F ext  0) causes a change in motion of an object,i.e.time rate change of velocity (acceleration) Newton’s third law: You cannot push without being pushed yourself! F A on B = – F B on A

38. 38 When things are not too small and its motion not too fast When is Newtonian Model valid ? Air France Concorde Mach 2.23 = 7.58 x 10 2 m/s << Speed of light (3 x 10 8 m/s ) Protons + Neutrons Electrons

39. 39 We know the net force on the object and want to know what its subsequent motion is OR We know the motion of an object and want to know details of the forces acting on the object How is Newtonian Model useful ? We know a concorde, What is F ejected gas on the concorde ? We know the gravitational forces between all the planets and the sun. When/Where is next total solar eclipse?

40. 40 Practice Newton’s Laws of Motion

41. 41 Practice Newton’s Laws of Motion

42. 42 Practice Newton’s Laws of Motion

43. 43 Practice Newton’s Laws of Motion

44. 44 Position vs Velocity vs Acceleration

45. 45 Position vs Velocity vs Acceleration

46. 46 Be sure to write your name, ID number & DL section!!!!! 1MR 10:30-12:50 Dan Phillips 2TR 2:10-4:30Abby Shockley 3TR 4:40-7:00John Mahoney 4TR 7:10-9:30Ryan James 5TF 8:00-10:20Ryan James 6TF 10:30-12:50John Mahoney 7W 10:30-12:50Brandon Bozek 7F 2:10-4:30Brandon Bozek 8MW 8:00-10:20Brandon Bozek 9MW 2:10-4:30Chris Miller 10MW 4:40-7:00Marshall Van Zijll 11MW 7:10-9:30Marshall Van Zijll